Conference Paper

Simple classes of constrained systems with unconstrained positions that outperform the maxentropic bound

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

The Wijngaarden-Immink (WI) scheme is a combined modulation/ECC coding scheme, where arbitrary user data are translated into a constrained sequence in which predefined positions are reserved for ECC parity. Besides offering the benefit of combined modulation/ECC coding, the WI scheme has two extra benefits. They are a) error propagation is limited to the constrained symbols, since symbols on the unconstrained positions are not related, and b) code hardware is limited to a look-up table of the coded part. We will describe classes of simple bit-stuffing schemes that require less redundancy than predicted by the bound based on the performance of maxentropic constrained systems presented by Campello et al. [1] and Poo et al. [21].

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... For completeness, we present these functions in Theorem 11. Lower bounds on the tradeoff function for RLL(0, k) are given in [19] and [21]. In this chapter, we determine the tradeoff functions for two other families of constraints: RLL(d, 2d+2), and RLL(d, ∞). ...
Conference Paper
Full-text available
It was recently shown that the code rate of a simple coding scheme is better than a previously established maxentropic bound for the Wijngaarden-Immink reversed modulation and error control scheme(W-I coding scheme). This paper analyzes code rates of coding schemes for a given insertion rate of the W-I coding scheme using finite state transition diagrams. A new coding scheme is proposed and a new bound for the code rate of the W-I coding scheme is derived. It is proved that the new bound is better than the maxentropic bound when the insertion rate is 1/2.
Book
Full-text available
Preface to the Second Edition About five years after the publication of the first edition, it was felt that an update of this text would be inescapable as so many relevant publications, including patents and survey papers, have been published. The author's principal aim in writing the second edition is to add the newly published coding methods, and discuss them in the context of the prior art. As a result about 150 new references, including many patents and patent applications, most of them younger than five years old, have been added to the former list of references. Fortunately, the US Patent Office now follows the European Patent Office in publishing a patent application after eighteen months of its first application, and this policy clearly adds to the rapid access to this important part of the technical literature. I am grateful to many readers who have helped me to correct (clerical) errors in the first edition and also to those who brought new and exciting material to my attention. I have tried to correct every error that I found or was brought to my attention by attentive readers, and seriously tried to avoid introducing new errors in the Second Edition. China is becoming a major player in the art of constructing, designing, and basic research of electronic storage systems. A Chinese translation of the first edition has been published early 2004. The author is indebted to prof. Xu, Tsinghua University, Beijing, for taking the initiative for this Chinese version, and also to Mr. Zhijun Lei, Tsinghua University, for undertaking the arduous task of translating this book from English to Chinese. Clearly, this translation makes it possible that a billion more people will now have access to it. Kees A. Schouhamer Immink Rotterdam, November 2004
Article
We introduce a new method for analyzing and constructing combined modulation and error-correcting codes (ECCs), in particular codes that utilize some form of reverse concatenation and whose ECC decoding scheme requires easy access to soft information. We expand the work of Immink and Wijngaarden and also of Campello, Marcus, New, and Wilson, in which certain bit positions in the modulation code are deliberately left unconstrained for the ECC parity bits, in the sense that such positions can take on either bit value without violating the constraint. Our method of analysis involves creating a single graph that incorporates information on these unconstrained positions directly into the constraint graph without any assumptions of periodicity or sets of unconstrained positions, and is thus completely general. We establish several properties of the tradeoff function that relates the density of unconstrained positions to the maximum code rate. In particular, the tradeoff function is shown to be concave and continuous. Algorithms for computing lower and upper bounds for this function are presented. We also show how to compute the maximum possible density of unconstrained positions and give explicit values for the runlength-limited (RLL(d,k)) and maximum-transition-run (MTR(j,k)) constraints.
Article
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
Article
A new coding technique is proposed that translates user information into a constrained sequence using very long codewords. Huge error propagation resulting from the use of long codewords is avoided by reversing the conventional hierarchy of the error control code and the constrained code. The new technique is exemplified by focusing on (d, k)-constrained codes. A storage-effective enumerative encoding scheme is proposed for translating user data into long dk sequences and vice versa. For dk runlength-limited codes, estimates are given of the relationship between coding efficiency versus encoder and decoder complexity. We show that for most common d, k values, a code rate of less than 0.5% below channel capacity can be obtained by using hardware mainly consisting of a ROM lookup table of size 1 kbyte. For selected values of d and k, the size of the lookup table is much smaller. The paper is concluded by an illustrative numerical example of a rate 256/466, (d=2, k=15) code, which provides a serviceable 10% increase in rate with respect to its traditional rate 1/2, (2, 7) counterpart