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 discrete memoryless channel (DMC), we construct an implementable zero-delay joint source-channel coding scheme that is based on the "follow the perturbed leader" scheme of Gyoumlrgy 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

The Wasserstein distortion has proved useful in a variety of mathematical, signal processing and coding problems as a measure of how different two distributions are. In this paper we provide an expression for the performance of the optimal entropy constrained quantizer in terms of the Wasserstein distortion. The proof presented is significantly different from that previously shown by Linder (2002) and also provides an algorithm to achieve the optimal performance as the block size increases.