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Sequential Decoding Algorithms for Block Error-Correcting Codes

Yibin Ng, Wai Ho Mow

Published Jan 1, 1998• 0 citations
OpenAlex

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In the Shannon Lecture at the 2019 International Symposium on Information Theory (ISIT), Professor Arikan proposed a new coding scheme called polarization-adjusted convolutional (PAC) codes. These codes exhibit excellent error-correction performance for short-to-medium block lengths. Currently, the mainstream decoding algorithms for PAC codes mainly include sequential decoding and list decoding. Fano decoding, a type of sequential decoding, offers good error-correction performance; however, its time complexity is relatively high due to the presence of extensive backtracking processes. In this paper, a fast Fano decoding algorithm based on backtracking optimization mechanism for PAC codes is proposed. The improved algorithm we put forward mitigate the time complexity of the decoding process from two aspects: path backtracking and threshold updating strategy. It enhances the error-correcting performance of the Fano decoding algorithm by introducing the first error node metric and the second error node metric. With the efforts in the above aspects, our decoding algorithm achieves good performance in both complexity and error-correction capability.

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The (23,12,7) Golay code is a perfect linear error-correcting code that can correct all patterns of three or fewer errors in 23 bit positions. A simple BCH decoding algorithm, given in E. Berlekamp (1968), can decode the (23,12,7) Golay code provided there are no more than two errors. The shift-search algorithm, developed by Reed et a. (1990), sequentially inverts the information bits until the third error is canceled. It then utilizes the BCH decoding algorithm to correct the remaining two errors. In this paper a simplified decoding algorithm, called the reliability-search algorithm, is proposed. This algorithm uses bit-error probability estimates to cancel the third error and then uses the BCH decoding algorithm to correct the remaining two errors. Simulation results show that this new algorithm significantly reduces the decoding complexity for correcting the third error while maintaining the same BER performance.

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In the Shannon Lecture at the 2019 International Symposium on Information Theory (ISIT), Professor Arikan proposed a new coding scheme called polarization-adjusted convolutional (PAC) codes. These codes exhibit excellent error-correction performance for short-to-medium block lengths. Currently, the mainstream decoding algorithms for PAC codes mainly include sequential decoding and list decoding. Fano decoding, a type of sequential decoding, offers good error-correction performance; however, its time complexity is relatively high due to the presence of extensive backtracking processes. In this paper, a fast Fano decoding algorithm based on backtracking optimization mechanism for PAC codes is proposed. The improved algorithm we put forward mitigate the time complexity of the decoding process from two aspects: path backtracking and threshold updating strategy. It enhances the error-correcting performance of the Fano decoding algorithm by introducing the first error node metric and the second error node metric. With the efforts in the above aspects, our decoding algorithm achieves good performance in both complexity and error-correction capability.
The (23,12,7) Golay code is a perfect linear error-correcting code that can correct all patterns of three or fewer errors in 23 bit positions. A simple BCH decoding algorithm, given in E. Berlekamp (1968), can decode the (23,12,7) Golay code provided there are no more than two errors. The shift-search algorithm, developed by Reed et a. (1990), sequentially inverts the information bits until the third error is canceled. It then utilizes the BCH decoding algorithm to correct the remaining two errors. In this paper a simplified decoding algorithm, called the reliability-search algorithm, is proposed. This algorithm uses bit-error probability estimates to cancel the third error and then uses the BCH decoding algorithm to correct the remaining two errors. Simulation results show that this new algorithm significantly reduces the decoding complexity for correcting the third error while maintaining the same BER performance.