Distributed source coding using syndromes (DISCUS)

We study the problem of compressing correlated distributed sources, i.e. correlated sources which are not co-located or cannot co-operate to directly exploit their correlation. First, we consider the strongly related problem of compressing a source which is correlated with another source that is available only at the decoder. This problem has been studied in the information theory literature under the name of the Slepian-Wolf source coding problem for the lossless coding case, and as “rate-distortion with side information” for the lossy coding case. In this work we provide a constructive practical algorithm dubbed as Distributed Source Coding Using Syndromes (DISCUS), that can be applicable in a variety of settings. Simulation results are presented for source coding of independently and identically distributed Gaussian sources with side information available at the decoder in the form of a noisy version of the Gaussian source to be coded. To get further insight into the construction of group-codes for this problem, we study the achievability of the rate-distortion function with side information at decoder, for the Gaussian case using only geometric arguments. We then consider a generalization of this problem to the encoding of Gaussian vector sources with the presence of a jointly Gaussian side information at the decoder.; We develop a bit-allocation algorithm based on the innovation spectrum which is applied to the following application: digital transmission for enhancing, in a backward compatible way, the quality of analog image transmission systems. We propose a practical algorithm that treats the problem as one of wavelet image compression with side information (available in the form of a noisy analog version of the image) present at the decoder. We propose a rate allocation technique to efficiently allocate the bits among the wavelet coefficients of the image. Then, we consider the generalization of the above constructions to the problem of distributed source coding with symmetric rates of transmission where every encoder sends only partial information about its corresponding source so that the availability of such information at the remote joint decoder ensures the reconstruction of any/all of the sources of interest. This approach, based on generalized coset codes, is very general and encompasses a large class of coding techniques such as trellis codes and lattice codes. We give several examples to illustrate the concepts.