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We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded (using codes of fixed rate) and transmitted over two independent binary memoryless symmetric channels. The capacity of each channel is characterized by a single parameter that is not known at the transmitter. System performance is evaluated by computing the set of channel parameters for which the system can successfully decode. This set is called the achievable channel parameter region (ACPR). The goal is to design systems whose ACPRs are as large as possible. The main result is the design of irregular low-density parity-check (LDPC) ensembles whose ACPRs are significantly larger than previous designs. Some previous attempts to achieve large ACPRs with LDPC codes failed because systematic codes were used. In this work, we start with systematic encoders but puncture all the systematic bits before transmission. We also show that additional gains are possible using a staggered structure which enables codes optimized for single-user channels to perform well under symmetric channel conditions. The main analysis tool is a generic density-evolution framework for the analysis of joint iterative decoding for this problem. [ABSTRACT FROM PUBLISHER]

A new verification-based message-passing decoder for low-density parity-check (LDPC) codes is introduced and analyzed for the q-ary symmetric channel (q-SC). Rather than passing messages consisting of symbol probabilities, this decoder passes lists of possible symbols and marks some lists as verified. The density evolution (DE) equations for this decoder are derived and used to compute decoding thresholds. If the maximum list size is unbounded, then one finds that any capacity-achieving LDPC code for the binary erasure channel can be used to achieve capacity on the q-SC for large q. The decoding thresholds are also computed via DE for the case where each list is truncated to satisfy a maximum list-size constraint. Simulation results are also presented to confirm the DE results. During the simulations, we observed differences between two verification-based decoding algorithms, introduced by Luby and Mitzenmacher, that were implicitly assumed to be identical. In this paper, the node-based algorithms are evaluated via analysis and simulation. The probability of false verification (FV) is also considered and techniques are discussed to mitigate the FV. Optimization of the degree distribution is also used to improve the threshold for a fixed maximum list size. Finally, the proposed algorithm is compared with a variety of other algorithms using both density evolution thresholds and simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method based on combinatorial designs for constructing high-girth low-density parity-check (LDPC) codes. We use a 3-D lattice to generate balanced incomplete block designs based on planes and lines in the lattice. This gives families of regular LDPC codes with girths of at least 6, 8, and 10, whose parity-check matrices are all block circulant. The main advantage of this construction is that the algebraic structure leads to efficient encoders and decoders. Based on the block-circulant structure of a parity-check matrix, we present an efficient encoder that can be parallelized to improve the speed of encoding. The simulation results show that these families of LDPC codes perform very well on additive-white-Gaussian noise channels (roughly 0.45 dB from the channel capacity) and Rayleigh fading channels (roughly 0.51 dB from the channel capacity). [ABSTRACT FROM AUTHOR]

This paper investigates the joint iterative decoding of low-density parity-check (LDPC) codes and channels with memory. Sequences of irregular LDPC codes are presented that achieve, under joint iterative decoding, the symmetric information rate of a class of channels with memory and erasure noise. This gives proof, for the first time, that joint iterative decoding can be information rate lossless with respect to maximum-likelihood decoding. These results build on previous capacity-achieving code constructions for the binary erasure channel. A two state intersymbol-interference channel with erasure noise, known as the dicode erasure channel, is used as a concrete example throughout the paper. [ABSTRACT FROM AUTHOR]

We design multilevel coding (MLC) and bit-interleaved coded modulation (BICM) schemes based on low-density parity-check (LDPC) codes. The analysis and optimization of the LDPC component codes for the MLC and BICM schemes are complicated because, in general, the equivalent binary-input component channels are not necessarily symmetric. To overcome this obstacle, we deploy two different approaches: one based on independent and identically distributed (i.i.d.) channel adapters and the other based on coset codes. By incorporating i.i.d. channel adapters, we can force the symmetry of each binary-input component channel. By considering coset codes, we extend the concentration theorem based on previous work by Richardson et al. and Kavčić et al. We also discuss the relation between the systems based on the two approaches and show that they indeed have the same expected decoder behavior. Next, we jointly optimize the code rates and degree distribution pairs of the LDPC component codes for the MLC scheme. The optimized irregular LDPC codes at each level of MLC with multistage decoding (MSD) are able to perform well at signal-to-noise ratios (SNR) very close to the capacity of the additive white Gaussian noise (AWGN) channel. We also show that the optimized BICM scheme can approach the parallel independent decoding (PID) capacity as closely as does the MLC/PID scheme. Simulations with very large codeword length verify the accuracy of the analytical results. Finally, we compare the simulated performance of these coded modulation schemes at finite codeword lengths, and consider the results from the perspective of a random coding exponent analysis. [ABSTRACT FROM AUTHOR]