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INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences

Improved Decoding Algorithms Based on Oscillation Log-likelihood Ratio for Low-density Parity Check Codes

DONG Zijian -, BI Xuyin -

Published Sep 30, 2011• 1 citation
Publisher

Abstract

Several decoding algorithms based on oscillation Log-likelihood ratio (LLR) for Lowdensity parity-check (LDPC) codes are investigated in this paper, based on which, an improved decoding algorithm which uses the accumulated LLR as the final bit decision merit is proposed. This approach improves the decoding performance with only a very small increase in storage and computation. Combined with normalized belief-propagation (BP), two algorithms are given, which are named as accumulate normalized BP (ACC-Nor-BP) and compare-add normalized BP (CA-Nor-BP). The storage requirements and computational complexity of ACC-Nor-BP is lower than that of CA-Nor-BP and CA-BP, but performance is close to the CA-Nor-BP and better than CA-BP; therefore ACC-Nor-BP algorithm is an effectively improved BP algorithm which has a good balance between performance and complexity.

DOI
10.4156/aiss.vol3.issue8.12

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Several decoding algorithms based on oscillation Log-likelihood ratio (LLR) for Lowdensity parity-check (LDPC) codes are investigated in this paper, based on which, an improved decoding algorithm which uses the accumulated LLR as the final bit decision merit is proposed. This approach improves the decoding performance with only a very small increase in storage and computation. Combined with normalized belief-propagation (BP), two algorithms are given, which are named as accumulate normalized BP (ACC-Nor-BP) and compare-add normalized BP (CA-Nor-BP). The storage requirements and computational complexity of ACC-Nor-BP is lower than that of CA-Nor-BP and CA-BP, but performance is close to the CA-Nor-BP and better than CA-BP; therefore ACC-Nor-BP algorithm is an effectively improved BP algorithm which has a good balance between performance and complexity.
A great deal of experiment indicate that, during the decoding course of message passing for LDPC codes, a phenomenon of oscillating always exists in some variable messages named extrinsic log-likelihood rate (ex-LLR). It could arose bit error. This paper tells of why the magnitudes of a posterior LLRs and ex-LLRs of some bits would oscillated, and thus two improved algorithms are proposed, which could improve the decoding performance being deteriorated by ex-LLR oscillation. The computer simulation shows that, for short and middle length LDPC codes, the proposed algorithms could lower the error floor without increasing the complexity, so these two algorithms could achieve better BER and BLER than the conventional LLR-BP decoding algorithm.
To improve the decoding speed and reduce the complexity of low-density parity-check (LDPC) codes, this paper proposes a hybrid LDPC decoding algorithm that combined with the distribution characteristics of log-likelihood ratio (LLR) of all variable node information before each iteration. During the process of decoding, there is a judgment based on an interval value and a threshold value to select the Belief Propagation (BP) algorithm or the Minimal Sum (MS) algorithm to decode, so the proposed hybrid algorithm effectively combines the excellent performance of BP algorithm and the simple operation of MS algorithm. The simulation results show that the algorithm can greatly reduce the computational complexity and achieve similar decoding performance compared with the BP algorithm.
Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
According to no-convergence of falsely oscillating iteration in the low-density parity-check(LDPC) decoding at the range from medium to high SNRs(Signal to Noise Ratios),we propose a modified LDPC belief propagation(BP) decoding algorithm,i.e.soft value zero-forcing BP algorithm.By setting extrinsic information of the oscillating iteration bit nodes into zero,the impact on the iteratively decoding from false channel information is greatly reduced.And it also improves the performance of the decoding algorithm.Furthermore,a decision criterion of oscillating iteration nodes is presented to increase the accuracy of the decision.Simulation results show that the proposed algorithm has better decoding performance than that of the BP algorithm with the same iterations at medium and high SNRs.