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Generalized Arithmetic Coding using discrete Chaotic Maps

Making use of the Lebesgue measure preserving property of the piecewise linear chaotic map, a discrete piecewise linear chaotic map is employed to perform the generalized arithmetic coding, which is an optimal entropy coding algorithm adopted by international standards. After a number of message symbols have been encoded by the reverse interval mapping, an enlargement on the encoding interval is performed and some codeword bits are exported accordingly. Based on the enlarged encoding interval, the subsequent symbols are encoded with the modified chaotic maps, the lower and upper bounds of which are determined by the final encoding interval of the symbols already encoded. In the decoding process, the message symbols are recovered by iterating the corresponding chaotic map from an appropriate initial value. The encoding interval enlargement is tracked by performing reverse interval mapping on the decoded symbols. More codeword bits are shifted into the register to form the initial value for decoding the subsequent symbols. Simulation results verify that the compression performance of our scheme is very close to the entropy bound and is comparable to traditional finite-precision arithmetic coding. In addition, cryptographic capability can be integrated into our scheme to make it a joint compression and encryption scheme. Its security is enhanced when compared with the existing schemes based on traditional arithmetic coding.