Codes with bounded synchronization delay
Solomon W. Golomb,Basil Gordon +1 more
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TLDR
This class is shown to attain the upper bound on codebook size previously encountered (but not always attained) for the familiar subclass of “comma-free codes”, which has the property that every message can be uniquely decoded by examining a segment of bounded length, from any starting point.Abstract:
In this paper we study “bounded delay codes,≓ which have the property that every message can be uniquely decoded by examining a segment of bounded length, from any starting point. This class is shown to attain the upper bound on codebook size previously encountered (but not always attained) for the familiar subclass of “comma-free codes.≓ The problem of determining the smallest message length s0 which guarantees unique decipherability for such codes is discussed. The bounded delay codes are classified according to the value of s0. An extension is made to the case of variable length codes, in which the upper bound formula of the uniform word-length case is replaced by a system of inequalities.read more
Citations
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Frame Synchronization Techniques
TL;DR: A basic theory of frame synchronization for a singlechannel digital communication system is presented and comparisons are drawn with more exotic techniques such as comma-free coding.
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A survey of error-correcting codes for channels with symbol synchronization errors
TL;DR: A comprehensive survey of error-correcting codes for channels corrupted by synchronization errors and potential applications as well as the obstacles that need to be overcome before such codes can be used in practical systems are presented.
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Combinatorial problems motivated by comma-free codes
TL;DR: In the paper some combinatorial problems motivated by comma‐free codes are considered and the most significant known results and methods used are given.
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A characterization of strictly locally testable languages and its application to subsemigroups of a free semigroup
Aldo de Luca,Antonio Restivo +1 more
TL;DR: The main result of the paper states that a recognizable subset X of a free semigroup A + is strictly locally testable if and only if all the idempotents of the syntactic semigroup S ( X ) of X are constants for X′ = XΦ , where Φ : A + → S (X ) is the syntact morphism.
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On a question of McNaughton and Papert
TL;DR: The solution relates the concept of local testability with that of synchronization in a code and the algebraic notion of conjugacy in a monoid to show that under what conditions a free submonoid of a free monoid is locally testable.
References
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Book
Introduction to Number Theory
TL;DR: A specific feature of this text on number theory is the rather extensive treatment of Diophantine equations of second or higher degree as discussed by the authors, and a large number of non-routine problems are given.
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Introduction to Number Theory. By T. Nagell. Second Edition. Pp. 309. $5.50. 1964. (Chelsea.)
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Variable-length binary encodings
E. N. Gilbert,Edward F. Moore +1 more
TL;DR: This paper gives a theoretical treatment of several properties which describe certain variable-length binary encodings of the sort which could be used for the storage or transmission of information, such as the prefix and finite delay properties.
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Two inequalities implied by unique decipherability
TL;DR: A consequence of (1) and work of Shannon is that this more restricted kind of list suffices in the search for codes with specified amounts of redundancy.
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Comma-free codes
TL;DR: In this paper, the authors consider an alphabet consisting of the numbers 1, 2, …, n, and consider all possible k-letter words (a 1 a 2, a k ), where k is also fixed.