Simplified 2-Dimensional Scaled Min-Sum Algorithm for LDPC Decoder

Abstract

-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.

An FPGA Design with High Memory Efficiency and Decoding Performance for 5G LDPC Decoder

“…The HOMS is set with β = 0.5 and δ = 0.375 [19]. For comparison purposes, the performances of the NMS (1/α = 0.75) [14], OMS (β = 0.5) [14], IOMS ( γ = 0.875 and η = 0.5) [16], SMA-MSA ( α2 = 0.25 and γ = 0.75) [17], S2DS [18], and VOMS ( β = 0.5 and τ = 0.875) [19] algorithms are also evaluated.…”

“…In an effort to improve this performance loss, numerous approaches have been presented in the state-of-the-art, including some well-known algorithms such as the Offset Min-Sum (OMS) and the Normalized Min-Sum (NMS) [14,15]. Moreover, several enhancements have been further proposed in the literature, such as the Improved Offset Min-Sum (IOMS) algorithm [16], the Second Minimum Approximation Min-Sum algorithm (SMA-MSA) [17], the Simplified 2-Dimensional Scaled (S2DS) algorithm [18], the Hybrid Offset Min-Sum (HOMS), and the Variable Offset Min-Sum (VOMS) algorithms [19].…”

Certain investigations on recent advances in the design of decoding algorithms using low‐density parity‐check codes and its applications

“…Cho et al 61 proposed an improvement to the Oh and Parhi scheme 60 . This improved version involves upgrading of the scaling factor which is approximated by estimating the difference between the first minimum message and second minimum message magnitudes.…”

“…With the growing demand for bandwidth utilization increasing exponentially in the past few years, the need for secure data storage and processing poses a new conceptual research challenge for the scientists. During the past decade, many variations of NMSA and OMSA were put into existence by many researchers from diverse backgrounds 61,62,64,67,68,70 . These algorithms have proven their significance through their decoding stability, convergence speed and decoder design complexity.…”

Further Improvements in Decoding Performance for 5G LDPC Codes Based on Modified Check-Node Unit

“…This iterative process continuously proceeds until the correct codeword is successfully found or until the maximum number of iterations has been reached. Depending on the update rules that are used to compute check and variable-node messages, there are several message-passing decoding algorithms, such as Belief-Propagation (BP), Min-Sum (MS), and MS-based algorithms [27][28][29][30][31][32][33][34][35]. Although MS and MS-based algorithms have lower error correction capacity than BP, they are simpler and more suitable for hardware implementations.…”