A General Method for Finding Low Error Rates of LDPC Codes

TL;DR

This paper introduces a three-step method to accurately estimate very low bit error rates of LDPC codes across various decoders without exhaustive error event analysis or extensive simulations.

Contribution

A novel, efficient approach for evaluating low error rate performance of LDPC codes applicable to multiple decoding algorithms, bypassing exhaustive error event enumeration.

Findings

Enables estimation of extremely low BER without Monte Carlo simulations.

Applicable to different decoding algorithms including belief propagation and min-sum.

Provides a foundation for designing LDPC codes with guaranteed low error rates.

Abstract

This paper outlines a three-step procedure for determining the low bit error rate performance curve of a wide class of LDPC codes of moderate length. The traditional method to estimate code performance in the higher SNR region is to use a sum of the contributions of the most dominant error events to the probability of error. These dominant error events will be both code and decoder dependent, consisting of low-weight codewords as well as non-codeword events if ML decoding is not used. For even moderate length codes, it is not feasible to find all of these dominant error events with a brute force search. The proposed method provides a convenient way to evaluate very low bit error rate performance of an LDPC code without requiring knowledge of the complete error event weight spectrum or resorting to a Monte Carlo simulation. This new method can be applied to various types of decoding such as the full belief propagation version of the message passing algorithm or the commonly used min-sum approximation to belief propagation. The proposed method allows one to efficiently see error performance at bit error rates that were previously out of reach of Monte Carlo methods. This result will provide a solid foundation for the analysis and design of LDPC codes and decoders that are required to provide a guaranteed very low bit error rate performance at certain SNRs.