Lossless and near-lossless source coding for multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of correlated information sequences =1 and =1 is drawn independent and identically distributed (i.i.d.) according to joint probability mass function (p.m.f.) ( ); the encoder for each source operates without knowledge of the other source; the decoder jointly decodes the encoded bit streams from both sources. The work of Slepian and Wolf describes all rates achievable by MASCs of infinite coding dimension ( ) and asymptotically negligible error probabilities ( ( ) 0). In this paper, we consider the properties of optimal instantaneous MASCs with finite coding dimension ( ) and both lossless ( ( ) = 0) and nearlossless ( ( ) 0) performance. The interest in near-lossless codes is inspired by the discontinuity in the limiting rate region at ( ) = 0 and the resulting performance benefits achievable by using near-lossless MASCs as entropy codes within lossy MASCs. Our central results include generalizations of Huffman and arithmetic codes to the MASC framework for arbitrary ( ), , and ( ) and polynomial-time design algorithms that approximate these optimal solutions.