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A Improved Min-Sum Algorithm for LDPC Codes

Zhang Rong-rong

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Among the decoding algorithm for low-density parity-check(LDPC) code,belief propagation(BP) algorithm has good performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering the trade-off between performance and complexity,the relationship between the value of overestimate under min-sum algorithm and the input information is analyzed,and an improved min-sum algorithm is proposed.Simulation results show that the improved min-sum algorithm remains similar performance with the traditional BP algorithm,but has less complexity.

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Among the decoding algorithm for low-density parity-check(LDPC) code,belief propagation(BP) algorithm has good performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering the trade-off between performance and complexity,the relationship between the value of overestimate under min-sum algorithm and the input information is analyzed,and an improved min-sum algorithm is proposed.Simulation results show that the improved min-sum algorithm remains similar performance with the traditional BP algorithm,but has less complexity.
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.
To improve the decoding performance of Low Density Parity Check(LDPC) code,an efficient decoding algorithm based on min-sum algorithm is proposed. The proposed algorithm analyzes the check node update equation and at the view of probability to form an approximation min-sum equation. It adopts a dynamic normalization factor to improve the decoding performance. Detailed simulation results and comparisons with Belief Propagation(BP) algorithm show that,with little decoding performance loss,the proposed algorithm not only decreases computational load,but also improves decoding efficiency.
A check node degree-based modified min-sum algorithm which classifies the codes was developed to reduce the complexity and improve the performance of decoding algorithm for low-density parity-check(LDPC) codes.The algorithm corrects both the minimum and sub-minimum absolute values of incoming messages in the check nodes.Two correction factors are obtained by calculating the offset between the belief propagation(BP) algorithm and the min-sum algorithm based on the check node degree.Simulations show that the algorithm achieves better performance than the BP algorithm at high signal noise ratio.The algorithm is also less complex than the BP algorithm and provides a good tradeoff between performance and complexity for any check node degree distribution in the LDPC codes.
Layered decoding is well appreciated in Low-Density Parity-Check (LDPC) decoder implementation since it provides efficient and high-throughput implementation of LDPC decoders. Variable-Node Layered Belief Propagation (VL-BP) algorithm and their reduced-complexity derivatives for LDPC codes are presented. The VL-BP algorithm is a modification of Belief Propagation algorithm (BP), where the variable nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. Some simplifications can also be made to lower the complexity of both BP and CL-BP algorithms, and particularly the complexity of the check node update rule. In this paper, we consider Variable Node Layered BP (VL-BP) algorithm and propose an optimized min-sum VL-BP (MS VL-BP) algorithm for decoding LDPC code which has better performance not only from MS VL-BP algorithm but also from BP algorithm. In this decoding method, unlike other layered algorithms, we consider for the first layer a set of variable nodes that has a low value of the intrinsic information. Simulation results show that good performance can be achieved, and which can even be improved by the addition of either a normalization term or an additive offset term.
Among the decoding algorithms for low-density parity-check(LDPC) code,sum-product algorithm(SPA) has the optimal performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering this performance-complexity contradiction,some modified min-sum algorithms are proposed.In this paper,researches are done based on one of the modified min-sum algorithms that is close to SPA in performance but the way modifying fraction works is simplified.Simplified algorithm remains similar in performance to sum-product algorithm but has a remarkably reduced implementation complexity.
In this paper, a modified min-sum decoding algorithm based on classified correction is proposed for low density parity check (LDPC) codes. Different from the single correction in the normalized belief propagation (BP)-based and offset BP-based algorithms [4], the proposed algorithm utilizes two corrections for both minimum and sub-minimum magnitudes of input messages in check nodes. These two correction factors can be obtained by analyzing the offset of updated messages in check nodes between the BP and the min-sum algorithms associated with check node degree. Simulation results show that the proposed algorithm can achieve performance very close to that of the BP algorithm. Furthermore, the FPGA implementation of this algorithm can reach a throughput of 200 Mbps at BER=10-6with lower complexity and fewer resources than the BP algorithm.