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Journal articles on the topic 'Viterbi decoding algorithm'

Author: Grafiati

Published: 4 June 2025

Last updated: 8 July 2025

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1

Muhammad, Shamsuddeen Hassan, and Abdulrasheed Mustapha. "A Form of List Viterbi Algorithm for Decoding Convolutional Codes." U.Porto Journal of Engineering 4, no. 2 (2018): 42–48. http://dx.doi.org/10.24840/2183-6493_004.002_0004.

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Viterbi algorithm is a maximum likelihood decoding algorithm. It is used to decode convolutional code in several wireless communication systems, including Wi-Fi. The standard Viterbi algorithm gives just one decoded output, which may be correct or incorrect. Incorrect packets are normally discarded thereby necessitating retransmission and hence resulting in considerable energy loss and delay. Some real-time applications such as Voice over Internet Protocol (VoIP) telephony do not tolerate excessive delay. This makes the conventional Viterbi decoding strategy sub-optimal. In this regard, a modified approach, which involves a form of List Viterbi for decoding the convolutional code is investigated. The technique employed combines the bit-error correction capabilities of both the Viterbi algorithm and the Cyclic Redundancy Check (CRC) procedures. It first uses a form of ‘List Viterbi Algorithm’ (LVA), which generates a list of possible decoded output candidates after the trellis search. The CRC check is then used to determine the presence of correct outcome. Results of experiments conducted using simulation shows considerable improvement in bit-error performance when compared to classical approach.

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2

Reeve, J. S. "A parallel Viterbi decoding algorithm." Concurrency and Computation: Practice and Experience 13, no. 2 (2001): 95–102. http://dx.doi.org/10.1002/cpe.539.

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3

Sosnenko, Kateryna. "Improved Decoding Algorithms for Convolutional Codes." Cybernetics and Computer Technologies, no. 2 (June 9, 2024): 39–46. http://dx.doi.org/10.34229/2707-451x.24.2.4.

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Introduction. The considered implementation of the Viterbi algorithm provides a reduction in hardware and time costs for decoding convoluted code sequences, and can be used for semi-realistic modeling of existing means of data transmission (for example, in satellite communication). The purpose of the article. Show how when modeling the processes of encoding and decoding convolutional codes according to the improved Viterbi algorithm, as well as its implementation based on programmable logic devices of the FPGA type, it was possible to reduce the number of clocks of reading metrics and tracks from RAM by 2 times. The results. A two-fold decrease in the number of reading cycles of metrics and tracks (input sequences or reverse pointers) from RAM is achieved by joint processing of two receiver nodes that share two source nodes. Relatively small costs for a hardware calculator of edge metrics allow you to organize parallel calculation, comparison and multiplexing of metrics and tracks of two sources at the inputs of block RAM. Two-port block memory makes it possible to significantly (up to two times) speed up the decoding process, to abandon metric and track buffer registers. Conclusions: The Viterbi decoder is widely used in communication systems and is a practical method of error correction at high signal transmission speed in modern telecommunication systems. The Viterbi decoder is designed for decoding convolutional codes and is optimal in the sense of minimizing the probability of an error. The advantage of the Viterbi decoder is that its complexity is a linear function of the number of symbols in the codeword sequence. In addition, the Viterbi algorithm is widely used in pattern recognition systems using hidden Markov models. Keywords: Convolutional codes, Viterbi algorithm, FPGA basis, metrics.

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4

Suman, Chandel, and Mathur Manju. "Viterbi Decoder Plain Sailing Design for TCM Decoders." International Journal of Trend in Scientific Research and Development 3, no. 5 (2019): 1794–97. https://doi.org/10.5281/zenodo.3591497.

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Convolutional codes are error correction technique used in noisy channels. Viterbi Algorithm is the most widely used decoding Algorithm, which decodes the sequence in a maximum likelihood sense. But the complexity of the Viterbi decoder increases with the coding rate of the system. Viterbi decoder is the most power hungry module in the Trellis coded modulation system. Viterbi decoding is the best technique for decoding the convolutional codes but it is limited to smaller constraint lengths. The basic building blocks of Viterbi decoder are branch metric unit, add compare and select unit and survivor memory management unit. From the simulation results it is observed that the proposed Viterbi decoder architecture with modified Branch metric calculation can reduce significant amount of computations in order to decrease the hardware usage and to simplify the proceedings. Suman Chandel | Manju Mathur "Viterbi Decoder Plain Sailing Design for TCM Decoders" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26710.pdf

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5

Monfared, Saleh Khalaj, Omid Hajihassani, Vahid Mohsseni, Dara Rahmati, and Saeid Gorgin. "A High-throughput Parallel Viterbi Algorithm via Bitslicing." ACM Transactions on Parallel Computing 8, no. 4 (2021): 1–25. http://dx.doi.org/10.1145/3470642.

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In this work, we present a novel bitsliced high-performance Viterbi algorithm suitable for high-throughput and data-intensive communication. A new column-major data representation scheme coupled with the bitsliced architecture is employed in our proposed Viterbi decoder that enables the maximum utilization of the parallel processing units in modern parallel accelerators. With the help of the proposed alteration of the data scheme, instead of the conventional bit-by-bit operations, 32-bit chunks of data are processed by each processing unit. This means that a single bitsliced parallel Viterbi decoder is capable of decoding 32 different chunks of data simultaneously. Here, the Viterbi’s Add-Compare-Select procedure is implemented with our proposed bitslicing technique, where it is shown that the bitsliced operations for the Viterbi internal functionalities are efficient in terms of their performance and complexity. We have achieved this level of high parallelism while keeping an acceptable bit error rate performance for our proposed methodology. Our suggested hard and soft-decision Viterbi decoder implementations on GPU platforms outperform the fastest previously proposed works by and , achieving 21.41 and 8.24 Gbps on Tesla V100, respectively.

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6

Wang, Haocheng, Yafeng Wang, and Yue Hu. "Bidirectional Viterbi decoding algorithm for OvTDM." China Communications 17, no. 7 (2020): 183–92. http://dx.doi.org/10.23919/j.cc.2020.07.013.

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7

Han, Ke, Zhong Liang Deng, and Lian Ming Xu. "The Viterbi Decoding Scheme for FPGA." Applied Mechanics and Materials 63-64 (June 2011): 835–40. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.835.

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This paper analyzes the principle of Viterbi algorithm which can be used in the norm of the mobile communication system. Then a new Viterbi decoding scheme of (2, 1, 7) convolutional code is presented for FPGA implementation. To take advantage of the FPGA, a new branch weight algorithm and uniform state weight memories is used. At last, a new decoding circuit which can work on 35MHz and can achieve 120 kbs in decoding speed was designed. To use the design of survival path exchange register module, it can decrease the power consumption and the RAM size.

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8

Kahina, Rekkal, and Abdesselam Bassou. "Improving the Performance of Viterbi Decoder using Window System." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 1 (2018): 611. http://dx.doi.org/10.11591/ijece.v8i1.pp611-621.

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An efficient Viterbi decoder is introduced in this paper; it is called Viterbi decoder with window system. The simulation results, over Gaussian channels, are performed from rate 1/2, 1/3 and 2/3 joined to TCM encoder with memory in order of 2, 3. These results show that the proposed scheme outperforms the classical Viterbi by a gain of 1 dB. On the other hand, we propose a function called RSCPOLY2TRELLIS, for recursive systematic convolutional (RSC) encoder which creates the trellis structure of a recursive systematic convolutional encoder from the matrix “H”. Moreover, we present a comparison between the decoding algorithms of the TCM encoder like Viterbi soft and hard, and the variants of the MAP decoder known as BCJR or forward-backward algorithm which is very performant in decoding TCM, but depends on the size of the code, the memory, and the CPU requirements of the application.

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9

Rekkal, Kahina, and Bassou Abdesselam. "Improving The Performance of Viterbi Decoder using Window System." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 1 (2018): 611–21. https://doi.org/10.11591/ijece.v8i1.pp611-621.

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An efficient Viterbi decoder is introduced in this paper; it is called Viterbi decoder with window system. The simulation results, over Gaussian channels, are performed from rate 1/2, 1/3 and 2/3 joined to TCM encoder with memory in order of 2, 3. These results show that the proposed scheme outperforms the classical Viterbi by a gain of 1 dB. On the other hand, we propose a function called RSCPOLY2TRELLIS, for recursive systematic convolutional (RSC) encoder which creates the trellis structure of a recursive systematic convolutional encoder from the matrix “H”. Moreover, we present a comparison between the decoding algorithms of the TCM encoder like Viterbi soft and hard, and the variants of the MAP decoder known as BCJR or forward-backward algorithm which is very performant in decoding TCM, but depends on the size of the code, the memory, and the CPU requirements of the application.

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10

Al-Rabadi, Anas. "Closed-system quantum logic network implementation of the Viterbi algorithm." Facta universitatis - series: Electronics and Energetics 22, no. 1 (2009): 1–33. http://dx.doi.org/10.2298/fuee0901001a.

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New convolution-based multiple-stream error-control coding and decoding schemes are introduced. The new coding method applies the reversibility property in the convolution-based encoder for multiple-stream error-control encoding and implements the reversibility property in the new reversible Viterbi decoding algorithm for multiple-stream error-correction decoding. The complete design of quantum circuits for the quantum realization of the new quantum Viterbi cell in the quantum domain is also introduced. In quantum mechanics, a closed system is an isolated system that can't exchange energy or matter with its surroundings and doesn't interact with other quantum systems. In contrast to open quantum systems, closed quantum systems obey the unitary evolution and thus they are reversible. Reversibility property in error-control coding can be important for the following main reasons: (1) reversibility is a basic requirement for low-power circuit design in future technologies such as in quantum computing (QC), (2) reversibility leads to super-speedy encoding/decoding operations because of the superposition and entanglement properties that emerge in the quantum computing systems that are naturally reversible and therefore very high performance is obtained, and (3) it is shown in this paper that the reversibility relationship between multiple-streams of data can be used for further correction of errors that are uncorrectable using the implemented decoding algorithm such as in the case of triple-errors that are uncorrectable using the classical irreversible Viterbi algorithm. .

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11

Yoon, Sang-Hun, and Jun-Mo Jung. "Viterbi-based Decoding Algorithm for DBO-CSS." Journal of information and communication convergence engineering 9, no. 6 (2011): 657–60. http://dx.doi.org/10.6109/ijice.2011.9.6.657.

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12

Kuei-Ann Wen, Ting-Shiun Wen, and Jhing-Fa Wang. "A new transform algorithm for Viterbi decoding." IEEE Transactions on Communications 38, no. 6 (1990): 764–72. http://dx.doi.org/10.1109/26.57468.

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13

N., Glory Priscilla, and M. Ramesh Patnaik Dr. "Reconfigurable Adaptive Viterbi Algorithm for Conventional Decoding." Journal of VLSI Design and its Advancement 2, no. 3 (2019): 1–4. https://doi.org/10.5281/zenodo.3561938.

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<strong><em>ABSTRACT</em></strong> <em>Conventional encoder is widely applied to lots of wireless communications including 3G/4G communication and digital video Broad casting (DVB), IOT (Internet of things) transmission and so on. A reconfigurable Viterbi decoder design is proposed for LTE-A, WiMAX, LTECDMA, GSM and TD-SCDMA. The proposed flexible architecture supports a polynomial reconfiguration. More over both tail biting and zero trellis terminating modes are supported. The transmitter encoder and receiver decoder are designed for verifying functionality .The purpose is to determine the feasible to design data error correcting to reduce the decoding latency and complexity it employs forward trace back method and sliding window technology.</em>

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14

AL-RABADI, ANAS N. "REVERSIBLE VITERBI ALGORITHM AND ITS CLOSED-SYSTEM Q-DOMAIN CIRCUIT DESIGN AND COMPUTATION." Journal of Circuits, Systems and Computers 18, no. 08 (2009): 1627–49. http://dx.doi.org/10.1142/s0218126609005903.

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Novel convolution-based multiple-stream error-control coding and decoding methods and their corresponding circuits are introduced. The new coding method applies the reversibility property in (1) the convolution-based encoder for multiple-stream error-control encoding and (2) in the new reversible Viterbi decoding algorithm for multiple-stream error-correction decoding. The complete synthesis of quantum circuits for the quantum realization of the new quantum Viterbi cell in the quantum domain (Q-domain) is also introduced, and the associated quantum computing representations and operations are presented. In quantum mechanics, a closed system is an isolated system that cannot exchange energy or matter with its surroundings and does not interact with other quantum systems. Closed quantum systems obey the unitary evolution and thus they are reversible. Reversibility property in error-control coding can be important for the following main reasons: (1) reversibility is a basic requirement for low-power circuit design in future technologies such as in closed-system quantum computing (QC), (2) reversibility leads to super-speedy encoding/decoding operations because of the superposition and entanglement properties that exist in the reversible closed-system quantum computing circuits and systems, and (3) the reversibility relationship between multiple-streams of data can be used for the correction of errors that are usually uncorrectable using the implemented decoding algorithm such as in the case of triple-errors that are uncorrectable using the irreversible Viterbi algorithm.

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15

Sánchez, Victoria, and Antonio M. Peinado. "An efficient parallel algorithm for list Viterbi decoding." Signal Processing 83, no. 3 (2003): 511–15. http://dx.doi.org/10.1016/s0165-1684(02)00448-6.

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16

Louet, Yves, Rami Othman, and Alexandre Skrzypczak. "A Soft-Output STBC Decoder for Aeronautical Telemetry." Journal of Telecommunications and Information Technology 1 (March 31, 2020): 13–20. http://dx.doi.org/10.26636/jtit.2020.138319.

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Alamouti encoding is a well-known space time block encoding technique used to improve the received signal quality in Rayleigh fading channels. In aeronautical telemetry, this encoding technique is applied to shaped oﬀset quadrature phase shift keying tier generation (SOQPSK-TG) modulation in order to handle the two-antenna issue. It is provided for in telemetry-related IRIG standards. In this paper, we propose a unique decoding architecture for Alamouti-encoded SOQPSK-TG signals, taking advantage of pulse amplitude modulation decomposition with soft and hard outputs. We exploit this result to obtain a Viterbi algorithm (VA) for hard decoding and a soft output Viterbi algorithm (SOVA) for soft and hard decoding, with a twofold beneﬁt: operation using one trellis structure, unlike decoders that are based on the 8-waveforms cross-correlated trellis-coded quadrature modulation (XTCQM) approximation, and very attractive bit error rate performance, as well as a complexity trade-oﬀ

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17

Ashtari Esfahani, A., Z. Bogorad, S. Böser, et al. "Viterbi decoding of CRES signals in Project 8." New Journal of Physics 24, no. 5 (2022): 053013. http://dx.doi.org/10.1088/1367-2630/ac66f6.

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Abstract Cyclotron radiation emission spectroscopy (CRES) is a modern approach for determining charged particle energies via high-precision frequency measurements of the emitted cyclotron radiation. For CRES experiments with gas within the fiducial volume, signal and noise dynamics can be modelled by a hidden Markov model. We introduce a novel application of the Viterbi algorithm in order to derive informational limits on the optimal detection of cyclotron radiation signals in this class of gas-filled CRES experiments, thereby providing concrete limits from which future reconstruction algorithms, as well as detector designs, can be constrained. The validity of the resultant decision rules is confirmed using both Monte Carlo and Project 8 data.

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18

Hueske, K., J. Geldmacher, and J. Götze. "Adaptive decoding of convolutional codes." Advances in Radio Science 5 (June 13, 2007): 209–14. http://dx.doi.org/10.5194/ars-5-209-2007.

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Abstract. Convolutional codes, which are frequently used as error correction codes in digital transmission systems, are generally decoded using the Viterbi Decoder. On the one hand the Viterbi Decoder is an optimum maximum likelihood decoder, i.e. the most probable transmitted code sequence is obtained. On the other hand the mathematical complexity of the algorithm only depends on the used code, not on the number of transmission errors. To reduce the complexity of the decoding process for good transmission conditions, an alternative syndrome based decoder is presented. The reduction of complexity is realized by two different approaches, the syndrome zero sequence deactivation and the path metric equalization. The two approaches enable an easy adaptation of the decoding complexity for different transmission conditions, which results in a trade-off between decoding complexity and error correction performance.

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Santhosh Kumar, K. B., B. R. Sujatha, N. Sushma, and Venkateswara Rao Kolli. "Smart and Sustainable Energy Systems: Enhanced Transmission of EEG Signals in Telemedicine Applications using Soft Output Viterbi Turbo Decoder." IOP Conference Series: Earth and Environmental Science 1375, no. 1 (2024): 012022. http://dx.doi.org/10.1088/1755-1315/1375/1/012022.

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Abstract In the era of telemedicine, where remote treatment is gaining traction, the reliable transmission of biomedical signals is paramount. Turbo Coding has emerged as a pivotal method due to its robust performance and quality of service. However, the inherent complexity of Turbo decoders presents a significant hurdle. This paper investigates the efficacy of Soft Output Viterbi Algorithm (SOVA), Logarithmic MAP (Log-MAP), and Maximum A posteriori Probability (MAP) decoding techniques within Turbo decoding, crucial for real-time telemedicine applications. Focusing specifically on EEG signal transmission, we employ wireless channels and Turbo coding to enhance reliability. Viterbi decoding is leveraged to mitigate complexity, with an in-depth analysis of the SOVA algorithm’s Bit Error Rate performance across various parameters. This research enhances telemedicine by improving the reliability of biomedical signal transmission. Through efficient decoding techniques like Soft Output Viterbi Turbo Decoder, it ensures timely and accurate healthcare delivery. By reducing the need for patient travel and optimizing energy consumption, it aligns with Smart and Sustainable Energy Systems goals. This contributes to global healthcare accessibility and sustainability by minimizing carbon footprint and resource utilization. Ultimately, it promotes efficient, dependable, and eco-friendly healthcare solutions for all.

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20

Lu, Ying, Quan Yuan Xu, and Zhi Gang Liu. "Realization of the Viterbi Algorithm in MLSE with Intersymbol Interference." Applied Mechanics and Materials 214 (November 2012): 208–12. http://dx.doi.org/10.4028/www.scientific.net/amm.214.208.

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Optimum receiver model for channels with Intersymbol Interference (ISI) and Additive White Gaussian Noise (AWGN) are introduced to deduce the Viterbi algorithm in the Maximum-Likelihood Sequence Estimation (MLSE). Finally, we use Matlab to simulate the algorithm in three different channels and analyze the experiment results. Analyses show that the Viterbi algorithm is applicable for any channel which is optimum from a probability of error viewpoint; the MLSE for channels with ISI has a computational complexity that grows exponentially with the length of channels time dispersion L; the loss of performance is negligible when the decoding delay achieves 5L.

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21

Md., Abdul Rawoof, Ch Umasankar., Naresh Kumar D., Khalandar Basha D., and Madhu N. "Verilog based efficient convolution encoder and viterbi decoder." TELKOMNIKA Telecommunication, Computing, Electronics and Control 8, no. 1 (2019): 75–80. https://doi.org/10.11591/ijres.v8.i1.pp75-80.

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In thetoday"sdigital communication Systems,transmission of data with more reliability and efficiency is the most challenging issue for data communication through channels. In communication systems, error correction technique plays a vital role. In error correction techniques, The capacity of data can be enhanced by adding the redundant information for the source data while transmitting the data through channel. It mainly focuses on the awareness of convolution encoder and Viterbi decoder. For decoding convolution codes Viterbi algorithm is preferred.

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22

Tajima, Masato, Keiji Takida, and Zenshiro Kawasaki. "Symbol Reliability Estimation Using the Bidirectional Viterbi Decoding Algorithm." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 1998 (May 5, 1998): 285–90. http://dx.doi.org/10.5687/sss.1998.285.

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23

Harvey, B. A. "Adaptive Viterbi Algorithm With ARQ for Bounded Complexity Decoding." IEEE Transactions on Wireless Communications 3, no. 6 (2004): 1948–52. http://dx.doi.org/10.1109/twc.2004.837451.

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24

Fettweis, G., and H. Meyr. "High-speed parallel Viterbi decoding: algorithm and VLSI-architecture." IEEE Communications Magazine 29, no. 5 (1991): 46–55. http://dx.doi.org/10.1109/35.79382.

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Plotnikov, A. I., A. B. Levina, A. A. Lanina, and I. A. Zikratov. "COMPARISON OF METHODS SYNDROME AND SOFT DECODING FOR HAMMING CODE." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 245 (November 2024): 46–53. https://doi.org/10.14489/vkit.2024.11.pp.046-053.

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Information technology and computer technology are rapidly developing, which leads to increased requirements for information transmission systems. To meet current security requirements, it is necessary to ensure a high level of information integrity and accessibility. One of the most effective ways to ensure the integrity of information is noise-resistant coding. The speed of data acquisition and the correctness of their recovery largely depends on the choice of the decoding method. Many decoding methods have a high complexity of implementation, so their use is not always effective. This article discusses a comparison of syndromic decoding and soft decoding methods for a linear Hamming code. The paper presents a comparison of the speed and correctness of the soft decoding algorithm described in patent RU 2738724C1 with hard decoding methods – syndrome decoding and the Viterbi algorithm. The implementation of the decoding algorithms and algorithm of parallel syndromes table computation without thread blocks on Java programming language has been carried out in this work. The paper provides a detailed description of the Hamming code, syndrome decoding and soft decoding, and a comparison of these decoding methods is demonstrated and analyzed in detail. Conclusions are presented showing that the proposed probabilistic decoding method has better characteristics in terms of speed and correctness than all other methods, and hard decoding methods have on average more errors than the soft decoding algorithm for a certain number of iterations.

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Kao, Johnny W. H., Stevan M. Berber, and Abbas Bigdeli. "A General Rate K/N Convolutional Decoder Based on Neural Networks with Stopping Criterion." Advances in Artificial Intelligence 2009 (June 18, 2009): 1–11. http://dx.doi.org/10.1155/2009/356120.

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A novel algorithm for decoding a general rate K/N convolutional code based on recurrent neural network (RNN) is described and analysed. The algorithm is introduced by outlining the mathematical models of the encoder and decoder. A number of strategies for optimising the iterative decoding process are proposed, and a simulator was also designed in order to compare the Bit Error Rate (BER) performance of the RNN decoder with the conventional decoder that is based on Viterbi Algorithm (VA). The simulation results show that this novel algorithm can achieve the same bit error rate and has a lower decoding complexity. Most importantly this algorithm allows parallel signal processing, which increases the decoding speed and accommodates higher data rate transmission. These characteristics are inherited from a neural network structure of the decoder and the iterative nature of the algorithm, that outperform the conventional VA algorithm.

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Chan, Jason Chin-Tiong, and Hong Choon Ong. "A Novel Entropy-Based Decoding Algorithm for a Generalized High-Order Discrete Hidden Markov Model." Journal of Probability and Statistics 2018 (2018): 1–15. http://dx.doi.org/10.1155/2018/8068196.

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The optimal state sequence of a generalized High-Order Hidden Markov Model (HHMM) is tracked from a given observational sequence using the classical Viterbi algorithm. This classical algorithm is based on maximum likelihood criterion. We introduce an entropy-based Viterbi algorithm for tracking the optimal state sequence of a HHMM. The entropy of a state sequence is a useful quantity, providing a measure of the uncertainty of a HHMM. There will be no uncertainty if there is only one possible optimal state sequence for HHMM. This entropy-based decoding algorithm can be formulated in an extended or a reduction approach. We extend the entropy-based algorithm for computing the optimal state sequence that was developed from a first-order to a generalized HHMM with a single observational sequence. This extended algorithm performs the computation exponentially with respect to the order of HMM. The computational complexity of this extended algorithm is due to the growth of the model parameters. We introduce an efficient entropy-based decoding algorithm that used reduction approach, namely, entropy-based order-transformation forward algorithm (EOTFA) to compute the optimal state sequence of any generalized HHMM. This EOTFA algorithm involves a transformation of a generalized high-order HMM into an equivalent first-order HMM and an entropy-based decoding algorithm is developed based on the equivalent first-order HMM. This algorithm performs the computation based on the observational sequence and it requires OTN~2 calculations, where N~ is the number of states in an equivalent first-order model and T is the length of observational sequence.

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Bhattarai, Bhuwan, and Joonwhoan Lee. "Korean Pansori Vocal Note Transcription Using Attention-Based Segmentation and Viterbi Decoding." Applied Sciences 14, no. 2 (2024): 492. http://dx.doi.org/10.3390/app14020492.

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In this paper, first, we delved into the experiment by comparing various attention mechanisms in the semantic pixel-wise segmentation framework to perform frame-level transcription tasks. Second, the Viterbi algorithm was utilized by transferring the knowledge of the frame-level transcription model to obtain the vocal notes of Korean Pansori. We considered a semantic pixel-wise segmentation framework for frame-level transcription as the source task and a Viterbi algorithm-based Korean Pansori note-level transcription as the target task. The primary goal of this paper was to transcribe the vocal notes of Pansori music, a traditional Korean art form. To achieve this goal, the initial step involved conducting the experiments with the source task, where a trained model was employed for vocal melody extraction. To achieve the desired vocal note transcription for the target task, the Viterbi algorithm was utilized with the frame-level transcription model. By leveraging this approach, we sought to accurately transcribe the vocal notes present in Pansori performances. The effectiveness of our attention-based segmentation methods for frame-level transcription in the source task has been compared with various algorithms using the vocal melody task of the MedleyDB dataset, enabling us to measure the voicing recall, voicing false alarm, raw pitch accuracy, raw chroma accuracy, and overall accuracy. The results of our experiments highlight the significance of attention mechanisms for enhancing the performance of frame-level music transcription models. We also conducted a visual and subjective comparison to evaluate the results of the target task for vocal note transcription. Since there was no ground truth vocal note for Pansori, this analysis provides valuable insights into the preservation and appreciation of this culturally rich art form.

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Scholl, S., E. Leonardi, and N. Wehn. "FPGA implementation of trellis decoders for linear block codes." Advances in Radio Science 12 (November 10, 2014): 61–67. http://dx.doi.org/10.5194/ars-12-61-2014.

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Abstract. Forward error correction based on trellises has been widely adopted for convolutional codes. Because of their efficiency, they have also gained a lot of interest from a theoretic and algorithm point of view for the decoding of block codes. In this paper we present for the first time hardware architectures and implementations for trellis decoding of block codes. A key feature is the use of a sophisticated permutation network, the Banyan network, to implement the time varying structure of the trellis. We have implemented the Viterbi and the max-log-MAP algorithm in different folded versions on a Xilinx Virtex 6 FPGA.

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Kumar, K. Santhosh, and M. V. H. Bhaskara Murthy. "FPGA Implementation of Viterbi Algorithm for Decoding of Convolution Codes." IOSR journal of VLSI and Signal Processing 4, no. 5 (2014): 46–53. http://dx.doi.org/10.9790/4200-04514653.

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Grice, Jon R., and David A. Meyer. "A quantum algorithm for Viterbi decoding of classical convolutional codes." Quantum Information Processing 14, no. 7 (2015): 2307–21. http://dx.doi.org/10.1007/s11128-015-1003-3.

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32

Amat, Alexandre Graell i., Sergio Benedetto, and Paul H. Siegel. "A modified Viterbi decoding algorithm for high-rate convolutional codes." European Transactions on Telecommunications 16, no. 6 (2005): 527–36. http://dx.doi.org/10.1002/ett.1074.

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Raviv, Tomer, Asaf Schwartz, and Yair Be’ery. "Deep Ensemble of Weighted Viterbi Decoders for Tail-Biting Convolutional Codes." Entropy 23, no. 1 (2021): 93. http://dx.doi.org/10.3390/e23010093.

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Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, and each decoder specializes in decoding words from a specific region of the channel words’ distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75 dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high signal-to-noise ratios (SNRs).

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Raviv, Tomer, Asaf Schwartz, and Yair Be’ery. "Deep Ensemble of Weighted Viterbi Decoders for Tail-Biting Convolutional Codes." Entropy 23, no. 1 (2021): 93. http://dx.doi.org/10.3390/e23010093.

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Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, and each decoder specializes in decoding words from a specific region of the channel words’ distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75 dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high signal-to-noise ratios (SNRs).

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Sidorenko, Vladimir, Wenhui Li, Onur Günlü, and Gerhard Kramer. "Skew Convolutional Codes." Entropy 22, no. 12 (2020): 1364. http://dx.doi.org/10.3390/e22121364.

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A new class of convolutional codes, called skew convolutional codes, that extends the class of classical fixed convolutional codes, is proposed. Skew convolutional codes can be represented as periodic time-varying convolutional codes but have a description as compact as fixed convolutional codes. Designs of generator and parity check matrices, encoders, and code trellises for skew convolutional codes and their duals are shown. For memoryless channels, one can apply Viterbi or BCJR decoding algorithms, or a dualized BCJR algorithm, to decode skew convolutional codes.

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Lukusa, Tedy, Khmaies Ouahada, and Hendrik C. Ferreira. "Mathematical Approach and Implementation of Frequency Mapping Techniques in Power-Line Communications Channel." Communications in Applied and Industrial Mathematics 10, no. 1 (2019): 88–108. http://dx.doi.org/10.2478/caim-2019-0015.

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Abstract Power-line channel is considered to be a very hostile channel compared to other channels in view of the different types of noise that could exist. Therefore, the choice of the error correcting code and the modulation scheme can play a big role in combating the noise in such a channel. M -FSK modulation has shown its robustness for such a type of channel. Two frequency mappings techniques are presented in this paper. In the first technique, M orthogonal frequencies are arranged in sequences based on the value and the position of permutation symbols, while in the second technique, the frequencies are rearranged based on the sign changes of the Walsh-Hadamard transform (WHT). The obtained M-FSK modulation is combined to codes based on Viterbi decoding algorithms since Viterbi decoder is considered to be the maximum-likelihood decoding algorithm for convolutional codes and codes with state machine representation. A mathematical approach and implementation of frequency mappings is introduced to investigate the performance of the new designed communication system in the presence of permanent frequency disturbances, also known as narrow-band interference (NBI), such as those encountered in power line communications (PLC) channel.

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Kadhim, Qusay, Abdullah Al-Husseini, and Mohanad Al-Ibadi. "Accuracy Comparison of Hard, Soft, and UnQuantized Decisions across Diverse MIMO Channels and M-QAM Demodulation." Asian Journal of Computing and Engineering Technology 6, no. 1 (2025): 1–16. https://doi.org/10.47604/ajcet.3199.

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Purpose: In this paper, hard, soft, and non-quantized Viterbi decision algorithms are examined and compared over multiple-input multiple-output (MIMO), Quadratic amplitude modulation, QAM schemes, and M-ary channels. Methodology: The proposed system supports the design methodology of a decoding scheme of the LLR algorithm between MIMO and M-ary channels. The proposed system is designed and tested using MATLAB. Findings: The results provide valuable insights into the balance between computational efficiency and decoding accuracy, which helps in choosing appropriate decision algorithms for specific MIMO and M-QAM communication systems. The results demonstrated different scenarios, including MIMO (2x2), (4x4), and M-ary (4,16, and 32 QAM) technologies. Unique Contribution to Theory, Practice, and Policy: Experimental results show that although non-quantized decisions achieve the highest accuracy, they require significantly more computational resources. Hard decisions provide simpler implementation with lower computational costs but lower accuracy. The soft decision-making method balances performance and complexity and outperforms hard choices regarding bit error rate (BER) in all tested scenarios. It also enhances our understanding of Viterbi decoding in LLR estimation across different connectivity conditions. The scenarios showed that the soft solution is better than the hard solution, as previously known, depending on the conditions. However, from the results obtained using Matlab simulations, the silky solution appears to be the best in terms of the balance between complexity and better performance as the data show.

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Singh, Dr Balkar. "TURBO CODE RE-ANALYSIS USING DIFFERENT ALGORITHMS." International Journal of Engineering Science and Humanities 14, Special Issue 1 (2024): 27–31. http://dx.doi.org/10.62904/k2aydz44.

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Turbo codes are a novel type of forward error correcting codes that have proved to give a perfor- mance close to the channel capacity as proposed by C. Shannon. The parallel concatenation of two identical recursive convolutional encoders that are spaced apart by an interleaver results in a turbo code encoder. The two cascaded decoding blocks used by the turbo code decoder pass along a priori knowledge generated by each block in turn. The decoding approach has the advantage of working iteratively, allowing for an increase in total performance. This study does a performance analysis of turbo codes. The performance study includes two decoding methods: the soft output Viterbi algo- rithm (SOVA), which uses the log-likelihood ratio to produce soft outputs, and the log maximum a posteriori probability (Log-MAP) algorithm. Both punctured and unpunctured codes are studied to determine the impact of utilizing various decoding algorithms. The performance of the two various decoding techniques is then contrasted in terms of bit error rate. MATLAB tools are utilized to per- form simulations.

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Ye, Fei, and Yifei Wang. "A Novel Method for Decoding Any High-Order Hidden Markov Model." Discrete Dynamics in Nature and Society 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/231704.

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This paper proposes a novel method for decoding any high-order hidden Markov model. First, the high-order hidden Markov model is transformed into an equivalent first-order hidden Markov model by Hadar’s transformation. Next, the optimal state sequence of the equivalent first-order hidden Markov model is recognized by the existing Viterbi algorithm of the first-order hidden Markov model. Finally, the optimal state sequence of the high-order hidden Markov model is inferred from the optimal state sequence of the equivalent first-order hidden Markov model. This method provides a unified algorithm framework for decoding hidden Markov models including the first-order hidden Markov model and any high-order hidden Markov model.

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Wang, Xiao-tao, Hua Qian, and Kai Kang. "Viterbi-bidirectional Searching Based ML Decoding Algorithm for Tail-biting Codes." Journal of Electronics & Information Technology 35, no. 5 (2014): 1017–22. http://dx.doi.org/10.3724/sp.j.1146.2012.01219.

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Park, Chulhyun, Yongchul Jung, Jihoon Kim, and Yunho Jung. "Joint Viterbi detection and decoding algorithm for bluetooth low energy systems." Electronics Letters 56, no. 6 (2020): 310–12. http://dx.doi.org/10.1049/el.2019.2621.

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Nair, Nishanth Ulhas, and T. V. Sreenivas. "Multi-Pattern Viterbi Algorithm for joint decoding of multiple speech patterns." Signal Processing 90, no. 12 (2010): 3278–83. http://dx.doi.org/10.1016/j.sigpro.2010.05.006.

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HUANG, Yu,a, Weiming XIONG, and Huixian SUN. "Auxiliary Trellis Based Viterbi Decoding Algorithm Research of 4D-8PSK-TCM." Chinese Journal of Space Science 28, no. 6 (2008): 578. http://dx.doi.org/10.11728/cjss2008.06.578.

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Rawoof, Md Abdul, Umasankar Ch., D. Naresh Kumar, D. Khalandar Basha, and N. Madhur. "Verilog based efficient convolution encoder and viterbi decoder." International Journal of Reconfigurable and Embedded Systems (IJRES) 8, no. 1 (2019): 75. http://dx.doi.org/10.11591/ijres.v8.i1.pp75-80.

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In the<strong><em> </em></strong>today’s<strong><em> </em></strong>digital communication Systems,<strong><em> </em></strong>transmission of data with more reliability and efficiency is the most challenging issue for data communication through channels. In communication systems, error correction technique plays a vital role. In error correction techniques, The capacity of data can be enhanced by adding the redundant information for the source data while transmitting the data through channel. It mainly focuses on the awareness of convolution encoder and Viterbi decoder. For decoding convolution codes Viterbi algorithm is preferred.

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Satybaldina, Dina, Valery Zolotarev, Gennady Ovechkin, and Zhuldyz Sailau kyzy. "NEW CONCATENATION SCHEMES BASED ON THE MULTITHRESHOLD DECODERS OF CONVOLUTIONAL SELF-ORTHOGONAL CODES FOR GAUSSIAN CHANNELS." Eurasian Journal of Mathematical and Computer Applications 9, no. 4 (2021): 51–62. http://dx.doi.org/10.32523/2306-6172-2021-9-4-51-62.

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New serial concatenation schemes based on the multithreshold decoders and di- vergent principle for the convolutional self-orthogonal codes under Gaussian channels are proposed. Using both binary and symbolic decoders on the second decoding stage of the convolutional codes are considered. Simulation results are indicated the higher performance characteristics of the proposed cascade schemes on majority decoders in comparison with clas- sical schemes based on the Viterbi algorithm and Reed-Solomon codes. A moderate increase in decoding delay during concatenation is revealed. It is determined by the absence of the need to use traditional two-dimensional concatenated structures.

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Tumilaar, Kezia, Yohanes Langi, and Altien Rindengan. "Hidden Markov Model." d'CARTESIAN 4, no. 1 (2015): 86. http://dx.doi.org/10.35799/dc.4.1.2015.8104.

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Hidden Markov Models (HMM) is a stochastic model and is essentially an extension of Markov Chain. In Hidden Markov Model (HMM) there are two types states: the observable states and the hidden states. The purpose of this research are to understand how hidden Markov model (HMM) and to understand how the solution of three basic problems on Hidden Markov Model (HMM) which consist of evaluation problem, decoding problem and learning problem. The result of the research is hidden Markov model can be defined as . The evaluation problem or to compute probability of the observation sequence given the model P(O|) can solved by Forward-Backward algorithm, the decoding problem or to choose hidden state sequence which is optimal can solved by Viterbi algorithm and learning problem or to estimate hidden Markov model parameter to maximize P(O|) can solved by Baum – Welch algorithm. From description above Hidden Markov Model with state 3 can describe behavior from the case studies. Key words: Decoding Problem, Evaluation Problem, Hidden Markov Model, Learning Problem

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Cox, R. V., and C. E. W. Sundberg. "An efficient adaptive circular Viterbi algorithm for decoding generalized tailbiting convolutional codes." IEEE Transactions on Vehicular Technology 43, no. 1 (1994): 57–68. http://dx.doi.org/10.1109/25.282266.

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Tao Li, Wai Ho Mow, and Manhung Siu. "Joint Erasure Marking and Viterbi Decoding Algorithm for Unknown Impulsive Noise Channels." IEEE Transactions on Wireless Communications 7, no. 9 (2008): 3407–16. http://dx.doi.org/10.1109/twc.2008.061129.

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Habib, Irfan, Özgün Paker, and Sergei Sawitzki. "Design Space Exploration of Hard-Decision Viterbi Decoding: Algorithm and VLSI Implementation." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 18, no. 5 (2010): 794–807. http://dx.doi.org/10.1109/tvlsi.2009.2017024.

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Said, SM, and KR Dimond. "Realtime implementation of the Viterbi decoding algorithm on a high-performance microprocessor." Microprocessors and Microsystems 10, no. 1 (1986): 11–16. http://dx.doi.org/10.1016/0141-9331(86)90003-7.

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