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A List Decoding Algorithm for Short Low-Density Parity-Check Codes

Telex M. N. Ngatched, Fambirai Takawira

Published Apr 3, 2006• 0 citations
OpenAlex

Abstract

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.

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IEEE Access•Jan 1, 2026•0 citations
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 reliability-based iterative majority-logic decoding algorithm for regular low-density parity-check (LDPC) codes was recently proposed by Huang et al. In this paper we present an improved version of that algorithm by introducing a different reliability measure for each check-sum of the parity-check matrix, and taking it into account in the computation of the extrinsic information that is used to update the reliability measure of each received bit in each iteration. Some simulations results are given, which show that the new algorithm, while requiring very little additional computational complexity, not only achieves a considerable error performance gain over the standard one, but also, importantly, outperforms the iterative decoding based on belief propagation (IDBP), especially for short and medium block length finite-geometry (FG) LDPC codes.
In this paper, a new low-complexity symbol-flipping algorithm to decode nonbinary low-density parity-check (LDPC) codes is proposed. The decoding procedure updates iteratively the hard-decision received symbol vector in search of a valid codeword in the symbol vector space. Only one symbol is changed in each iteration, and symbol flipping function combines the number of failed checks and reliability of the received bits and calculated symbols. An optional mechanism to avoid infinite loops in high Galois field search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity over relatively low Galois field for short to medium code length.
In this letter, a low complexity decoding algorithm for binary linear block codes is applied to low-density paritycheck (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performances at smaller complexity.
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.
A novel bit-flipping (BF) algorithm with low complexity for high-throughput decoding of low-density parity-check (LDPC) codes is presented. At each iteration, a novel threshold pattern is used to determine the code bits whether to be flipped or not, and the flipping error probability is effectively decreased. Compared with the weighted BF algorithm and its modifications, the modified BF algorithm has significantly lower complexity and decoding time. Through simulations the proposed BF algorithm is shown to achieve excellent performance and fast convergence speed while maintaining significantly low complexity thus facilitating high-throughput decoding.
Low-density parity-check (LDPC) codes have been widely used in practice due to their excellent error correction capabilities. However, the error correction performance of traditional decoding algorithms for LDPC codes is limited under short block lengths. To address this problem, this paper proposes an effective scheme that contains two stages for decoding short LDPC codes. In the first stage, the traditional belief propagation (BP) iterative algorithm is used to decode an LDPC code. The decoding process terminates if a codeword is obtained in this stage. Otherwise, the second stage decoding is invoked, in which the ordered reliability bits guessing random additive noise decoding (ORBGRAND) algorithm is applied. The accumulated log-likelihood ratios in the first stage are used to order the test error patterns in the ORBGRAND algorithm. Simulation results indicate that the proposed BP-ORBGRAND scheme can outperform the traditional BP iterative algorithm with relatively low additional complexity. Compared with the decoding scheme that concatenates the BP algorithm and the order statistics decoding (OSD) algorithm, the proposed decoding scheme has similar performance and the operations involved can be efficiently implemented in the hardware platform. All these indicate that the proposed scheme is desirable for practical purposes.