On near-capacity code design for partial-response channels

The advent of turbo codes and low-density parity-check (LDPC) codes has revolutionized channel coding, resulting in implementable systems which can communicate very near the Shannon capacity of many classical channels. Building on these ideas, we develop near-capacity coding techniques for binary input partial-response channels, which are relevant to digital information storage.; The capacity of these channels has not been known accurately until recent simulation-based calculation methods. We review one such method, and show how it can be used to evaluate the achievable information rates of concatenated systems involving an inner finite-state encoder and an outer parity-check code. We also determine the minimum signal-to-noise ratio (SNR) per information bit required for reliable communication, and provide a concatenated coding system which can achieve it.; We then focus on multilevel coding (MLC) and multistage decoding (MSD). Here, multiple component codes are interleaved, and then recovered successively, whereby decisions from previously decoded codewords are used for decoding subsequent interleaves. An analysis of MLC/MSD shows that reliable communication is possible up to the symmetric information rate, i.e., the mutual information rate for an independent and identically distributed (i.i.d.) equiprobable input process. The scheme is also observed to be effective for a small number of interleaves/stages. By further optimizing component LDPC codes, we are able to implement systems that nearly achieve these rates. Extensions are given for two-dimensional partial-response channels models used in holographic data storage.; The symmetric information rate, however, can be appreciably lower than capacity if the SNR is moderately low. Therefore, we conclude by exploring the design of finite-state encoders which transform an i.i.d. equiprobable binary process into an optimized channel in put process, from the perspective of minimizing the Kullback-Leibler divergence rate between the encoder output process and the optimized process; such encoders can be concatenated with an outer parity-check code to provide reliable communication near-capacity. Two construction methods are devised which can achieve an arbitrarily small divergence rate, and near-capacity achieving concatenated coding systems are constructed using one of these methods and an outer MLC/MSD system.