159 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
Polytope of Correct (Linear Programming) Decoding and Low-Weight Pseudo-Codewords
We analyze Linear Programming (LP) decoding of graphical binary codes
operating over soft-output, symmetric and log-concave channels. We show that
the error-surface, separating domain of the correct decoding from domain of the
erroneous decoding, is a polytope. We formulate the problem of finding the
lowest-weight pseudo-codeword as a non-convex optimization (maximization of a
convex function) over a polytope, with the cost function defined by the channel
and the polytope defined by the structure of the code. This formulation
suggests new provably convergent heuristics for finding the lowest weight
pseudo-codewords improving in quality upon previously discussed. The algorithm
performance is tested on the example of the Tanner [155, 64, 20] code over the
Additive White Gaussian Noise (AWGN) channel.Comment: 6 pages, 2 figures, accepted for IEEE ISIT 201
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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