Channel Resolvability with a Full-Duplex Decode-and-Forward Relay

Abstract

We study the minimum randomness required at a source node to approximately produce a chosen i.i.d. distribution at a destination, while a relay assists in the process. In the classical relay problem, the relay does not have any message of its own to transmit, and only re-transmits a function of its observation. In the resolvability problem the variable of interest is the randomness rate, therefore we assume the relay does not have access to any randomness outside what it observes at its input, i.e., the relay output is a deterministic function of its input. A block-Markov scheme is used in which the relay decodes the source message to assist with the approximation of the i.i.d. output. In addition, the relay extracts randomness from its noisy channel observation in each block and uses it in the next block to improve the resolvability rate. The careful handling of this randomness recycling, in order to avoid the introduction of unwanted dependencies, is a key part of the contribution of this paper.