Abstract
In this work, given n,ϵ > 0, two efficient encoding (decoding) methods are presented for mapping arbitrary data to (from) n×n binary arrays in which the weight of every row and every column is within [(1/2-ϵ)n, (1/2+ϵ)n], which is referred to as the ϵ-balanced constraint. The first method combines the divide and conquer algorithm and a modification of the Knuth's balancing technique, resulting a redundancy of Θ(n) bits. On the other hand, for sufficiently large n, the second method uses the sequence replacement technique, which costs only 1 redundant bit. The latter method reduces significantly the redundancy of the best known encoder for two-dimensional p-bounded weight constrained codes from (n + 3) bits to a single bit.