Mixed Joint Source-Channel Coding Schemes for the Multiple-Access Relay Channel: Error Probability Analysis

In the following we denote random variables with upper case letters, e.g. X , Y , and their realizations with lower case letters , e.g. x, y. A discrete random variable X takes values in a set X . We use pX(x) to denote the probability mass function (p.m.f.) of a discrete RV X on X ; for brevity we may omit the subscript X when it is the uppercase version of the sample symbol x. We denote vectors with boldface letters, e.g. x, y; the i’th element of a vector x is denoted by xi and we use x j i where i < j to denote (xi, xi+1, ..., xj−1, xj); x j is a short form notation for xj1, and unless specified otherwise x , x . We use A (X) to denote the set of -strongly typical sequences w.r.t. distribution pX(x) on X , as defined in [2, ch. 13.6]. When referring to a typical set we may omit the random variables from the notation, when these variables are clear from the context. We denote the empty set with φ, and the complement of the set B by B. The MARC consists of two transmitters (sources), a receiver (destination) and a relay. Transmitter i has access to the source sequence S i , for i = 1, 2. The receiver is interested in the lossless reconstruction of the source sequences observed by the two transmitters. The objective of the relay is to help the receiver decode the source sequences. The relay and the receiver each has its own side information, denoted by W 3 and W , respectively, correlated with the source sequences. In the multiple-access broadcast relay channel (MABRC) both the relay and the destination are interested a lossless reconstruction of the sources. Figure 1 depicts the MARC with side information setup.