Issue No. 04 - April (1982 vol. 31)

ISSN: 0018-9340

pp: 318-321

null Chung Ho Chen , Research Department, Sperry Univac

ABSTRACT

Arithmetic codes use a structured redundancy technique for binary number representation such that errors in an arithmetic operation of a digital computer can be detected or corrected. This correspondence studies the code structures by treating the set of redundant coded binary representations as a finite Abelian group. An algebraic model of arithmetic codes is developed, which shows that an arithmetic code is a pair of cyclic group isomorphisms. Two theorems are derived which describe the necessary and sufficient conditions for the existence of an arithmetic code. It is also shown that the group of redundant coded binary numbers is isomorphic to a cyclic group, or the direct sum of two cyclic groups. For a given code generator A and the information cardinality m, the two theorems may be applied to find all existing arithmetic codes up to an isomorphism. The algebraic structures of all codes published to date are covered by the mathematical model described in this correspondence.

INDEX TERMS

isomorphic pair, Algebraic model, algebraic structure, arithmetic code, cyclic group isomorphism, decoding function, encoding function, finite Abelian group

CITATION

null Chung Ho Chen, "An Algebraic Model of Arithmetic Codes",

*IEEE Transactions on Computers*, vol. 31, no. , pp. 318-321, April 1982, doi:10.1109/TC.1982.1675998