1,152 research outputs found
Non-Binary LDPC Codes with Large Alphabet Size
We study LDPC codes for the channel with input and
output . The aim of this paper is to evaluate
decoding performance of -ary non-binary LDPC codes for large . We give
density evolution and decoding performance evaluation for regular non-binary
LDPC codes and spatially-coupled (SC) codes. We show the regular codes do not
achieve the capacity of the channel while SC codes do
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
How to Achieve the Capacity of Asymmetric Channels
We survey coding techniques that enable reliable transmission at rates that
approach the capacity of an arbitrary discrete memoryless channel. In
particular, we take the point of view of modern coding theory and discuss how
recent advances in coding for symmetric channels help provide more efficient
solutions for the asymmetric case. We consider, in more detail, three basic
coding paradigms.
The first one is Gallager's scheme that consists of concatenating a linear
code with a non-linear mapping so that the input distribution can be
appropriately shaped. We explicitly show that both polar codes and spatially
coupled codes can be employed in this scenario. Furthermore, we derive a
scaling law between the gap to capacity, the cardinality of the input and
output alphabets, and the required size of the mapper.
The second one is an integrated scheme in which the code is used both for
source coding, in order to create codewords distributed according to the
capacity-achieving input distribution, and for channel coding, in order to
provide error protection. Such a technique has been recently introduced by
Honda and Yamamoto in the context of polar codes, and we show how to apply it
also to the design of sparse graph codes.
The third paradigm is based on an idea of B\"ocherer and Mathar, and
separates the two tasks of source coding and channel coding by a chaining
construction that binds together several codewords. We present conditions for
the source code and the channel code, and we describe how to combine any source
code with any channel code that fulfill those conditions, in order to provide
capacity-achieving schemes for asymmetric channels. In particular, we show that
polar codes, spatially coupled codes, and homophonic codes are suitable as
basic building blocks of the proposed coding strategy.Comment: 32 pages, 4 figures, presented in part at Allerton'14 and published
in IEEE Trans. Inform. Theor
Decoding of Non-Binary LDPC Codes Using the Information Bottleneck Method
Recently, a novel lookup table based decoding method for binary low-density
parity-check codes has attracted considerable attention. In this approach,
mutual-information maximizing lookup tables replace the conventional operations
of the variable nodes and the check nodes in message passing decoding.
Moreover, the exchanged messages are represented by integers with very small
bit width. A machine learning framework termed the information bottleneck
method is used to design the corresponding lookup tables. In this paper, we
extend this decoding principle from binary to non-binary codes. This is not a
straightforward extension, but requires a more sophisticated lookup table
design to cope with the arithmetic in higher order Galois fields. Provided bit
error rate simulations show that our proposed scheme outperforms the log-max
decoding algorithm and operates close to sum-product decoding.Comment: This paper has been presented at IEEE International Conference on
Communications (ICC'19) in Shangha
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
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