13 research outputs found
Optimized puncturing distributions for irregular non-binary LDPC codes
In this paper we design non-uniform bit-wise puncturing distributions for
irregular non-binary LDPC (NB-LDPC) codes. The puncturing distributions are
optimized by minimizing the decoding threshold of the punctured LDPC code, the
threshold being computed with a Monte-Carlo implementation of Density
Evolution. First, we show that Density Evolution computed with Monte-Carlo
simulations provides accurate (very close) and precise (small variance)
estimates of NB-LDPC code ensemble thresholds. Based on the proposed method, we
analyze several puncturing distributions for regular and semi-regular codes,
obtained either by clustering punctured bits, or spreading them over the
symbol-nodes of the Tanner graph. Finally, optimized puncturing distributions
for non-binary LDPC codes with small maximum degree are presented, which
exhibit a gap between 0.2 and 0.5 dB to the channel capacity, for punctured
rates varying from 0.5 to 0.9.Comment: 6 pages, ISITA1
Multiplicatively Repeated Non-Binary LDPC Codes
We propose non-binary LDPC codes concatenated with multiplicative repetition
codes. By multiplicatively repeating the (2,3)-regular non-binary LDPC mother
code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9,
1/12,... Surprisingly, such simple low-rate non-binary LDPC codes outperform
the best low-rate binary LDPC codes so far. Moreover, we propose the decoding
algorithm for the proposed codes, which can be decoded with almost the same
computational complexity as that of the mother code.Comment: To appear in IEEE Transactions on Information Theor
Pairwise Check Decoding for LDPC Coded Two-Way Relay Block Fading Channels
Partial decoding has the potential to achieve a larger capacity region than
full decoding in two-way relay (TWR) channels. Existing partial decoding
realizations are however designed for Gaussian channels and with a static
physical layer network coding (PLNC). In this paper, we propose a new solution
for joint network coding and channel decoding at the relay, called pairwise
check decoding (PCD), for low-density parity-check (LDPC) coded TWR system over
block fading channels. The main idea is to form a check relationship table
(check-relation-tab) for the superimposed LDPC coded packet pair in the
multiple access (MA) phase in conjunction with an adaptive PLNC mapping in the
broadcast (BC) phase. Using PCD, we then present a partial decoding method,
two-stage closest-neighbor clustering with PCD (TS-CNC-PCD), with the aim of
minimizing the worst pairwise error probability. Moreover, we propose the
minimum correlation optimization (MCO) for selecting the better
check-relation-tabs. Simulation results confirm that the proposed TS-CNC-PCD
offers a sizable gain over the conventional XOR with belief propagation (BP) in
fading channels.Comment: to appear in IEEE Trans. on Communications, 201
Analysis and Design of Finite Alphabet Iterative Decoders Robust to Faulty Hardware
This paper addresses the problem of designing LDPC decoders robust to
transient errors introduced by a faulty hardware. We assume that the faulty
hardware introduces errors during the message passing updates and we propose a
general framework for the definition of the message update faulty functions.
Within this framework, we define symmetry conditions for the faulty functions,
and derive two simple error models used in the analysis. With this analysis, we
propose a new interpretation of the functional Density Evolution threshold
previously introduced, and show its limitations in case of highly unreliable
hardware. However, we show that under restricted decoder noise conditions, the
functional threshold can be used to predict the convergence behavior of FAIDs
under faulty hardware. In particular, we reveal the existence of robust and
non-robust FAIDs and propose a framework for the design of robust decoders. We
finally illustrate robust and non-robust decoders behaviors of finite length
codes using Monte Carlo simulations.Comment: 30 pages, submitted to IEEE Transactions on Communication
Source Coding with Side Information at the Decoder and Uncertain Knowledge of the Correlation
International audienceThis paper considers the problem of lossless source coding with side information at the decoder, when the correlation model between the source and the side information is uncertain. Four parametrized models representing the correlation between the source and the side information are introduced. The uncertainty on the correlation appears through the lack of knowledge on the value of the parameters. For each model, we propose a practical coding scheme based on non-binary Low Density Parity Check Codes and able to deal with the parameter uncertainty. At the encoder, the choice of the coding rate results from an information theoretical analysis. Then we propose decoding algorithms that jointly estimate the source vector and the parameters. As the proposed decoder is based on the Expectation-Maximization algorithm, which is very sensitive to initialization, we also propose a method to produce first a coarse estimate of the parameters
Density Evolution for the Design of Non-Binary Low Density Parity Check Codes for Slepian-Wolf Coding
International audienceIn this paper, we investigate the problem of designing good non-binary LDPC codes for Slepian-Wolf coding. The design method is based on Density Evolution which gives the asymptotic error probability of the decoder for given code degree distributions. Density Evolution was originally introduced for channel coding under the assumption that the channel is symmetric. In Slepian-Wolf coding, the correlation channel is not necessarily symmetric and the source distribution has to be taken into account. In this paper, we express the non-binary Density Evolution recursion for Slepian-Wolf coding. From Density Evolution, we then perform code degree distribution optimization using an optimization algorithm called differential evolution. Both asymptotic performance evaluation and finite-length simulations show the gain at considering optimized degree distributions for SW coding