AWGN Channel Analysis of Terminated LDPC Convolutional Codes

TL;DR

This paper demonstrates that terminated LDPC convolutional codes achieve near-capacity performance on the AWGN channel, with linearly growing minimum distance and trapping sets, extending previous results from the BEC.

Contribution

It extends the analysis of LDPC convolutional codes from the BEC to the AWGN channel, showing capacity-approaching thresholds and linear growth of trapping sets.

Findings

Threshold improvement extends to AWGN channel

Minimum distance grows linearly with block length

Smallest trapping set size grows linearly with block length

Abstract

It has previously been shown that ensembles of terminated protograph-based low-density parity-check (LDPC) convolutional codes have a typical minimum distance that grows linearly with block length and that they are capable of achieving capacity approaching iterative decoding thresholds on the binary erasure channel (BEC). In this paper, we review a recent result that the dramatic threshold improvement obtained by terminating LDPC convolutional codes extends to the additive white Gaussian noise (AWGN) channel. Also, using a (3,6)-regular protograph-based LDPC convolutional code ensemble as an example, we perform an asymptotic trapping set analysis of terminated LDPC convolutional code ensembles. In addition to capacity approaching iterative decoding thresholds and linearly growing minimum distance, we find that the smallest non-empty trapping set of a terminated ensemble grows linearly with block length.