The goal of the project is to develop effective joint source-channel coding techniques. The main objectives are to achieve a deep theoretical understanding of combined source-channel codes and to develop practical algorithms that can effectively be used in real applications such as low-bandwidth video compression and low-delay speech coding. Very narrow bandwidth transmission channels, such as mobile cellular telephony, require efficient coding schemes to protect the transmitted source information from the corruptive effects of channel errors. Some previous work on joint source-channel coding has yielded limited success at protecting source coded information. In particular, low complexity techniques are needed for low delay real time implementations. This project will investigate channel coding techniques for source coding applications with an emphasis on image, video, and speech coding applications. A summary of the topics to be investigated is: Classes of low-complexity redundancy free codes for discrete memoryless channels; error control coding will be incorporated into the source code design and the index assignment problem will be addressed for codes with redundancy. High resolution quantizer theory will be studied for sources transmitting across noisy channels. Some preliminary results give useful formulas for randomized index assignments, but a much stronger theory is needed for optimal index assignment. Lattice codes will be studied both for quantization and channel coding. A goal will be to develop efficient encoding algorithms for lattice source codes (respectively, decoding algorithms for channel codes). Preliminary results so far have yielded very fast algorithms for the leech lattice, as well as some of the best-known low dimensional lattices. Efficient decoding techniques will be developed for channel codes in Euclidean space using specific source coding information. In particular, trellis decoding algorithms and theory will be studied for unequal input probabilitie s and unequal error protection. This is currently an unsolved problem though extensions of techniques from traditional decoding algorithms have yielded some limited preliminary success.
