33 research outputs found
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
Strong Secrecy for Erasure Wiretap Channels
We show that duals of certain low-density parity-check (LDPC) codes, when
used in a standard coset coding scheme, provide strong secrecy over the binary
erasure wiretap channel (BEWC). This result hinges on a stopping set analysis
of ensembles of LDPC codes with block length and girth , for some
. We show that if the minimum left degree of the ensemble is
, the expected probability of block error is
\calO(\frac{1}{n^{\lceil l_\mathrm{min} k /2 \rceil - k}}) when the erasure
probability , where
depends on the degree distribution of the ensemble. As long as and , the dual of this LDPC code provides strong secrecy over a
BEWC of erasure probability greater than .Comment: Submitted to the Information Theory Workship (ITW) 2010, Dubli
Distance Properties of Short LDPC Codes and their Impact on the BP, ML and Near-ML Decoding Performance
Parameters of LDPC codes, such as minimum distance, stopping distance,
stopping redundancy, girth of the Tanner graph, and their influence on the
frame error rate performance of the BP, ML and near-ML decoding over a BEC and
an AWGN channel are studied. Both random and structured LDPC codes are
considered. In particular, the BP decoding is applied to the code parity-check
matrices with an increasing number of redundant rows, and the convergence of
the performance to that of the ML decoding is analyzed. A comparison of the
simulated BP, ML, and near-ML performance with the improved theoretical bounds
on the error probability based on the exact weight spectrum coefficients and
the exact stopping size spectrum coefficients is presented. It is observed that
decoding performance very close to the ML decoding performance can be achieved
with a relatively small number of redundant rows for some codes, for both the
BEC and the AWGN channels
Instanton-based Techniques for Analysis and Reduction of Error Floors of LDPC Codes
We describe a family of instanton-based optimization methods developed
recently for the analysis of the error floors of low-density parity-check
(LDPC) codes. Instantons are the most probable configurations of the channel
noise which result in decoding failures. We show that the general idea and the
respective optimization technique are applicable broadly to a variety of
channels, discrete or continuous, and variety of sub-optimal decoders.
Specifically, we consider: iterative belief propagation (BP) decoders, Gallager
type decoders, and linear programming (LP) decoders performing over the
additive white Gaussian noise channel (AWGNC) and the binary symmetric channel
(BSC).
The instanton analysis suggests that the underlying topological structures of
the most probable instanton of the same code but different channels and
decoders are related to each other. Armed with this understanding of the
graphical structure of the instanton and its relation to the decoding failures,
we suggest a method to construct codes whose Tanner graphs are free of these
structures, and thus have less significant error floors.Comment: To appear in IEEE JSAC On Capacity Approaching Codes. 11 Pages and 6
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