Asymptotically Good LDPC Convolutional Codes Based on Protographs
David G. M. Mitchell, Ali E. Pusane, Kamil Sh. Zigangirov, and Daniel, J. Costello, Jr
TL;DR
This paper demonstrates that protograph-based LDPC convolutional codes can asymptotically achieve high free distance relative to their constraint length, matching capacity-approaching performance with improved distance properties.
Contribution
It introduces asymptotic methods to bound the free distance of protograph-based LDPC convolutional codes and shows their superior distance ratios compared to LDPC block codes.
Findings
Lower bounds on free distance for code ensembles
Free distance to constraint length ratio exceeds block code ratio
Codes achieve capacity-approaching performance
Abstract
LDPC convolutional codes have been shown to be capable of achieving the same capacity-approaching performance as LDPC block codes with iterative message-passing decoding. In this paper, asymptotic methods are used to calculate a lower bound on the free distance for several ensembles of asymptotically good protograph-based LDPC convolutional codes. Further, we show that the free distance to constraint length ratio of the LDPC convolutional codes exceeds the minimum distance to block length ratio of corresponding LDPC block codes.
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