Expansion Coding for Channel and Source Coding

A general method of coding over expansion is proposed, which allows one to reduce the highly non-trivial problems of coding over analog channels and compressing analog sources to a set of much simpler subproblems, coding over discrete channels and compressing discrete sources. More specifically, the focus of this paper is on the additive exponential noise (AEN) channel, and lossy compression of exponential sources. Taking advantage of the essential decomposable property of these channels (sources), the proposed expansion method allows for mapping of these problems to coding over parallel channels (respectively, sources), where each level is modeled as an independent coding problem over discrete alphabets. Any feasible solution to the resulting optimization problem after expansion corresponds to an achievable scheme of the original problem. Utilizing this mapping, even for the cases where the optimal solutions are difficult to characterize, it is shown that the expansion coding scheme still performs well with appropriate choices of parameters. More specifically, theoretical analysis and numerical results reveal that expansion coding achieves the capacity of AEN channel in the high SNR regime. It is also shown that for lossy compression, the achievable rate distortion pair by expansion coding approaches to the Shannon limit in the low distortion region. Remarkably, by using capacityachieving codes with low encoding and decoding complexity that are originally designed for discrete The material in this paper was presented in part at the 2012 IEEE International Symposium on Information Theory, Boston, MA, Jul. 2012, and in part at the 2014 IEEE International Symposium on Information Theory, Honolulu, HI, Jul. 2014. H. Si and S. Vishwanath are with the Laboratory for Informatics, Networks, and Communications, Wireless Networking and Communications Group, The University of Texas at Austin, Austin, TX 78712. Email: [email protected], [email protected]. O. O. Koyluoglu is with the Department of Electrical and Computer Engineering, The University of Arizona, Tucson, AZ 85721. Email: [email protected]. K. Appaiah is with the Department of Electrical Engineering, Indian Institute of Technology Bombay. Email: [email protected]. ar X iv :1 50 5. 05 48 1v 1 [ cs .I T ] 2 0 M ay 2 01 5