434 research outputs found
A Unified Framework for Linear-Programming Based Communication Receivers
It is shown that a large class of communication systems which admit a
sum-product algorithm (SPA) based receiver also admit a corresponding
linear-programming (LP) based receiver. The two receivers have a relationship
defined by the local structure of the underlying graphical model, and are
inhibited by the same phenomenon, which we call 'pseudoconfigurations'. This
concept is a generalization of the concept of 'pseudocodewords' for linear
codes. It is proved that the LP receiver has the 'maximum likelihood
certificate' property, and that the receiver output is the lowest cost
pseudoconfiguration. Equivalence of graph-cover pseudoconfigurations and
linear-programming pseudoconfigurations is also proved. A concept of 'system
pseudodistance' is defined which generalizes the existing concept of
pseudodistance for binary and nonbinary linear codes. It is demonstrated how
the LP design technique may be applied to the problem of joint equalization and
decoding of coded transmissions over a frequency selective channel, and a
simulation-based analysis of the error events of the resulting LP receiver is
also provided. For this particular application, the proposed LP receiver is
shown to be competitive with other receivers, and to be capable of
outperforming turbo equalization in bit and frame error rate performance.Comment: 13 pages, 6 figures. To appear in the IEEE Transactions on
Communication
Proving Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel
We analyze nonbinary spatially-coupled low-density parity-check (SC-LDPC)
codes built on the general linear group for transmission over the binary
erasure channel. We prove threshold saturation of the belief propagation
decoding to the potential threshold, by generalizing the proof technique based
on potential functions recently introduced by Yedla et al.. The existence of
the potential function is also discussed for a vector sparse system in the
general case, and some existence conditions are developed. We finally give
density evolution and simulation results for several nonbinary SC-LDPC code
ensembles.Comment: in Proc. 2014 XXXIth URSI General Assembly and Scientific Symposium,
URSI GASS, Beijing, China, August 16-23, 2014. Invited pape
Design and Analysis of Nonbinary LDPC Codes for Arbitrary Discrete-Memoryless Channels
We present an analysis, under iterative decoding, of coset LDPC codes over
GF(q), designed for use over arbitrary discrete-memoryless channels
(particularly nonbinary and asymmetric channels). We use a random-coset
analysis to produce an effect that is similar to output-symmetry with binary
channels. We show that the random selection of the nonzero elements of the
GF(q) parity-check matrix induces a permutation-invariance property on the
densities of the decoder messages, which simplifies their analysis and
approximation. We generalize several properties, including symmetry and
stability from the analysis of binary LDPC codes. We show that under a Gaussian
approximation, the entire q-1 dimensional distribution of the vector messages
is described by a single scalar parameter (like the distributions of binary
LDPC messages). We apply this property to develop EXIT charts for our codes. We
use appropriately designed signal constellations to obtain substantial shaping
gains. Simulation results indicate that our codes outperform multilevel codes
at short block lengths. We also present simulation results for the AWGN
channel, including results within 0.56 dB of the unconstrained Shannon limit
(i.e. not restricted to any signal constellation) at a spectral efficiency of 6
bits/s/Hz.Comment: To appear, IEEE Transactions on Information Theory, (submitted
October 2004, revised and accepted for publication, November 2005). The
material in this paper was presented in part at the 41st Allerton Conference
on Communications, Control and Computing, October 2003 and at the 2005 IEEE
International Symposium on Information Theor
Nonbinary Spatially-Coupled LDPC Codes on the Binary Erasure Channel
We analyze the asymptotic performance of nonbinary spatially-coupled
low-density parity-check (SC-LDPC) codes built on the general linear group,
when the transmission takes place over the binary erasure channel. We propose
an efficient method to derive an upper bound to the maximum a posteriori
probability (MAP) threshold for nonbinary LDPC codes, and observe that the MAP
performance of regular LDPC codes improves with the alphabet size. We then
consider nonbinary SC-LDPC codes. We show that the same threshold saturation
effect experienced by binary SC-LDPC codes occurs for the nonbinary codes,
hence we conjecture that the BP threshold for large termination length
approaches the MAP threshold of the underlying regular ensemble.Comment: Submitted to IEEE International Conference on Communications 201
Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes
In this work, we consider pseudocodewords of (relaxed) linear programming
(LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP
decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo
codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is
proper and -symmetric, and make a connection to finite graph covers of the
3D-TC factor graph. This connection is used to show that the support set of any
pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum
a posteriori constituent decoders on the binary erasure channel. Furthermore,
we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a
finite-length minimum pseudoweight analysis for small cover degrees. Also, an
explicit description of the fundamental cone of the 3D-TC polytope is given.
Finally, we present an extensive numerical study of small-to-medium block
length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the
minimum distance and/or the stopping distance is
high, the minimum pseudoweight (on the additive white Gaussian noise channel)
is strictly smaller than both the and the , and 2)
the minimum pseudoweight grows with the block length, at least for
small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication
An Iterative Joint Linear-Programming Decoding of LDPC Codes and Finite-State Channels
In this paper, we introduce an efficient iterative solver for the joint
linear-programming (LP) decoding of low-density parity-check (LDPC) codes and
finite-state channels (FSCs). In particular, we extend the approach of
iterative approximate LP decoding, proposed by Vontobel and Koetter and
explored by Burshtein, to this problem. By taking advantage of the dual-domain
structure of the joint decoding LP, we obtain a convergent iterative algorithm
for joint LP decoding whose structure is similar to BCJR-based turbo
equalization (TE). The result is a joint iterative decoder whose complexity is
similar to TE but whose performance is similar to joint LP decoding. The main
advantage of this decoder is that it appears to provide the predictability of
joint LP decoding and superior performance with the computational complexity of
TE.Comment: To appear in Proc. IEEE ICC 2011, Kyoto, Japan, June 5-9, 201
Spatially Coupled Turbo Codes: Principles and Finite Length Performance
In this paper, we give an overview of spatially coupled turbo codes (SC-TCs),
the spatial coupling of parallel and serially concatenated convolutional codes,
recently introduced by the authors. For presentation purposes, we focus on
spatially coupled serially concatenated codes (SC-SCCs). We review the main
principles of SC-TCs and discuss their exact density evolution (DE) analysis on
the binary erasure channel. We also consider the construction of a family of
rate-compatible SC-SCCs with simple 4-state component encoders. For all
considered code rates, threshold saturation of the belief propagation (BP) to
the maximum a posteriori threshold of the uncoupled ensemble is demonstrated,
and it is shown that the BP threshold approaches the Shannon limit as the
coupling memory increases. Finally we give some simulation results for finite
lengths.Comment: Invited paper, IEEE Int. Symp. Wireless Communications Systems
(ISWCS), Aug. 201
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