A Polygonal Line Min-Sum Decoding Scheme for Low Density Parity Check Codes

Abstract

Low-density parity-check (LDPC) codes are widely used as error correction codes in new generation digital TV standards, such as the second generation of terrestrial digital video broadcasting standard (DVB-T2), Advanced Television Systems Committee (ATSC) 3.0, etc. The nonlinear belief propagation (BP) algorithm has excellent decoding performance for LDPC codes, but is often simplified in hardware implementations by linear min-sum (MS) algorithm due to its high complexity. This simplification also leads to over-estimation problems, which can be corrected by adding factors in conventional algorithms (e.g., normalized min-sum (NMS), offset min-sum (OMS), and variable scaling normalized min-sum (VMS) algorithms). However, the correction factors of these modified MS algorithms cannot adapt to different channels and modulations, and the performance needs further improvement. In this paper, the concepts of over-estimation value (OEV) and over-estimation rate (OER) are introduced to describe the over-estimation problem of the MS algorithm. Then, under the guidance of OEV and OER, a polygonal line min-sum (PMS) algorithm with correction factors adapted to different channels and modulations is proposed according to LLR distribution. Following the properties of OEV and OER, PMS algorithm is further simplified into Simplified PMS (SPMS) algorithm. LDPC codes from ATSC 3.0 are adopted in this paper to evaluate SPMS algorithm in comparison with the conventional algorithms. Extensive simulation results show that the SPMS algorithm for ATSC 3.0 LDPC decoder has at most 1.61dB, 0.24dB and 0.36dB gain over NMS, OMS and VMS algorithms respectively when frame error rate (FER) is at 10⁻⁴ level over additive white Gaussian noise (AWGN) channel with QPSK modulation. More importantly, the simulation results show that the SPMS algorithm can achieve much better performance than these modified MS algorithms over AWGN and Rayleigh channel with higher-order modulations or under limited maximum iteration number.