Application of chaos theory in joint coding schemes

Abstract

Traditionally, the three major operations in a digital communication system, i.e., source coding, cryptography and channel coding, are operated separately. However, recent investigations reveal that the joint operations of them may lead to advantages when compared with the traditional separate operating approach. In this thesis, the compression capability of chaotic maps is investigated in detail. Then it is extended to perform the joint operations, such as simultaneous source coding and encryption, and joint source-channel coding. Recently, it was found that iterating a piecewise linear chaotic map reversely is equivalent to performing arithmetic coding, which is a traditional source coding method adopted in international multimedia compression standards such as JPEG2000 and H.264/AVC. However, the precision problem will be encountered when more and more source symbols are encoded. To solve this problem, an efficient variable-length arithmetic coding scheme using chaotic maps is proposed, which has a higher coding speed than traditional arithmetic coding with minor loss in compression ratio. In order to preserve the optimal entropy coding rate, a discrete piecewise linear chaotic map is employed to perform generalized arithmetic coding. The high sensitivity on the initial state makes chaotic systems very suitable for encryption. With the compression capability, it is possible to have simultaneous source coding and encryption using chaotic maps. The advantages of such joint operation include a simpler system design and an improved operating efficiency as the two operations are completed in a single step. In this thesis, a simultaneous variable-length arithmetic coding and encryption scheme using chaotic maps is presented by maintaining the secrecy of the selected mode of the map. Its security is enhanced by a stream cipher generated by another chaotic map. Channel coding is generally performed after source coding to protect the codeword bits against channel noise. As certain amount of implicit redundancy may remain after source coding, it can be employed to further improve the overall transmission performance. Here, an improved error correction technique for arithmetic coding with the forbidden symbol is suggested. By estimating the occurrence of the subsequent forbidden symbols, the effective forbidden region is expanded and theoretically, a better error correction performance can be achieved. To further enhance the error correction performance, an improved soft-in-soft-out iterative decoding scheme for arithmetic coding is proposed, where a better estimation of the a posteriori probability is adopted to exchange soft information between the error-resistant arithmetic code and the channel code. In conclusion, this thesis introduces some novel and practical source coding schemes using chaotic maps. A discrete piecewise linear chaotic map is presented to perform generalized arithmetic coding. Making use of the favorable properties of chaotic maps, a simultaneous source coding and encryption scheme is proposed, which possesses high security and runs faster than the traditional separate approach. Moreover, an effective joint source-channel coding scheme for arithmetic coding is presented, which is further enhanced by iterative decoding approach. It outperforms the separate source and channel coding approach in terms of error correcting capability.

Date of Award	14 Feb 2014
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Kwok Wo WONG (Supervisor)