Belief propagation (bp) is a soft-decision (SD) decoder that is commonly used to obtain near-optimal decoding performance for linear codes defined over sparse parity-check matrix. Nevertheless, the bp yields poor perf...
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Belief propagation (bp) is a soft-decision (SD) decoder that is commonly used to obtain near-optimal decoding performance for linear codes defined over sparse parity-check matrix. Nevertheless, the bp yields poor performance when used in the decoding of algebraic block codes, usually described by a dense parity-check matrix. Hence, enhanced bp decoders transform the parity check matrix of such codes at each iteration for efficient decoding. In this article, the performance of the transformed parity-check matrix of the iterative SD decoder is analysed for the class of binary cyclic codes using a perfect knowledge model (PKM). The PKM computes a list of candidate matrices and selects a baseline parity-check matrix according to a distance metric. The selected matrix is optimal since it minimizes the probability of error over various choices in the list. Results show that, for a given channel condition, the conventional transformed matrix obtained by Gaussian elimination is sub-optimal and does not necessarily contain unitary weighted columns at corresponding columns of the unreliable bits. Moreover, PKM can be used to verify the performances of newly developed iterative SD decoders for binary cyclic codes based on parity-check equations instead of maximum-likelihood decoding.
Low-density parity-check (LDPC) codes have very good performance when they are decoded by iterative belief-propagation (bp) decodingalgorithms and are widely used in many applications. However, the iterative decoding...
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ISBN:
(纸本)9788132225805;9788132225799
Low-density parity-check (LDPC) codes have very good performance when they are decoded by iterative belief-propagation (bp) decodingalgorithms and are widely used in many applications. However, the iterative decoding of LDPC codes has a huge complexity, especially for LDPC codes constructed over the nonbinary field GF(q). Traditionally, the iterative process is performed until the maximum number of iterations is reached or a codeword is found, which is unnecessary for undecodable code blocks. Hence, it is important to develop certain stopping criterion to identify these undecodable blocks and terminate the decoding process in advance. Based on the analysis of check-sum variations in the decoding process, a stopping criterion is proposed in this paper. Simulation results indicate the proposed criterion can greatly reduce the average number of iterations (ANI) over a wide range of signal-to-noise ratio (SNR) values, with little performance degradation compared with the traditional bpdecoding.
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