Toward constructive Slepian-Wolf coding schemes

This chapter deals with practical solutions for the Slepian Wolf (SW) coding problem, which refers to the problem of lossless compression of correlated sources with coders which do not communicate. Here, we will consider the case of two binary correlated sources X and Y , characterized by their joint distribution. If the two coders communicate, it is well known from Shannon’s theory that the minimum lossless rate for X and Y is given by the joint entropy H(X,Y ). Slepian and Wolf established in 1973 [30] that this lossless compression rate bound can be approached with a vanishing error probability for infinitely long sequences, even if the two sources are coded separately, provided that they are decoded jointly and that their correlation is known to both the encoder and the decoder. Hence, the challenge is to construct a set of encoders which do not communicate and a joint decoder which can achieve the theoretical limit. This chapter gives an overview of constructive solutions both for the asymmetric and the non asymmetric SW coding problems. Asymmetric SW coding refers to the case where one source, for example Y , is transmitted at its entropy rate and used as side information to decode the second source X. Non asymmetric SW coding refers to the case where both sources are compressed at a rate lower than their respective entropy rates. Sections 2 and 3 recall the principles and then describe practical schemes for asymmetric and symmetric coding respectively. Practical solutions for which the compression rate is a priori fixed according to the correlation between the two sources are first described. In this case, the correlation between the two sources needs to be known or estimated at the transmitter. Rate-adaptive schemes in which the SW code is incremental are then presented. This chapter ends with Section 4 covering various advanced SW coding topics such as the design of schemes based on source codes and the generalization to the case of non-binary sources, and to the case of M sources.