Algorithms for sliding block codes - An application of symbolic dynamics to information theory

Ideas which have origins in Shannon's work in information theory have arisen independently in a mathematical discipline called symbolic dynamics. These ideas have been refined and developed in recent years to a point where they yield general algorithms for constructing practical coding schemes with engineering applications. In this work we prove an extension of a coding theorem of Marcus and trace a line of mathematics from abstract topological dynamics to concrete logic network diagrams.

[1]  Raymond E Miller Switching theory , 1979 .

[2]  B. McMillan The Basic Theorems of Information Theory , 1953 .

[3]  R. Bowen Entropy for group endomorphisms and homogeneous spaces , 1971 .

[4]  Masakazu Nasu Uniformly finite-to-one and onto extensions of homomorphisms between strongly connected graphs , 1982, Discret. Math..

[5]  T. Horiguchi,et al.  An optimization of modulation codes in digital recording , 1976 .

[6]  E. Gorog,et al.  Redundant alphabets with desirable frequency spectrum properties , 1968 .

[7]  Michael E. Paul,et al.  Sofic systems , 1975 .

[8]  D. Lindholm,et al.  Power spectra of channel codes for digital magnetic recording , 1978 .

[9]  M. Hassner A nonprobabilistic source and channel coding theory , 1981 .

[10]  Lalit R. Bahl,et al.  Block Codes for a Class of Constrained Noiseless Channels , 1970, Inf. Control..

[11]  Daniel L. Ostapko,et al.  Codes for Self-Clocking, AC-Coupled Transmission: Aspects of Synthesis and Analysis , 1975, IBM J. Res. Dev..

[12]  Benjamin Weiss,et al.  SIMILARITY OF AUTOMORPHISMS OF THE TORUS , 1970 .

[13]  Abraham Lempel,et al.  Look-ahead coding for input- restricted channels , 1982, IEEE Trans. Inf. Theory.

[14]  Toby Berger,et al.  On binary sliding block codes , 1977, IEEE Trans. Inf. Theory.

[15]  F. R. Gantmakher The Theory of Matrices , 1984 .

[16]  Peter A. Franaszek,et al.  On Synchronous Variable Lenght Coding for Discrete Noiseless Channels , 1969, Inf. Control..

[17]  Peter A. Franaszek Construction of Bounded Delay Codes for Discrete Noiseless Channels , 1982, IBM J. Res. Dev..

[18]  Brian Marcus,et al.  Topological entropy and equivalence of dynamical systems , 1979 .

[19]  Robert M. Gray,et al.  Sliding-block source coding , 1975, IEEE Trans. Inf. Theory.

[20]  D. Bloomberg,et al.  Channel capacity of charge-constrained run-length limited codes , 1981 .

[21]  P. A. Franasnek On future-dependent block coding for input-restricted channels , 1979 .

[22]  Bruce Pruitt Kitchens Continuity properties of factor maps in ergodic theory , 1981 .

[23]  Hisashi Kobayashi Coding schemes for reduction of intersymbol interference in data transmission systems , 1970 .

[24]  Benjamin Weiss,et al.  Equivalence of topological Markov shifts , 1977 .

[25]  William Parry A Finitary Classification of Topological Markov Chains and Sofic Systems , 1977 .

[26]  Hisashi Kobayashi,et al.  A Survey of Coding Schemes for Transmission or Recording of Digital Data , 1971 .

[27]  R. F. Williams Errata to "Classification of Subshifts of Finite Type" , 1974 .

[28]  Peter A. Franaszek Synchronous Bounded Delay Coding for Input Restricted Channels , 1980, IBM J. Res. Dev..

[29]  Michael E. Paul,et al.  Finite procedures for sofic systems , 1977 .

[30]  P. Franaszek Sequence-state methods for run-length-limited coding , 1970 .

[31]  Peter A. Franaszek A General Method for Channel Coding , 1980, IBM J. Res. Dev..

[32]  P. A. Franaszek,et al.  Sequence-state coding for digital transmission , 1968 .

[33]  B. Weiss Subshifts of finite type and sofic systems , 1973 .

[34]  Arvind M. Patel Zero-modulation encoding in magnetic recording , 1975 .

[35]  Brian Marcus,et al.  Factors and extensions of full shifts , 1979 .

[36]  W. Parry Intrinsic Markov chains , 1964 .

[37]  T. Goodman,et al.  Relating Topological Entropy and Measure Entropy , 1971 .

[38]  E. Dinaburg ON THE RELATIONS AMONG VARIOUS ENTROPY CHARACTERISTICS OF DYNAMICAL SYSTEMS , 1971 .

[39]  G. O'Brien,et al.  The road-colouring problem , 1981 .

[40]  Peter Lancaster,et al.  The theory of matrices , 1969 .