A Universal Systematic Method to Generate Error Patterns on Memoryless Channels

TL;DR

This paper introduces a systematic method leveraging the channel's PDF to generate error patterns applicable across various memoryless channels, improving decoding performance.

Contribution

A novel, universal approach to generate error patterns based on channel PDF, enhancing existing decoding algorithms like GRAND, OSD, and POSD.

Findings

Method matches or outperforms existing error pattern sets on multiple channels.

Applicable to AWGN, Gaussian mixture, and Rayleigh fading channels.

Improves decoding efficiency without channel-specific error pattern design.

Abstract

The high computational cost of approaching the performance of Maximum-likelihood (ML) decoding has limited its practical use for decades. Because the complexity grows exponentially with the message length, researchers have spent years developing algorithms like Ordered Statistics Decoding (OSD), Partial Ordered Statistics Decoding (POSD) and Guessing Random Additive Noise decoding (GRAND) which try to approach ML performance. OSD, POSD and GRAND work by trying to guess the error patterns affecting the received signals. However, there does not exist a systematic method to extend the error pattern guesses to novel channels. This work introduces a systematic method that uses the Probability Density Function (PDF) of a memoryless channel to generate a set of error patterns that can be applied on any future received signal on this channel. Simulation results show that our proposed method applied on GRAND, OSD and POSD generally matches or outperforms current pre-generated error patterns on additive white Gaussian noise (AWGN) channel, mixture of Gaussian distribution channels, Rayleigh fading channel with perfect knowledge of Channel State Information (CSI) and Rayleigh fading channel with no perfect knowledge of Channel State Information (NCSI).