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.

A statistical simulation method is introduced to estimate the sector error rate (SER) of proposed triply concatenated coding systems for magnetic hard disk drives. The outer code is a standard interleaved Reed-Solomon code. The 'middle' codes are run length limiting codes used to demonstrate the effect of error propagation. The inner code(s) are block codes with 1 or 3 parity check bits. First, a baud rate simulation is used to estimate sufficient statistics to extrapolate ECC performance. Second, a Monte Carlo error event simulator generates error instances which are simply checked for correctability. In all code combinations the apparent SNR gains when considering error (or bit) event rates are considerably lessened or completely lost when considering SER.

In todays high-speed disk drive read channel ICs maximum likelihood detection using the Viterbi algorithm is a key component in reconstructing digital data sequences. The presented Viterbi decoder was realized in a 0.25 /spl mu/m CMOS technology. Using the proposed comparison approach, it achieves a throughput rate of 550 Mb/s.

Partial-response (PR) signaling is used to model communications channels with intersymbol interference (ISI) such as the magnetic recording channel and the copper-wire channel for digital subscriber lines. Coding for improving noise immunity in higher order partial-response channels, such as the "extended" class-4 channels denoted EPR4, E/sup 2/PR4, E/sup 3/PR4, has become an important subject as the linear densities in magnetic recording approach those at which these partial-response channels are the best models of real channels. In this paper, we consider partial-response channels for which ISI is so severe that the channels fail to achieve the matched-filter bound (MFB) for symbol error rate, assuming maximum-likelihood decoding. We show that their performance can be improved to the MFB by high-rate codes based on constrained systems, some of which may even simplify the Viterbi (1979) detectors relative to the uncoded channels. We present several examples of high-rate constrained codes for E/sup 2/PR4 and E/sup 3/PR4 channels and evaluate their performance by simulation.

A constrained system, or sofic system, S is the set of symbol strings generated by the finite-length paths through a finite labeled, directed graph. Karabed and Marcus (1988), extending the work of Adler, Coppersmith, and Hassner (1983), used the technique of state-splitting to prove the existence of a noncatastrophic, rate p:q finite-state encoder from binary data into S for any input word length p and codeword length q satisfying p/q/spl les/cap(S), the Shannon (1948) capacity. For constrained systems that are almost-finite-type, they further proved the existence of encoders enjoying a stronger form of decodability-namely, sliding-block decodability. In particular, their result implies the existence of a 100% efficient (rate 1/2), sliding-block code for the charge-constrained, runlength-limited constraint with parameters (d, k; c)=(1,3; 3), an almost-finite-type system with capacity precisely 1/2. We describe two quite different constructions of such codes. The constructions highlight connections between the problem of determining sliding-block decodability of a finite-state encoder and certain problems of colorability for graphs and sets. Using these connections, we show that the problem of determining the existence of a block-decodable input tag assignment for a given rate p:q, finite-state encoder is NP-complete, for p>1. We also prove NP-completeness results for several related problems in combinatorics and coding.

A new family of codes that improve the reliability of digital communication over noisy, partial-response channels is described. The codes are intended for use on channels where the input alphabet size is limited. These channels arise in the context of digital data recording and certain data transmission applications. The codes-called matched-spectral-null codes-satisfy the property that the frequencies at which the code power spectral density vanishes correspond precisely to the frequencies at which the channel transfer function is zero. It is shown that matched-spectral-null sequences provide a distance gain on the order of 3 dB and higher for a broad class of partial-response channels. The embodiment of the system incorporates a sliding-block code and a Viterbi detector based upon a reduced-complexity trellis structure. The detectors are shown to achieve the same asymptotic average performance as maximum-likelihood sequence detectors, and the sliding-block codes exclude quasi-catastrophic trellis sequences in order to reduce the required path memory length and improve worst-case detector performance. Several examples are described in detail.>

Summary form only given. The real-time application of trellis coding to partial response channels is described for a rate 8/10 matched-spectral-null (MSN) trellis code on the (1-D) partial response channel. The architectural and design issues of an experimental chip that implements the functions of encoding, decoding, and Viterbi detection are discussed. Two novel techniques in the design of the Viterbi detector are introduced. Modulo normalization of the path metrics, and area-efficient pipelining for the add-compare-select units. Both techniques are effective in producing a regular structure and reducing the number of required interconnections. Area-efficient realization is achieved with little speed degradation. The circuit and layout were designed using LAGER CAD tool. The chip was fabricated in 1.2 mu m CMOS.>

Work on coding arbitrary sequences into a constrained system of sequences (called a sofic system) is presented. Such systems model the input constraints for input-restricted channels (e.g., run-length limits and spectral constraints for the magnetic recording channel). In this context it is important that the code be noncatastrophic to ensure that the decoder has limited error propagation. A constructive proof is given of the existence of finite-state invertible noncatastrophic codes from arbitrary n-ary sequences to a sofic system S at constant rate p:q provided only that Shannon's condition (p/q)>