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Improved min-sum decoding of LDPC codes using 2-dimensional normalization

Juntan Zhang, M.P.C. Fossorier, Daqing Gu, Jinyun Zhang

Published Jan 1, 2005• 25 citations
Publisher

Abstract

A two-dimensional post normalization scheme is proposed to improve the performance of conventional min-sum (MS) and normalized MS decoding of irregular low density parity check codes. An iterative procedure based on parallel differential optimization algorithm is presented to obtain the optimal two-dimensional normalization factors. Both density evolution analysis and specific code simulation show that the proposed method provides a comparable performance as belief propagation decoding while requiring less complexity. Interestingly, the new method exhibits a lower error floor than that of belief propagation decoding in the high SNR region. With respect to standard MS and one-dimensional normalized MS decodings, the two-dimensional normalized MS offers a considerably better performance.

DOI
10.1109/glocom.2005.1577841

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A two-dimensional post normalization scheme is proposed to improve the performance of conventional min-sum (MS) and normalized MS decoding of irregular low density parity check codes. An iterative procedure based on parallel differential optimization algorithm is presented to obtain the optimal two-dimensional normalization factors. Both density evolution analysis and specific code simulation show that the proposed method provides a comparable performance as belief propagation decoding while requiring less complexity. Interestingly, the new method exhibits a lower error floor than that of belief propagation decoding in the high SNR region. With respect to standard MS and one-dimensional normalized MS decodings, the two-dimensional normalized MS offers a considerably better performance.
Two-dimensional (2-D) correction schemes are proposed to improve the performance of conventional min-sum (MS) decoding of irregular low density parity check codes. An iterative procedure based on parallel differential optimization is presented to obtain the optimal 2-D factors. Both density evolution analysis and simulation show that the proposed method provides a comparable performance as belief propagation (BP) decoding while requiring less complexity. Interestingly, the new method exhibits a lower error floor than that of BP decoding. With respect to conventional MS and 1-D normalized MS decodings, the 2-D normalized MS offers a better performance. The 2-D offset MS decoding exhibits a similar behavior.
In this paper, a modified normalized Min-Sum algorithm (MNMSA) is proposed for decoding irregular Low Density Parity Check Codes (LDPC) with non-uniform degree distribution. The proposed algorithm provides an efficient decoding scheme to enhance the error performance of an irregular LDPC code without increasing the hardware complexity. An efficient 6- bit quantization scheme is utilized in the proposed algorithm with optimally combined normalization and down scaling factors to resolve the magnitude overestimation issue which occurs during iterative message passing process between the nodes. The simulation results demonstrate that the proposed algorithm achieves good decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without the requirement of complex arithmetic calculations. Compared to other min- sum based decoding algorithms the decoding process of the proposed MNMSA requires only fewer decoding iterations over wide range of signal- to- noise ratio (SNR) to achieve comparable decoding performance to that of Belief Propagation (BP) algorithm without increasing the hardware complexity.
In this paper, we present an improvement on the normalized min-sum (NMS) decoding algorithm for low density parity check codes. The modified NMS (M-NMS) algorithm introduces a more efficient adjustment for check node update computation. Taking the sub-minimum value among extrinsic information from the variable nodes into consideration, we make the correction factor varies with different iterations. Results show that, compared with standard min-sum (MS) and NMS decoding algorithms, the proposed method not only offers a better performance but also achieves a lower error floor in the high SNR region.
In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correction factors is simply based on estimating the mean square difference (MSD) between the transmitted codeword and the posteriori information of both bit and check node that produced at the MS decoder. Semi-practical tests using software-defined radio (SDR) and specific code simulations show that the proposed quasi-optimal algorithm provides a comparable error performance as Sum-Product (SP) decoding while requiring less complexity.
In this paper a modified Offset Min-Sum decoding algorithm for Low-Density Parity Check Codes is presented. In this modified algorithm, the offset factor in the original Offset Min-Sum algorithm is adjusted iteratively with the assistance of the check-node computation outputs of the Normalized Min-Sum algorithm. As a result, the offset factor in our modified algorithm can be calculated adaptively and more efficiently according to the previous decoding procedure, which can minimize the decoding degradation compared with the Belief Propagation decoding algorithm. The simulation results show that, compared with the original Offset Min-Sum decoding algorithm, our modified algorithm can achieve noticeable performance improvement with minor extra hardware complexity. For example, when BER is 10−5, our algorithm can achieve 0.1dB and 0.2dB decoding gain over Offset Min-Sum algorithm for regular and irregular LDPC codes respectively.