From the Publisher:
Although it originated as a method to study general dynamical systems, symbolic dynamics is useful in coding for data storage and transmission as well as in linear algebra. Requiring only a undergraduate knowledge of linear algebra, this first general textbook includes over 500 exercises.

An Introduction to Symbolic Dynamics and Coding

This paperd escribes a byte-oriented binary transmission code and its implementation. This code is particularly well suited for high-speed local area networks and similar data links, where the information format consists of packets, variable in length, from about a dozen up to several hundred 8-bit bytes. The proposed transmission code translates each source byte into a constrained 10-bit binary sequence which hase excellent performance parameters near the theoretical limits for 8B/10B codes. The maximum run length is 5 and the maximum digital sum variation is 6. A single error in the encoded bits can, at most, generate an error burst of length 5 in the decoded domain. A very simple implementation of the code has been accomplished by partitioning the coder into 5B/6B and 3B/4B subordinate coders.

A DC-balanced, partitioned-block, 8B/10B transmission code

Publisher Summary
This chapter presents the field of finite automata, which is a branch of mathematics connected with the algebraic theory of semigroups and associative algebras. From another viewpoint, finite automata are a branch of algorithm design concerned with string manipulation and sequence processing. The chapter presents the basic definitions and a proof of the fundamental result of S. C. Kleene. The chapter discusses the notion of star-height, which is one of the fast developing areas of automata theory. The chapter discusses star-free sets, which is an important notion especially because of its connection with logic. The chapter presents a complete proof of P. Schutzenberger's theorem, stating the equality between star-free sets and aperiodic sets. It also presents the syntactic characterization of two important subfamilies of star-free sets, namely, locally testable and piecewise testable. The chapter describes the applications of finite automata, such as string matching or file indexing. The chapter introduces the field of automata recognizing numbers expanded at some basis. This is an aspect of finite automata regarding several fields in classical mathematics, such as number theory and ergodic theory.

CHAPTER 1 – Finite Automata

The realization of a digital recording system using partial-response class-IV signaling with maximum-likelihood sequence detection (MLSD) is described. To perform MLSD at the high data rates encountered in recording systems, a simple implementation of the Viterbi detector based on a difference-metric algorithm is developed. Decision-directed schemes for gain control and timing recovery, for tracking variations of the gain and timing phase during data readback, and for fast initial adjustment from a known preamble are presented. The dynamic behavior of the control algorithms was studied by computer simulations. Coding was used to facilitate timing recovery and gain control, to limit the path memory length of the Viterbi detector, and to allow fast and reliable startup of the receiver. The design and properties of rate 8/9 constrained codes are examined. The problem of equalization is addressed, and analog and combined analog/digital filter implementations are developed. A simple adaptive equalizer capable of compensating variations of the recording channel characteristics with track radius and/or head-to-medium distance is described. >

A PRML system for digital magnetic recording

Codes for mass data storage systems

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.

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M. Hassner

Papers

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