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Lecture notes in computer science

On the Theory of Low-Density Convolutional Codes

Karin Engdahl, Michael Lentmaier, Kamil Sh. Zigangirov

Published Jan 1, 1999• 35 citations
Publisher
DOI
10.1007/3-540-46796-3_8

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IEEE International Symposium on Circuits and Systems proceedings•Sep 22, 2006•20 citations
Irregular low-density parity-check (LDPC) codes constructed from small protographs are one of the most powerful LDPC block codes. In this paper, we introduce the convolutional version of these codes. LDPC convolutional codes constructed from protographs have some advantages in comparison to LDPC block codes constructed from protographs, e.g., an effective pipeline decoding. We show that LDPC convolutional codes constructed from protographs have much lower error rates than analogous LDPC block codes with the same complexity and that they operate with low error rates near the Shannon limits even for a relatively small memory size
Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, we use a protograph-based analysis of terminated LDPCC codes to obtain an upper bound on the free distance growth rate of ensembles of periodically time-varying LDPCC codes. This bound is compared to a lower bound and evaluated numerically. It is found that, for a sufficiently large period, the bounds coincide. This approach is then extended to obtain bounds on the trapping set numbers, which define the size of the smallest, non-empty trapping sets, for these asymptotically good, periodically time-varying LDPCC code ensembles.
Low-density parity-check convolutional codes offer the same good error-correcting performance as low-density parity-check block codes while having the ability to encode and decode arbitrary lengths of data. This makes these codes well suited to certain applications, such as forward error control on packet switching networks. In this paper we propose a decoder architecture for low-density parity-check convolutional codes with very large memories. These codes have very good error correcting properties and as such may be applicable in wireless sensor networks and space communication systems. We discuss a realization of this architecture for a (2048,3,6) code implemented on a field-programmable gate-array.