DocumentCode :
2478626
Title :
The Shannon capacity of M-ary constrained codes
Author :
Pimentel, Cecilio
Author_Institution :
Dept. of Electron. & Syst., Fed. Univ. Pernambuco, Recife, Brazil
fYear :
1998
fDate :
16-21 Aug 1998
Firstpage :
324
Abstract :
We consider a class of constrained codes that prohibits the occurrence of substrings from a finite set F of sequences of finite length over an alphabet ZA=(0,1,...,A-1). The set F is called the set of distinguished substrings. The capacity of the code S, denoted as C, was defined by Shannon as C=limn→∞log2 cn/n. The standard method of evaluating the capacity is to take log2λ, where λ is the largest real eigenvalue of the adjacent matrix that reflects the constraint. The purpose of this paper is to present a systematic method, based on combinatorial enumeration techniques, to find the number of sequences of length n in S,cn satisfying a specified constraint. The capacity is expressed as the base two logarithm of the inverse of the largest real root of the denominator polynomial in the generating series which enumerates the sequences
Keywords :
codes; combinatorial mathematics; eigenvalues and eigenfunctions; information theory; matrix algebra; polynomials; sequences; M-ary constrained codes; Shannon capacity; capacity; combinatorial enumeration; denominator polynomial; distinguished substrings; eigenvalue; matrix; sequences; substrings; Concatenated codes; Eigenvalues and eigenfunctions; Equations; Lapping; Polynomials;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
0-7803-5000-6
Type :
conf
DOI :
10.1109/ISIT.1998.708929
Filename :
708929
Link To Document :
بازگشت