Weakly constrained codes via row-by-row coding

Abstract

A constrained code is a set of finite-length codewords that entirely avoid the occurrences of certain patterns. In some applications, it may be preferable to merely limit the number of occurrences of certain patterns in codewords rather than to completely forbid them. Constrained codes that involve such weaker constraints are called weakly constrained codes. In this paper we construct capacity-achieving weakly constrained codes. The construction is based on a row-by-row coding scheme in which messages are encoded into the rows of a 2-dimensional array in which the frequency of occurrence of patterns along columns is controlled.