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A linear bound for sliding-block decoder window size .2.

IEEE TRANSACTIONS ON INFORMATION THEORY 1996年第6期42卷 1913-1924页

作者： Ashley, JJ IBM Research Division Almaden Research Center San Jose CA USA

An input-constrained channel is the set S of finite sequences of symbols generated by the walks on a labeled finite directed graph G (which is said to present S). We introduce a new construction of finite-state encoders for input-constrained channels. The construction is a hybrid of the state-splitting technique of Adler, Coppersmith, and Hassner and the stethering technique of Ashley, Marcus, and Roth. When S has finite memory, and p and q are integers where p/g is at most the capacity of S, the construction guarantees an encoder at rate p : q and having a sliding-block decoder (literally at rate q : p) with look-ahead that is linear in the number of states of the smallest graph G presenting S. This contrasts with previous constructions. The straight Adler, Coppersmith, and Hassner construction provides an encoder having a sliding-block decoder at rate q : p, but the best proven upper bound on the decoder look-ahead is exponential in the number of states of G. A previous construction of Ashley provides an encoder having a sliding-block decoder whose look-ahead has been proven to be linear in the number of states of G, but the decoding is at rate tq : tp, where t is linear in the number of states of G.

关键词： input-constrained channel sliding-block decoder bounds

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Time-varying encoders for constrained systems: An approach to limiting error propagation

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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第3期46卷 1038-1043页

作者： Ashley, JJ Marcus, BH Infineon Technol Santa Cruz CA 95060 USA IBM Almaden Res Ctr San Jose CA 95120 USA

Time-varying encoders for constrained systems are introduced. The approach generalizes the state-splitting (ACH) algorithm in a way that yields encoders consisting of multiple phases, with encoding proceeding cyclically from one phase to the next, The framework is useful for design of high-rate codes with reduced decoder error propagation and reduced complexity.

关键词： constrained systems finite-state encoder input-restricted channel PRML sliding-block decoder state splitting

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A NOTE ON THE METHOD OF POLES FOR CODE CONSTRUCTION

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IEEE TRANSACTIONS ON INFORMATION THEORY 1994年第2期40卷 512-517页

作者： ASHLEY, J BEAL, MP UNIV PARIS 07 INST BLAISE PASCALLITPF-75251 PARIS 05FRANCE

The method of poles is a method for constructing a rate 1:1 finite state code from k-ary data into a constrained channel S, where S is recognized by a given local automaton and S has capacity at least log(k). We characterize those automata to which the method of poles applies in the case where h(S) = log(k). The code produced by the method of poles has a sliding-block decoder. We also give an upper bound on the window length of the decoder that applies when h(S) greater-than-or-equal-to log(k).

关键词： METHOD OF POLES sliding-block decoder ENCODER SHIFT OF FINITE TYPE

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Complexity and sliding-block decodability

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IEEE TRANSACTIONS ON INFORMATION THEORY 1996年第6期42卷 1925-1947页

作者： Ashley, JJ Karabed, R Siegel, PH IBM Research Division Almaden Research Center San Jose CA USA University of California San Diego La Jolla CA USA

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, extending the work of Adler, Coppersmith, and Hassner, 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 less than or equal to cap(S), the Shannon 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, In this paper, 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.

关键词： complexity sliding-block decoder constrained system NP-complete graph coloring

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Extensions of the method of poles for code construction

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IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第6期49卷 1516-1523页

作者： Béal, MP Univ Marne Vallee Inst Gaspard Monge F-77454 Marne La Vallee 2 France

The method of poles is a method introduced by Franaszek for constructing a rate-1 : 1 finite-state code from k-ary data into a constrained channel of finite type whose capacity is strictly greater than log(k). The method is based on the computation of a set of states called poles. With each pole is associated, a set of paths going from this pole to others. Each set verifies an entropy condition. The code produced by the method of poles has a sliding-block decoder if each set of paths satisfies moreover an optimization condition based on the sum of the path lengths of the set. In this correspondence, we give a new optimization condition which guarantees the sliding-block window decoding property and has a lower computational complexity than the previous one. We also extend the method of poles to the more general case of sofic constrained channels.

关键词： encoder method of poles shift of finite type sliding-block decoder sofic system strongly synchronizing state

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A generalized state-splitting algorithm

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第4期43卷 1326-1338页

作者： Ashley, J Marcus, BH Laboratory of Chromatography DEPg.Fac.Quimica Universidad Nacional Autonoma de Mexico Circuito interior Cd Universitaria/CP 04510 Mexico D.F.Mexico

In this correspondence we describe a generalization of the state-splitting algorithm (also known as the ACH algorithm) for constructing encoders which encode arbitrary data into constrained systems of sequences. In the generalized algorithm, we replace approximate eigenvectors with approximate eigenmatrices to yield a framework for designing encoders with smaller sliding-block windows and therefore lower error propagation.

关键词： ACH algorithm constrained system modulation code run-length-limited system sliding-block decoder state-splitting algorithm

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