Extended Unary Coding

TL;DR

This paper introduces extended spread unary coding schemes that significantly increase the number of representable numbers compared to standard unary coding, with fixed code word length and varying spread strategies.

Contribution

The paper proposes two novel extended unary coding schemes that expand the representational capacity while maintaining fixed code length.

Findings

First scheme increases spread with representation capacity

Second scheme keeps spread constant while increasing capacity

Both schemes enable approximately n^2 representations for n bits

Abstract

Extended variants of the recently introduced spread unary coding are described. These schemes, in which the length of the code word is fixed, allow representation of approximately n^2 numbers for n bits, rather than the n numbers of the standard unary coding. In the first of two proposed schemes the spread increases, whereas in the second scheme the spread remains constant.