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International Symposium on Information Theory and its Applications

Improvement of the forced-convergence decoding for LDPC codes

Rumi Aoyama, Yuichi Kaji

Published Dec 1, 2008• 8 citations
Publisher

Abstract

An improvement of the forced-convergence decoding algorithm is discussed. Iterative decoding schemes such as the sum-product (SP) decoding bring out excellent performance of low-density parity check (LDPC) codes. The forced-convergence (FC) decoding is also an iterative decoding algorithm obtained by modifying the SP decoding. The FC decoding succeeds to reduce the decoding complexity of the SP decoding, but the error correcting performance is severely degraded by the modification. The performance degradation of the FC decoding is expected to be mitigated if the convergence criterion used in the algorithm is appropriately modified. This paper discusses several types of modifications of the convergence criteria. Computer simulation shows that the proposed modifications improve the performance of the FC decoding algorithm.

DOI
10.1109/isita.2008.4895536

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An improvement of the forced-convergence decoding algorithm is discussed. Iterative decoding schemes such as the sum-product (SP) decoding bring out excellent performance of low-density parity check (LDPC) codes. The forced-convergence (FC) decoding is also an iterative decoding algorithm obtained by modifying the SP decoding. The FC decoding succeeds to reduce the decoding complexity of the SP decoding, but the error correcting performance is severely degraded by the modification. The performance degradation of the FC decoding is expected to be mitigated if the convergence criterion used in the algorithm is appropriately modified. This paper discusses several types of modifications of the convergence criteria. Computer simulation shows that the proposed modifications improve the performance of the FC decoding algorithm.
This paper proposes a simplified forced-convergence (SFC) algorithm to reduce the computational complexity for low-density parity-check (LDPC) decoding. To reduce the computational complexity, the proposed algorithm uses the modified check node (CN) operation that does not use a condition for deactivating CNs. Therefore, the proposed SFC algorithm uses only one threshold value while the existing forced-convergence (FC) algorithm uses two threshold values. The simulation results show that SFC achieves a bit error rate (BER) performance close to min-sum (MS) algorithm. SFC can reduce the computational complexity of check node by approximately 22.21% compared to FC.
An improved parallel decoding approach of sum-product algorithm for low-density parity-check codes(LDPC) was presented in order to solve the problem of divergence in decoding iteration with finite precision,.In addition,the reason for improving the convergence speed was discussed detailedly and the pipeline structure was provided.By eliminating the unexpected state in which operation data didn't satisfy input rules due to the finite precision effect thus could not be preceded correctly,the iteration convergence was improved efficiently and led to decoding with no error.Compared with the original parallel approach,this improvement don't involve too much control logic and computational complexity.Simulation shows that the proposed decoding approach over additive white Gaussian noise(AWGN) channel achieves good performance,especially at high code rate,it suffers negligible performance loss compared with the forward-backward approach while reducing the operation complexity effectively.
Error floor properties of low-density parity-check(LDPC)codes using different decoding algorithms were statistically analyzed utilizing test data from a hardware evaluation platform.The analysis shows that the number of residual error bits in an error codeword after decoding failure using the sum-product(SP)algorithm or the modified min-sum(MMS)algorithm is usually quite small;therefore,LDPC codes can serve as the inner code in a concatenated coding system to achieve an ultra low bit error rate.The analysis also shows that SP algorithm is more suitable for a concatenated coding system than MMS algorithm since less residual error bits occur when using the SP algorithm.Concatenated codes based on the analysis achieve bit error rates lower than 10-10 with a low decoding threshold.
Abstract: In this paper, a fast-convergence algorithm is proposed for the decoding of low-density parity-check (LDPC) codes. By putting more weight on the message update from check node to variable node in current iteration, the proposed method speeds up the decoding significantly. Simulation results show that compared with the standard layered min-sum decoding algorithm, the proposed scheme may reduce about 1/6 iteration numbers for LDPC codes used in DVB-S2, with hardware complexity overhead less than 2%. Key–Words: LDPC code, fast convergence decoding algorithm, layered decoding, min-sum algorithm, hardware implementation 1
An efficient early stopping criterion based on the evolution of the number of reliable variable nodes (NRVN) is proposed for low density parity check (LDPC) codes in this paper. This criterion can significantly reduce the average number of iterations (ANI) at low to middle signal to noise ratios (SNRs) with minimal performance degradation. Furthermore, a hybrid decoding method is presented to reduce the decoding complexity of LDPC codes by combining the proposed stopping criterion and forced convergence (FC) decoding algorithm. Compared with the classic belief propagation (BP) decoding, significant computation complexity reduction can be achieved with small computation overhead.