Generalized simplified variable-scaled min sum LDPC decoder for irregular LDPC codes

Abstract

Abstract-In this paper, we propose a novel low complexity scaling strategy of min-sum decoding algorithm for irregular LDPC codes. In the proposed method, we generalize our previously proposed simplified Variable Scaled Min-Sum (SVS-minsum) by replacing the sub-optimal starting value and heuristic update for the scaling factor sequence by optimized values. Density evolution and Nelder-Mead optimization are used offline, prior to the decoding, to obtain the optimal starting point and per iteration updating step size for the scaling factor sequence of the proposed scaling strategy. The optimization of these parameters proves to be of noticeable positive impact on the decoding performance. We used different DVB-T2 LDPC codes in our simulation. Simulation results show the superior performance (in both WER and latency) of the proposed algorithm to other Min-Sum based algorithms. In addition to that, generalized SVSmin-sum algorithm has very close performance to LLR-SPA with much lower complexity.

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].…”

“…[16] and [17] adaptively adjust α according to the iteration count of the decoding process, and the adjustment is based on the fact that the reliability of the LLRs is improved as the iteration count goes up. Generalized simplified variable-scaled MS (GSVS) algorithm [17] divides the iteration count into four steps and the initial scaling factor α 0 is increased as follows: α 0 , 0.5 + 0.5·α 0 , 0.75 + 0.25·α 0 , and 0.875 + 0.125·α 0 .…”

“…Generalized simplified variable-scaled MS (GSVS) algorithm [17] divides the iteration count into four steps and the initial scaling factor α 0 is increased as follows: α 0 , 0.5 + 0.5·α 0 , 0.75 + 0.25·α 0 , and 0.875 + 0.125·α 0 .…”

“…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.…”