New methods are presented to protect maximum runlength-limited sequences against random and burst errors and to avoid error propagation. The methods employ parallel conversion techniques and enumerative coding algorithms that transform binary user information into constrained codewords. The new schemes have a low complexity and are very efficient. The approach can be used for modulation coding in recording systems and for synchronization and line coding in communication systems. The schemes enable the usage of high-rate constrained codes, as error control can be provided with similar capabilities as for unconstrained sequences. Index Terms---Burst correction codes, enumerative coding, forward error correction, modulation coding, Reed--Solomon codes, runlength codes, synchronization. I.

When block modulation codes are concatenated with an error-correction code (ECC) in the standard way, the use of long block lengths results in error-propagation. This paper analyzes the performance of modified concatenation, which involves reversing the order of modulation and ECC. This modified scheme reduces error propagation, provides greater flexibility in the choice of parameters, and facilitates soft-decision decoding, with little or no loss in transmission rate. In particular, examples are presented which show how this technique can allow fewer interleaves per sector in hard disk drives, and permit the use of sophisticated block modulation codes which are better suited to the channel. Index terms: concatenated codes, Reed-Solomon codes, modulation codes, magnetic data storage 1 Introduction This paper is concerned with the interaction between the modulation code and the error-correcting code (ECC). The idea of modulation is to ensure that the sequence of bits transm...

We report on the performance of a new class of...

We present an enumerative technique for encoding and decoding dc-free runlength-limited sequences. This technique enables the encoding and decoding of sequences approaching the maxentropic performance bounds very closely in terms of code rate and low-frequency suppression capability. Use of finite-precision floating-point notation to express the weight coefficients results in channel encoders and decoders of moderate complexity. For channel constraints of practical interest, the hardware required for implementing such a quasi-maxentropic coding scheme consists mainly of a ROM of at most 5 kB. Index Terms---Enumeration, modulation coding, recording. I.

A method is presented for designing lossless sliding-block compression schemes that map constrained sequences onto unconstrained ones. The new compression scheme is incorporated into a coding technique for noisy constrained channels, which has applications to magnetic and optical storage. As suggested recently by Immink, the use of a lossless compression code can improve the performance of a modified concatenation scheme where the positions of the error-correcting code and constrained code are reversed (primarily in order to eliminate error-propagation due to the constrained code). Examples are presented that demonstrate the advantage of using sliding-block compression over block compression in a noisy constrained setting. Keywords: Compression; Concatenated codes; Constrained systems; Noisy constrained channels; Sliding-block codes; Run-length-limited codes; State splitting. 1 Introduction Constrained coding is a special kind of channel coding in which unconstrained user sequences a...

Introduction The technique of enumerative coding [1] makes it possible to translate source words into codewords and vice versa by invoking an algorithmic procedure rather than performing the translation with a look-up table. The usage of long codewords makes it possible to approach a code rate which is arbitrarily close to Shannon's noiseless capacity of the constrained channel. The risk of extreme error propagation precluded its usage in practical systems. Single channel bit errors may result in error propagation that could corrupt the entire data in the decoded word, and, of course, the longer the codeword the greater the number of data symbols affected. This article will evaluate the effects of error propagation of enumerative coding, where it is assumed that the constrained code is used in the conventional code configuration. It will be shown that when certain measures are taken, the average error propagation can be controlled to a level which is quite acceptable for many

This paper concerns noisy channels that are also constrained channels, having maximum runlength limits: the maximum number of consecutive 1s and/or 0s is constrained to be r. The methods we discuss can also be applied to channels for which certain other long sequences are forbidden, but they are not applicable to channels with minimum runlength constraints.

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Summary- We will present coding techniques for the character-constrained channel, where information is conveyed using q-bit characters (nibbles), where w prescribed characters are disallowed. Using codes for the characterconstrained channel, we present simple and systematic constructions of high-rate binary maximum runlength constrained codes. The new constructions have the virtue that large look-up tables for encoding and decoding are not required. We will compare the error propagation performance of codes based on the new construction with that of prior art codes. I.

Abstract—A constant-rate encoder–decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block decodable. Essentially, the 2-D constraint is turned into a set of independent and relatively simple one-dimensional (1-D) constraints; this is done by dividing the array into fixed-width vertical strips. Each row in the strip is seen as a symbol, and a graph presentation of the respective 1-D constraint is constructed. The maxentropic stationary Markov chain on this graph is next considered: a perturbed version of the corresponding probability distribution on the edges of the graph is used in order to build an encoder which operates in parallel on the strips. This perturbation is found by means of a network flow, with upper and lower bounds on the flow through the edges. A key part of the encoder is an enumerative coder for constantweight binary words. A fast realization of this coder is shown, using floating-point arithmetic.