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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

An Efficient Decoding Algorithm for Low-Density Parity-Check Codes

Yang Cao

Published May 1, 2005• 1 citation
Publisher

Abstract

We present a simple decoding algorithm that modifies soft bit-flipping algorithm for decoding LDPC codes. In our method, a new parameter is explored to distinguish the variables (symbols) belonging to the same number of unsatisfied constraints. A token is also assigned in the method to avoid repeated flipping of the same variable, rather than using a constant taboo length. Our scheme shows a similar computational load as the taboo-based algorithm, while having a similar decoding performance as the belief propagation algorithm.

DOI
10.1093/ietfec/e88-a.5.1384

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We present a simple decoding algorithm that modifies soft bit-flipping algorithm for decoding LDPC codes. In our method, a new parameter is explored to distinguish the variables (symbols) belonging to the same number of unsatisfied constraints. A token is also assigned in the method to avoid repeated flipping of the same variable, rather than using a constant taboo length. Our scheme shows a similar computational load as the taboo-based algorithm, while having a similar decoding performance as the belief propagation algorithm.
An improved bit-flipping decoding algorithm is proposed for low-density parity-check(LDPC) codes in this paper.Two influences on error probabilities of code bits are considered: the influence of the number of code bits included in an unsatisfied check,and the influence of the number of unsatisfied checks of each code bit.No soft information is required for decoding.Simulation results show that improvement on performance is observed for the proposed algorithm,and it provides better performance over several soft-decision bit-flipping decoding algorithms for LDPC codes with large girth.
In this paper, a new method for improving hard-decision bit-flipping (BF) decoding is proposed for low-density parity-check codes. The flipping criterion is derived theoretically from the soft-decision belief-propagation decoding algorithm. The proposed BF decoding algorithm is channel independent and is improved by introducing a more efficient method for computing the reliability of the parity checks. Extensive simulations are provided to demonstrate the efficiency of the proposed algorithm. Simulation results show that the proposed algorithm can achieve about 1.5dB coding gain improvement at BER = 5×10−6while reducing up to 48% iterations for decoding and maintaining low decoding complexity, compared with the conventional weighted BF algorithm.
Abstract In this paper, a list decoding algorithm for lowdensity parity-check (LDPC) codes is presented. The algorithm uses a modification of the simple Gallager bit-flipping algorithm to generate a sequence of candidate codewords iteratively one at a time using a set of test error patterns based on the reliability information of the received symbols. It is particularly efficient for short block LDPC codes, both regular and irregular. Computer simulation results are used to compare the performance of the proposed algorithm with other known decoding algorithms for LDPC codes, with the result that the presented algorithm offers excellent performances. Performances comparable to those obtained with iterative decoding based on belief propagation can be achieved at a much smaller complexity. 1 I.
A hard-decision decoding algorithm based on parity-check sum for LDPC code was first described, and then a soft-decision decoding algorithm based on parity-check sum and symbol reliability was proposed. The soft-decision decoding algorithm incorporates received symbol reliability information and a simple taboo function that avoids repeated flipping of the same bit. A maximum votes queue algorithm for the numbers of which the parity-check functions were not satisfied was applied to quickly search the flipping bit. Approaches above all were used to improve the performance of the flipping-bit algorithm based on parity-check sum.
In this study, a new method for improving hard-decision bit-flipping (BF) decoding is proposed for low-density parity-check codes. The flipping criterion is derived theoretically from the soft-decision belief-propagation decoding algorithm. The proposed BF decoding algorithm is channel independent and is improved by introducing a more efficient method for computing the reliability of the parity checks. Extensive simulations are provided to demonstrate the efficiency of the proposed algorithm. Simulation results show that the proposed algorithm can achieve about 1.6 dB coding gain improvement at BER=10−5 while reducing up to 53% iterations for decoding and maintaining low-decoding complexity, compared with the conventional weighted BF algorithm.