415 research outputs found
The Effect of Saturation on Belief Propagation Decoding of LDPC Codes
We consider the effect of LLR saturation on belief propagation decoding of
low-density parity-check codes. Saturation occurs universally in practice and
is known to have a significant effect on error floor performance. Our focus is
on threshold analysis and stability of density evolution.
We analyze the decoder for certain low-density parity-check code ensembles
and show that belief propagation decoding generally degrades gracefully with
saturation. Stability of density evolution is, on the other hand, rather
strongly affected by saturation and the asymptotic qualitative effect of
saturation is similar to reduction of variable node degree by one.Comment: Submitted to ISIT. Longer version to be submitted to IT Transactions
in preparatio
Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes
We investigate the use of Gallager's low-density parity-check (LDPC) codes in
a broadcast channel, one of the fundamental models in network information
theory. Combining linear codes is a standard technique in practical network
communication schemes and is known to provide better performance than simple
timesharing methods when algebraic codes are used. The statistical physics
based analysis shows that the practical performance of the suggested method,
achieved by employing the belief propagation algorithm, is superior to that of
LDPC based timesharing codes while the best performance, when received
transmissions are optimally decoded, is bounded by the timesharing limit.Comment: 14 pages, 4 figure
Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes
We investigate the use of Gallager's low-density parity-check (LDPC) codes in
a broadcast channel, one of the fundamental models in network information
theory. Combining linear codes is a standard technique in practical network
communication schemes and is known to provide better performance than simple
timesharing methods when algebraic codes are used. The statistical physics
based analysis shows that the practical performance of the suggested method,
achieved by employing the belief propagation algorithm, is superior to that of
LDPC based timesharing codes while the best performance, when received
transmissions are optimally decoded, is bounded by the timesharing limit.Comment: 14 pages, 4 figure
Lossy Source Coding via Spatially Coupled LDGM Ensembles
We study a new encoding scheme for lossy source compression based on
spatially coupled low-density generator-matrix codes. We develop a
belief-propagation guided-decimation algorithm, and show that this algorithm
allows to approach the optimal distortion of spatially coupled ensembles.
Moreover, using the survey propagation formalism, we also observe that the
optimal distortions of the spatially coupled and individual code ensembles are
the same. Since regular low-density generator-matrix codes are known to achieve
the Shannon rate-distortion bound under optimal encoding as the degrees grow,
our results suggest that spatial coupling can be used to reach the
rate-distortion bound, under a {\it low complexity} belief-propagation
guided-decimation algorithm.
This problem is analogous to the MAX-XORSAT problem in computer science.Comment: Submitted to ISIT 201
Statistical Physics of Irregular Low-Density Parity-Check Codes
Low-density parity-check codes with irregular constructions have been
recently shown to outperform the most advanced error-correcting codes to date.
In this paper we apply methods of statistical physics to study the typical
properties of simple irregular codes.
We use the replica method to find a phase transition which coincides with
Shannon's coding bound when appropriate parameters are chosen.
The decoding by belief propagation is also studied using statistical physics
arguments; the theoretical solutions obtained are in good agreement with
simulations. We compare the performance of irregular with that of regular codes
and discuss the factors that contribute to the improvement in performance.Comment: 20 pages, 9 figures, revised version submitted to JP
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