Generalized Unary Coding

Abstract

Unary coding is useful, but it is redundant in its standard form. It can be seen as spatial coding where the value of the number is determined by its place in an array as is true in the generation of neural sequences in songbirds. Motivated by the biological finding that several neurons in the vicinity represent the same number, we propose a variant of unary numeration in its spatial form, where each number is represented by several 1s. We call this spread unary coding where the number of 1s used is the spread of the code. Spread unary coding is associated with saturation of the Hamming distance between code words. Extended variants of spread unary coding are described. These schemes, in which the length of the code word is fixed, allow representation of approximately $$n^{2}$$n2 numbers for n bits, rather than the n numbers of the standard unary coding. In the first scheme the spread increases, whereas in the second scheme the spread remains constant.