Sets of complementary LLRs to improve OSD post-processing of BP decoding

This article deals with Ordered Statistics Decoding (OSD) applied to the soft outputs of the Belief Propagation (BP) algorithm. We first model the weighted sum of the a posteriori LLRs across BP decoding iterations into a neuron. The neuron is then trained with the focal loss to compute for each BP decoding failure a set of accumulated Log Likelihood Ratios (LLRs) suited for OSD post-processing. Then, we propose a recursive selection procedure of LLRs sets, for multiple OSD post-processing. This selection is carried out from the sets of a posteriori LLRs calculated at each BP iteration, and from the accumulated LLRs optimized for the OSD, based on their joint probabilities of failure with OSD post-processing. An OSD is then applied to each set of LLRs belonging to the selection. In addition, we propose to reduce the OSD post-processing decoding complexity without significantly degrading its performance. Our results show that this new decoding method provides an effective way to bridge the gap to maximum likelihood decoding for short and long Low Density Parity Check (LDPC) codes.

I. Introduction

The emergence of communication systems for the Internet of Things (IoT), with the requirement of short-packet transmissions, has revitalized interest in research and practice of efficient error correcting codes for messages ranging from a few tens up to a few hundred bits. While important progress has been made over the last years in understanding the limits of coding at short block lengths [1], the design of efficient short codes and decoding algorithms still raises many challenges [2].