352 research outputs found
Efficient LDPC Codes over GF(q) for Lossy Data Compression
In this paper we consider the lossy compression of a binary symmetric source.
We present a scheme that provides a low complexity lossy compressor with near
optimal empirical performance. The proposed scheme is based on b-reduced
ultra-sparse LDPC codes over GF(q). Encoding is performed by the Reinforced
Belief Propagation algorithm, a variant of Belief Propagation. The
computational complexity at the encoder is O(.n.q.log q), where is the
average degree of the check nodes. For our code ensemble, decoding can be
performed iteratively following the inverse steps of the leaf removal
algorithm. For a sparse parity-check matrix the number of needed operations is
O(n).Comment: 5 pages, 3 figure
Tree-Structure Expectation Propagation for LDPC Decoding over the BEC
We present the tree-structure expectation propagation (Tree-EP) algorithm to
decode low-density parity-check (LDPC) codes over discrete memoryless channels
(DMCs). EP generalizes belief propagation (BP) in two ways. First, it can be
used with any exponential family distribution over the cliques in the graph.
Second, it can impose additional constraints on the marginal distributions. We
use this second property to impose pair-wise marginal constraints over pairs of
variables connected to a check node of the LDPC code's Tanner graph. Thanks to
these additional constraints, the Tree-EP marginal estimates for each variable
in the graph are more accurate than those provided by BP. We also reformulate
the Tree-EP algorithm for the binary erasure channel (BEC) as a peeling-type
algorithm (TEP) and we show that the algorithm has the same computational
complexity as BP and it decodes a higher fraction of errors. We describe the
TEP decoding process by a set of differential equations that represents the
expected residual graph evolution as a function of the code parameters. The
solution of these equations is used to predict the TEP decoder performance in
both the asymptotic regime and the finite-length regime over the BEC. While the
asymptotic threshold of the TEP decoder is the same as the BP decoder for
regular and optimized codes, we propose a scaling law (SL) for finite-length
LDPC codes, which accurately approximates the TEP improved performance and
facilitates its optimization
Tree-structure Expectation Propagation for Decoding LDPC codes over Binary Erasure Channels
Expectation Propagation is a generalization to Belief Propagation (BP) in two
ways. First, it can be used with any exponential family distribution over the
cliques in the graph. Second, it can impose additional constraints on the
marginal distributions. We use this second property to impose pair-wise
marginal distribution constraints in some check nodes of the LDPC Tanner graph.
These additional constraints allow decoding the received codeword when the BP
decoder gets stuck. In this paper, we first present the new decoding algorithm,
whose complexity is identical to the BP decoder, and we then prove that it is
able to decode codewords with a larger fraction of erasures, as the block size
tends to infinity. The proposed algorithm can be also understood as a
simplification of the Maxwell decoder, but without its computational
complexity. We also illustrate that the new algorithm outperforms the BP
decoder for finite block-siz
Coding with Scrambling, Concatenation, and HARQ for the AWGN Wire-Tap Channel: A Security Gap Analysis
This study examines the use of nonsystematic channel codes to obtain secure
transmissions over the additive white Gaussian noise (AWGN) wire-tap channel.
Unlike the previous approaches, we propose to implement nonsystematic coded
transmission by scrambling the information bits, and characterize the bit error
rate of scrambled transmissions through theoretical arguments and numerical
simulations. We have focused on some examples of Bose-Chaudhuri-Hocquenghem
(BCH) and low-density parity-check (LDPC) codes to estimate the security gap,
which we have used as a measure of physical layer security, in addition to the
bit error rate. Based on a number of numerical examples, we found that such a
transmission technique can outperform alternative solutions. In fact, when an
eavesdropper (Eve) has a worse channel than the authorized user (Bob), the
security gap required to reach a given level of security is very small. The
amount of degradation of Eve's channel with respect to Bob's that is needed to
achieve sufficient security can be further reduced by implementing scrambling
and descrambling operations on blocks of frames, rather than on single frames.
While Eve's channel has a quality equal to or better than that of Bob's
channel, we have shown that the use of a hybrid automatic repeat-request (HARQ)
protocol with authentication still allows achieving a sufficient level of
security. Finally, the secrecy performance of some practical schemes has also
been measured in terms of the equivocation rate about the message at the
eavesdropper and compared with that of ideal codes.Comment: 29 pages, 10 figure
A Refined Scaling Law for Spatially Coupled LDPC Codes Over the Binary Erasure Channel
We propose a refined scaling law to predict the finite-length performance in
the waterfall region of spatially coupled low-density parity-check codes over
the binary erasure channel. In particular, we introduce some improvements to
the scaling law proposed by Olmos and Urbanke that result in a better agreement
between the predicted and simulated frame error rate. We also show how the
scaling law can be extended to predict the bit error rate performance.Comment: Paper accepted to IEEE Information Theory Workshop (ITW) 201
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