Extended-Domain Golomb Code and Symmetry of Relative Redundancy

Abstract

This paper presents extended-domain Golomb (XDG) code, an extension of Golomb code for sparse geometric sources as well as a generalization of extended-domain Golomb-Rice (XDGR) code, based on the idea of almost instantaneous fixed-to-variable length (AIFV) codes. Showing that the XDGR encoding can be interpreted as extended usage of the code proposed in the previous works, this paper discusses the following two facts: The proposed XDG code can be constructed as an AIFV code relating to Golomb code as XDGR code does to Rice code; XDG and Golomb codes are symmetric in the sense of relative redundancy. The proposed XDG code can be efficiently used for losslessly compressing geometric sources too sparse for the conventional Golomb and Rice codes. According to the symmetry, its relative redundancy is guaranteed to be as low as Golomb code compressing non-sparse geometric sources. Awing to this fact, the parameter of the proposed XDG code, which is more finely tunable than the conventional XDGR code, can be optimized for given inputs using the conventional techniques. Therefore, it is expected to be more useful for many coding applications that deal with geometric sources at low bit rates.