We consider the problem of designing modulation codes for magnetic recording (MR) channels and other binary channels with ISI, where Markov sources are known to provide the best known lower bound on capacity. Our approach includes computing a costly channel matching a Markov source optimized for a given ISI channel. We then construct encoders and decoders for a modulation code matched to this costly channel.

We present a reverse concatenation (RC) architecture with maximum transition run (MTR) modulation codes and Reed-Solomon (RS) error-correction codes (ECCs). The scheme employs a high-rate primary (pre-RS) MTR code and a secondary (post-RS) MTR code, which controls error propagation. The two modulation codes are designed in such a way to maximize the overall code rate and maintain simple hardware implementation. Simulation results demonstrate superior performance compared to reverse concatenation with non-MTR codes, especially at a relatively high recording density.

Generalized Concatenation (GC) of Reed-Solomon (RS) Codes is a powerful technique to enhance the error-correcting capability of RS codes without resorting to large finite fields. However, interleaving a GC scheme in the standard column-wise way significantly reduces the burst-correcting capability of such scheme. In this paper, we present techniques that optimize the burst-correcting capability of some GC schemes.

A reverse concatenation scheme based on an efficient modulation encoder satisfying non-uniform constraints, a systematic Reed-Solomon encoder and a partial symbol interleaver is presented. This architecture achieves very tight modulation constraints and minimizes error propagation and rate loss. The modulation constraints considered are of the same type as the constraints that have been used in generalized partial-response maximum-likelihood (PRML) detection systems. A class of codes that is based on serial concatenation of a prefix-constrained code and two interleaved enumerative codes with non-uniform constraints is proposed. Specific rate-199/200 PRML(G, I) codes are constructed.

We propose new systematic constructions of Gray codes that improve reliability of the track identification field in the servo portion of a magnetic recording disk. In this application, it is beneficial to obtain good distance properties within a certain range of neighboring Gray codewords, because the servo positioning system typically gives a good estimate of the range of interest. With proposed Gray codes, we provide a high separation range between non-adjacent Gray codewords at Hamming distance one, which guarantees error detection within this range. In addition, we provide a certain level of separation between Gray codewords at Hamming distance two, which can be utilized for error correction.

We consider a particular family of Gray codes having the property that codewords ciand ci+2differ in a burst of length exactly two. These codes can be applied in the servo track-identification field to identify the correct track during seeks. We call these codes skew-tolerant Gray codes (STGC) and we present explicit constructions

We develop methods for analyzing and constructing combined modulation/error-correcting codes (ECC codes), in particular codes that employ some form of reversed concatenation and whose ECC decoding scheme requires easy access to soft information (e.g., turbo codes, low-density parity-check (LDPC) codes or parity codes). We expand on earlier work of Wijngaarden and Immink (1998, 2001), Immink (1999) and Fan (1999), in which certain bit positions are reserved for ECC parity, in the sense that the bit values in these positions can be changed without violating the constraint. Earlier work has focused more on block codes for specific modulation constraints. While our treatment is completely general, we focus on finite-state codes for maximum transition run (MTR) constraints. We (1) obtain some improved constructions for MTR codes based on short block lengths, (2) specify an asymptotic lower bound for MTR constraints, which is tight in very special cases, for the maximal code rate achievable for an MTR code with a given density of unconstrained positions, and (3) show how to compute the capacity of the set of sequences that satisfy a completely arbitrary constraint with a specified set of bit positions unconstrained.