Universal Zero-Delay Joint Source-Channel Coding

We consider zero-delay joint source-channel coding of individual source sequences for a general known channel. Given an arbitrary finite set of schemes with finite-memory (not necessarily time-invariant) decoders, a scheme is devised that does essentially as well as the best in the set on all individual source sequences. Using this scheme, we construct a universal zero-delay joint source-channel coding scheme that is guaranteed to achieve, asymptotically, the performance of the best zero-delay encoding-decoding scheme with a finite-state encoder and a Markov decoder, on all individual sequences. For the case where the channel is a DMC, we construct an implementable zero-delay joint source-channel coding scheme that is based on the “follow the perturbed leader” scheme of György et al. for lossy source coding of individual sequences. Our scheme is guaranteed to attain asymptotically the performance of the best in the set of all encoding-decoding schemes with a “symbol by symbol” decoder (and arbitrary encoder), on all individual sequences.