A new upper bound on the capacity of a class of primitive relay channels

Ravi Tandon, Sennur Ulukus
2008 2008 46th Annual Allerton Conference on Communication, Control, and Computing  
We obtain a new upper bound on the capacity of a class of discrete memoryless relay channels. For this class of relay channels, the relay observes an i.i.d. sequence T , which is independent of the channel input X. The channel is described by a set of probability transition functions p(y|x, t) for all (x, t, y) ∈ X × T × Y. Furthermore, a noiseless link of finite capacity R0 exists from the relay to the receiver. Although the capacity for these channels is not known in general, the capacity of
more » ... l, the capacity of a subclass of these channels, namely when T = g(X, Y ), for some deterministic function g, was obtained in [1] and it was shown to be equal to the cut-set bound. Another instance where the capacity was obtained was in [2], where the channel output Y can be written as Y = X ⊕ Z, where ⊕ denotes modulom addition, Z is independent of X, |X | = |Y| = m, and T is some stochastic function of Z. The compress-and-forward (CAF) achievability scheme [3] was shown to be capacity achieving in both cases. Using our upper bound we recover the capacity results of [1] and [2]. We also obtain the capacity of a class of channels which does not fall into either of the classes studied in [1] and [2] . For this class of channels, CAF scheme is shown to be optimal but capacity is strictly less than the cut-set bound for certain values of R0. We further illustrate the usefulness of our bound by evaluating it for a particular relay channel with binary multiplicative states and binary additive noise for which the channel is given as Y = T X + N . We show that our upper bound is strictly better than the cut-set upper bound for certain values of R0 but it lies strictly above the rates yielded by the CAF achievability scheme.
doi:10.1109/allerton.2008.4797748 fatcat:jnywtzxefbfsvc5ebzcveknygy