Relaxed Half-Stochastic Belief Propagation

TL;DR

The paper introduces the Relaxed Half-Stochastic (RHS) decoding algorithm for low-density parity-check codes, achieving high coding gain with binary messages suitable for efficient fully-parallel circuit implementations.

Contribution

It presents a new binary message belief propagation algorithm derived from the Sum-Product algorithm, optimized for low complexity and circuit implementation.

Findings

RHS achieves comparable coding gain to real-valued message BP algorithms.

Simulation results demonstrate RHS's effectiveness on standardized codes.

RHS outperforms existing algorithms in fully-parallel decoding scenarios.

Abstract

Low-density parity-check codes are attractive for high throughput applications because of their low decoding complexity per bit, but also because all the codeword bits can be decoded in parallel. However, achieving this in a circuit implementation is complicated by the number of wires required to exchange messages between processing nodes. Decoding algorithms that exchange binary messages are interesting for fully-parallel implementations because they can reduce the number and the length of the wires, and increase logic density. This paper introduces the Relaxed Half-Stochastic (RHS) decoding algorithm, a binary message belief propagation (BP) algorithm that achieves a coding gain comparable to the best known BP algorithms that use real-valued messages. We derive the RHS algorithm by starting from the well-known Sum-Product algorithm, and then derive a low-complexity version suitable for circuit implementation. We present extensive simulation results on two standardized codes having different rates and constructions, including low bit error rate results. These simulations show that RHS can be an advantageous replacement for the existing state-of-the-art decoding algorithms when targeting fully-parallel implementations.