Degree-Matched Check Node Decoding for Regular and Irregular LDPCs

Abstract

Abstract-This paper 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 degreematched check node decoding approximations are presented which depend on the check node degree dc. 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.

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

“…Therefore, various researches have followed in order to figure out α for the best error correcting performance or for the most efficient hardware implementation [15][16][17][18]20].…”

“…Most of them have tried to multiply the check to variable node (CTV) messages by a scaling factor to compensate for overestimated belief messages in comparison to the SP algorithm, and thus, these approaches are commonly called normalized MS (NMS) algorithms [13,14]. In [15], the CTV messages are adjusted by an offset based on the number of VNs connected to the CNs, and the CTV messages are adaptively scaled based on the iteration count [16,17]. In [18], the first two smallest CTV messages are scaled by different scaling factors using density evolution to improve the decoding performance.…”

“…In [18], the first two smallest CTV messages are scaled by different scaling factors using density evolution to improve the decoding performance. Even though the existing algorithms enhance the performance of LDPC decoders, [15,16], and [18] did not take the hardware implementation cost into account, and [17] suffered from the increased average iteration count until the decoding process is completed.…”

Self-adjustable offset min-sum algorithm for ISDB-S2 LDPC decoder

“…Some recent progress claims that techniques to adjust the offset factor according to either the degree of the check node (DegreeMatched Min-sum (DMMS) algorithm [3]) or the smallest message sent from bit nodes (Adaptive Offset Min-sum (AOMS) algorithm [4]) can achieve better performance. However, DMMS requires significant computation power to determine the offset factor while AOMS needs Look Up Table (LUT) for implementation which increases the hardware cost.…”

“…Min-sum (MS) algorithm approximates BP algorithm with easy hardware implementation but greatly degrades the BER performance. Recently, two categories of schemes have been proposed to trade off between BER performance and hardware complexity: MS-based algorithms [2,3,4] and BP-based algorithms [5,6]. Generally, BPbased algorithms outperform MS-based ones in BER performance with larger hardware cost.…”