Eliminating Trapping Sets in Low-Density Parity Check Codes by using Tanner Graph Covers

TL;DR

This paper introduces a universal method using Tanner graph covers to eliminate trapping sets in LDPC codes, significantly improving error floor performance across various channels and decoding algorithms without altering code regularity or rate.

Contribution

The paper presents a novel Tanner graph cover technique that removes trapping sets in LDPC codes, enhancing high SNR performance universally across different codes and channels.

Findings

Improved error floor performance on BSC and AWGN channels.

Method applicable to any LDPC code and decoding algorithm.

No change in code regularity or rate under certain conditions.

Abstract

We discuss error floor asympotics and present a method for improving the performance of low-density parity check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets from the original code. The advantages of the method are that it is universal, as it can be applied to any LDPC code/channel/decoding algorithm and it improves performance at the expense of increasing the code length, without losing the code regularity, without changing the decoding algorithm, and, under certain conditions, without lowering the code rate. The proposed method can be modified to construct convolutional LDPC codes also. The method is illustrated by modifying Tanner, MacKay and Margulis codes to improve performance on the binary symmetric channel (BSC) under the Gallager B decoding algorithm. Decoding results on AWGN channel are also presented to illustrate that optimizing codes for one channel/decoding algorithm can lead to performance improvement on other channels.