Decoding of Non-Binary LDPC Codes Using the Information Bottleneck Method

TL;DR

This paper extends a mutual-information based lookup table decoding approach from binary to non-binary LDPC codes, using the information bottleneck method to design efficient decoding tables that outperform traditional algorithms.

Contribution

It introduces a novel lookup table decoding scheme for non-binary LDPC codes using the information bottleneck method, addressing higher-order Galois field arithmetic.

Findings

Outperforms log-max decoding algorithm

Operates close to sum-product decoding

Uses small bit-width messages

Abstract

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension, but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.