In recent years performance prediction for communication systems utilizing iteratively decodable codes has been of considerable interest. There have been significant breakthroughs as far as the analysis of LDPC code ensembles is concerned but the more practical problem of predicting the FER/BER of a particular code has proved to be much more difficult. In this work we present a technique (based on the work of Richardson '03) for finding lower and upper bounds on the performance of LDPC coded BICM systems for a given code. The insight gained from the prediction technique is used to design interleavers that improve the error floors of these systems.

We propose an augmented belief propagation (BP) decoder for low-density parity check (LDPC) codes which can be utilized on memoryless or intersymbol interference channels. The proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the BP decoder. The augmented decoder is a multistage iterative decoder, where, at each stage, the original channel messages on select symbol nodes are replaced by saturated messages. The key element of the proposed method is the symbol selection process, which is based on the appropriately defined subgraphs of the code graph and/or the reliability of the information received from the channel. We demonstrate by examples that this decoder can be implemented to achieve substantial gains (compared to the standard locally-operating BP decoder) for short LDPC codes decoded on both memoryless and intersymbol interference Gaussian channels. Using the Margulis code example, we also show that the augmented decoder reduces the error floors. Finally, we discuss types of BP decoding errors and relate them to the augmented BP decoder.

Two incremental redundancy hybrid ARQ (IR-HARQ) schemes are compared: one is based on LDPC code ensembles with random transmission assignments, the other is based on recently introduced Raptor codes. A number of important issues, such as rate and power control, and error rate performance after each transmission on time varying binary-input, symmetric-output channels are addressed by analyzing performance of LDPC and Raptor codes on parallel channels. The theoretical results obtained for random code ensembles are tested on several practical code examples by simulation. Both theoretical and simulation results show that both LDPC and Raptor codes are suitable for HARQ schemes. Which codes would make a better choice depends mainly on the width of the signal-to-noise operating range of the HARQ scheme, prior knowledge of that range, and other design parameters and constraints dictated by standards.

We propose an augmented belief-propagation (BP) decoder for low-density parity-check (LDPC) codes which can be used on memoryless or intersymbol-interference (ISI) channels. The proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the BP decoder. The augmented decoder is a multistage iterative decoder, where at each stage, the original channel messages on select symbol nodes are replaced by saturated messages. The key element of the proposed method is the symbol-selection process, which is based on the appropriately defined subgraphs of the code graph and/or the reliability of the information received from the channel. We demonstrate by examples that this decoder can be implemented to achieve substantial gains (compared with the standard locally operating BP decoder) for short LDPC codes decoded on both memoryless and ISI Gaussian channels. Using the Margulis code example, we also show that the augmented decoder reduces the error floors. Finally, we discuss types of BP decoding errors and relate them to the augmented BP decoder.

An LDPC code based hybrid ARQ scheme with random transmission assignments is analyzed. The spectrum properties of LDPC code ensembles that are necessary for this analysis are derived. Very good estimates of maximum-likelihood decoding error rates after each transmission are provided. The results are tested on practical code examples by simulation

In this paper, we design capacity-approaching codes for partial response channels. The codes are constructed as concatenations of inner trellis codes and outer low-density parity- check (LDPC) codes. Unlike previous constructions of trellis codes for partial response channels, we disregard any algebraic properties (e.g., the minimum distance or the run-length limit) in our design of the trellis code. Our design is purely probabilistic in that we construct the inner trellis code to mimic the transition probabilities of a Markov process that achieves a high (capacity-approaching) information rate. Hence, we name it a matched information rate (MIR) design. We provide a set of five design rules for constructions of capacity-approaching MIR inner trellis codes. We optimize the outer LDPC code using density evolution tools specially modified to fit the superchannel consisting of the inner MIR trellis code concatenated with the partial response channel. Using this strategy, we design degree sequences of irregular LDPC codes whose noise tolerance thresholds are only fractions of a decibel away from the capacity. Examples of code constructions are shown for channels both with and without spectral nulls.

We propose an improved belief-propagation (BP) decoder for low-density parity-check (LDPC) codes based on channel information correction. We show that our algorithm achieves sizeable performance gains (in waterfall and error floor regions) compared to the standard BP decoder. We verify by examples that the proposed decoder almost achieves the maximum-likelihood decoding performance for short LDPC codes

We propose a numerical method to compute the capacity of a power constrained memoryless additive white Gaussian noise (AWGN) channel with finite and fixed input alphabets. The method is based on a two-part algorithm. The first part is a modified version of the Blahut-Arimoto algorithm and the second part is a simple maximization algorithm over a single parameter. The optimal input distribution we obtain can be utilized to construct probabilistic codes for this channel. These codes promise to bridge the shaping gap between the uniform-input information rate and the capacity of the channel.

Multiple description codes are data compression algorithms designed with the goal of minimizing the distortion caused by data loss in packet-based or diversity communications systems. Recently, techniques that achieve multiple description coding by combining embedded source codes with unequal error protection channel codes have become popular in the literature. These codes allow for data reconstruction with any subset of the transmitted packets and achieve progressively better source reconstructions as more and more packets are decoded. The given methods may be applied to any embedded source description. While applicability to all embedded source codes provides great flexibility, this separation approach begs the question of whether better performance could be achieved by taking advantage of the internal structure of a particular embedded code. In this paper, we investigate an extremely simple method for using an embedded source code's internal state information in the construction of a multiple description code. In particular, we protect an embedded SPIHT bitstream by adding to that bitstream periodic descriptions of state information from the encoder, and we demonstrate how the state information can be used to recover lost bits. For low probabilities of network packet loss, the proposed algorithm achieves performance within 0.35 dB of the performance of a more sophisticated channel coding algorithm when both algorithms are applied to same SPIHT embedded source code.