Optimal Golomb-Rice Code Extension for Lossless Coding of Low-Entropy Exponentially Distributed Sources

This paper presents an extension of Golomb-Rice (GR) code for coding low-entropy sources, which the gap between their entropy and the conventional GR code length gets larger. We mention here the following four facts related to the proposed code, extended-domain GR (XDGR) code: it is represented by multiple code trees, based on the idea of almost instantaneous fixed-to-variable length codes, with its algorithm being a generalization of unary coding; its structure naturally contains run-length coding; the gap between the entropy and its average code length is theoretically guaranteed to be asymptotically negligible as the entropy of the exponentially distributed sources tends to zero; and its coding parameter, corresponding to the negative-domain Rice parameter of GR code, can be estimated from the input source-symbol sequence. Experimental evaluations are also presented supporting the theorems. The proposed XDGR code, having simple algorithm and high compression performance, is expected to be used for many coding applications, which deals with exponentially distributed sources at low bit rates.