We present a serially concatenated coding scheme for partial response channels. The encoder consists of an outer irregular LDPC code and an inner matched spectrum trellis code. These codes are shown to offer considerable improvement over the i.i.d. capacity (> 1 dB) of the channel for low rates (approximately 0.1 bits per channel use). We also present a qualitative argument on the optimality of these codes for low rates. We also formulate a performance index for such codes to predict their performance for low rates. The results have been verified via simulations for the (1-D)/sqrt(2) and the (1-D+0.8D^2)/sqrt(2.64) channels. The structure of the encoding/decoding scheme is considerably simpler than the existing scheme to maximize the information rate of encoders over partial response channels.

We present a serially concatenated coding scheme for partial response channels. The encoder consists of an outer irregular LDPC code and an inner matched spectrum trellis code. These codes are shown to offer considerable improvement over the i.i.d. capacity (> 1 dB) of the channel for low rates (approximately 0.1 bits per channel use). We also present a qualitative argument on the optimality of these codes for low rates. We also formulate a performance index for such codes to predict their performance for low rates. The results have been verified via simulations for the (1-D)/sqrt(2) and the (1-D+0.8D^2)/sqrt(2.64) channels. The structure of the encoding/decoding scheme is considerably simpler than the existing scheme to maximize the information rate of encoders over partial response channels.

This dissertation considers several coding techniques based on Reed-Solomon (RS) and low-density parity-check (LDPC) codes. These two prominent families of error-correcting codes have attracted a great amount of interest from both theorists and practitioners and have been applied in many communication scenarios. In particular, data storage systems have greatly benefited from these codes in improving the reliability of the storage media. The first part of this dissertation presents a unified framework based on rate-distortion (RD) theory to analyze and optimize multiple decoding trials of RS codes. Finding the best set of candidate decoding patterns is shown to be equivalent to a covering problem which can be solved asymptotically by RD theory. The proposed approach helps understand the asymptotic performance-versus-complexity trade-off of these multiple-attempt decoding algorithms and can be applied to a wide range of decoders and error models. In the second part, we consider spatially-coupled (SC) codes, or terminated LDPC convolutional codes, over intersymbol-interference (ISI) channels under joint iterative decoding. We empirically observe the phenomenon of threshold saturation whereby the belief-propagation (BP) threshold of the SC ensemble is improved to the maximum a posteriori (MAP) threshold of the underlying ensemble. More specifically, we derive a generalized extrinsic information transfer (GEXIT) curve for the joint decoder that naturally obeys the area theorem and estimate the MAP and BP thresholds. We also conjecture that SC codes due to threshold saturation can universally approach the symmetric information rate of ISI channels. In the third part, a similar analysis is used to analyze the MAP thresholds of LDPC codes for several multiuser systems, namely a noisy Slepian-Wolf problem and a multiple access channel with erasures. We provide rigorous analysis and derive upper bounds on the MAP thresholds which are shown to be tight in some cases. This analysis is a first step towards proving threshold saturation for these systems which would imply SC codes with joint BP decoding can universally approach the entire capacity region of the corresponding systems.