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IEEE International Symposium on Information Theory (ISIT)

A degree-matched check node approximation for LDPC decoding

Sheryl L. Howard, Christian B. Schlegel, Vincent Gaudet

Published Jan 1, 2005• 27 citations
Publisher

Abstract

This paper examines ways to recoup the performance loss incurred when using the min-sum approximation instead of the exact sum-product algorithm for decoding low-density parity check codes (LDPCs). Approximations to the correction factor exactly expressing the difference between these two decoding algorithms exist for degree 3 check nodes, and can be applied to higher degree nodes by subdividing them into component degree 3 nodes. However, this results in replication of the approximation. An asymptotic expression for the correction factor at a check node of any degree is derived in this paper, and used to develop two simple approximations to the correction factor, matched to the check node degree. One has very low complexity, and both only need be applied once per check node extrinsic message. Simulation results are presented for each check node approximation when decoding a regular and an irregular LDPC. Both degree-matched check node approximations achieve sum-product decoding performance

DOI
10.1109/isit.2005.1523516

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This paper examines ways to recoup the performance loss incurred when using the min-sum approximation instead of the exact sum-product algorithm for decoding low-density parity check codes (LDPCs). Approximations to the correction factor exactly expressing the difference between these two decoding algorithms exist for degree 3 check nodes, and can be applied to higher degree nodes by subdividing them into component degree 3 nodes. However, this results in replication of the approximation. An asymptotic expression for the correction factor at a check node of any degree is derived in this paper, and used to develop two simple approximations to the correction factor, matched to the check node degree. One has very low complexity, and both only need be applied once per check node extrinsic message. Simulation results are presented for each check node approximation when decoding a regular and an irregular LDPC. Both degree-matched check node approximations achieve sum-product decoding performance
This brief examines different parity-check node decoding algorithms for low-density parity-check (LDPC) codes, seeking to recoup the performance loss incurred by the min-sum approximation compared to sum-product decoding. Two degree-matched check node decoding approximations that depend on the check node degree dcare presented. Both have low complexity and can be applied to any degree distribution. Simulation results show near sum-product decoding performance for both degree-matched check node approximations for regular and irregular LDPCs
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.
Abstract ― Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
One of the most important units of Low-Density Parity-Check (LDPC) decoders is the Check-Node Unit.Its main task is to find the first two minimum values among incoming variable-to-check messages and return check-tovariable messages.This block significantly affects the decoding performance, as well as the hardware implementation complexity.In this paper, we first propose a modification to the check-node update rule by introducing two optimal offset factors applied to the check-to-variable messages.Then, we present the Check-Node Unit hardware architecture which performs the proposed algorithm.The main objective of this work aims to improve further the decoding performance for 5 th Generation (5G) LDPC codes.The simulation results show that the proposed algorithm achieves essential improvements in terms of error correction performance.More precisely, the error-floor does not appear within Bit-Error-Rate (BER) of 10 -8 , while the decoding gain increases up to 0.21 dB compared to the baseline Normalized Min-Sum, as well as several state-ofthe-art LDPC-based Min-Sum decoders.
This paper proposes a new technique to improve bit error performance of the min-sum decoding algorithm for low density parity check codes. The proposed technique is based on two way normalization of min-sum LDPC decoding algorithm. The variable message is modified by two normalization factors to achieve the optimum approximation for the magnitude overestimation at the check node processing. This new method does not need exhaustive search for the optimum normalization factor when there is a change in code length and code rate. The performance has been evaluated for medium and short length codes using a small number of iterations. The results show improved performance of the proposed method, which makes it attractive for many practical applications.