109 research outputs found
Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes
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.Comment: To be presented at the 2011 IEEE International Symposium on
Information Theor
Trapping Set Enumerators for Repeat Multiple Accumulate Code Ensembles
The serial concatenation of a repetition code with two or more accumulators
has the advantage of a simple encoder structure. Furthermore, the resulting
ensemble is asymptotically good and exhibits minimum distance growing linearly
with block length. However, in practice these codes cannot be decoded by a
maximum likelihood decoder, and iterative decoding schemes must be employed.
For low-density parity-check codes, the notion of trapping sets has been
introduced to estimate the performance of these codes under iterative message
passing decoding. In this paper, we present a closed form finite length
ensemble trapping set enumerator for repeat multiple accumulate codes by
creating a trellis representation of trapping sets. We also obtain the
asymptotic expressions when the block length tends to infinity and evaluate
them numerically.Comment: 5 pages, to appear in proc. IEEE ISIT, June 200
On the Minimum Distance of Generalized Spatially Coupled LDPC Codes
Families of generalized spatially-coupled low-density parity-check (GSC-LDPC)
code ensembles can be formed by terminating protograph-based generalized LDPC
convolutional (GLDPCC) codes. It has previously been shown that ensembles of
GSC-LDPC codes constructed from a protograph have better iterative decoding
thresholds than their block code counterparts, and that, for large termination
lengths, their thresholds coincide with the maximum a-posteriori (MAP) decoding
threshold of the underlying generalized LDPC block code ensemble. Here we show
that, in addition to their excellent iterative decoding thresholds, ensembles
of GSC-LDPC codes are asymptotically good and have large minimum distance
growth rates.Comment: Submitted to the IEEE International Symposium on Information Theory
201
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