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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Self-Adaptive Scaled Min-Sum Algorithm for LDPC Decoders Based on Delta-Min

Keol Cho, Ki‐Seok Chung

Published Jan 1, 2016• 0 citations
Publisher

Abstract

A self-adaptive scaled min-sum algorithm for LDPC decoding based on the difference between the first two minima of the check node messages (Δmin) is proposed. Δmin is utilized for adjusting the scaling factor of the check node messages, and simulation results show that the proposed algorithm improves the error correcting performance compared to existing algorithms.

DOI
10.1587/transfun.e99.a.1632

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A self-adaptive scaled min-sum algorithm for LDPC decoding based on the difference between the first two minima of the check node messages (Δmin) is proposed. Δmin is utilized for adjusting the scaling factor of the check node messages, and simulation results show that the proposed algorithm improves the error correcting performance compared to existing algorithms.
This paper proposes a new min-sum algorithm for low-density parity-check decoding. In this paper, we first define the negative and positive effects of the received signal-to-noise ratio (SNR) in the min-sum decoding algorithm. To improve the performance of error correction by considering the negative and positive effects of the received SNR, the proposed algorithm applies adaptive scaling factors not only to extrinsic information but also to a received log-likelihood ratio. We also propose a combined variable and check node architecture to realize the proposed algorithm with low complexity. The simulation results show that the proposed algorithm achieves up to 0.4 dB coding gain with low complexity compared to existing min-sum-based algorithms.
Low-Density Parity-Check (LDPC) code is a linear block code approaching the Shannon limit. The improvement of the decoding performance of LDPC codes is a hot research direction today. To improve the decoding performance of the self-correcting min-sum (SCMS) algorithm, an improved self-correcting min-sum (ISCMS) algorithm is proposed based on this algorithm. In the iterative decoding process of the ISCMS algorithm, the update rule of the check node (CN) is optimized to the update rule of the CN of the IOMS algorithm, which improves the accuracy of decoding from the processing of the CN. Simulation results show that the proposed ISCMS algorithm has better error performance and convergence performance than the SCMS algorithm with a small increase in computational complexity.
In order to reduce the performance loss of SMMS( Single-Minimum,Min-Sum) algorithm for decoding LDPC( LowDensity Parity-Check) codes,the ACMS( adaptive configurable Min-Sum) algorithm is proposed in this paper. Only the absolute minimum is used in this algorithm to update the check-node message and the second minimum is determined by a configurable estimation weight factor based on the iteration and a correction factor based on the number of error bits in each hard decision. Compared to the original SMMS and VWMS algorithm,the simulation result shows the proposed ACMS algorithm reduce the performance loss in general by introducing only a little additional complexity.
The min-sum (MS) and approximate-min* (a-min*) algorithms are alternatives of the belief propagation (BP) algorithm for decoding low-density parity-check (LDPC) codes. To lower the BP decoding complexity, both algorithms compute two magnitudes at each check node (CN) and pass them to the neighboring variable nodes (VNs).In this work we propose a new algorithm, ga-min*, that generalizes the MS and a-min* in terms of number of incoming messages to a CN.We analyze and demonstrate a condition to improve the performance when applying self-correction to the ga-min*. Simulations on 5G LDPC codes show that the proposed decoding algorithm yields comparable performance to the a-min* with a significant reduction in complexity, and it is robust against LLR mismatch.
Among various decoding algorithms of low-density parity-check (LDPC) codes, the minsum (MS) algorithm and its modified algorithms are widely adopted because of their computational simplicity compared to the sum-product (SP) algorithm with slight loss of decoding performance.In the MS algorithm, the magnitude of the output message from a check node (CN) processing unit is decided by either the smallest or the next smallest input message which are denoted as min1 and min2, respectively.It has been shown that multiplying a scaling factor to the output of CN message will improve the decoding performance.Further, Zhong et al. have shown that multiplying different scaling factors (called a 2-dimensional scaling) to min1 and min2 much increases the performance of the LDPC decoder.In this paper, the simplified 2-dimensional scaled (S2DS) MS algorithm is proposed.In the proposed algorithm, we figure out a pair of the most efficient scaling factors which multiplications can be replaced with combinations of addition and shift operations.Furthermore, one scaling operation is approximated by the difference between min1 and min2.The simulation results show that S2DS achieves the error correcting performance which is close to or outperforms the SP algorithm regardless of coding rates, and its computational complexity is the lowest comparing to modified versions of MS algorithms.
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.