Real-Time Coding With Limited Lookahead

A real-time coding system with lookahead consists of a memoryless source, a memoryless channel, an encoder, which encodes the source symbols sequentially with knowledge of future source symbols up to a fixed finite lookahead d , with or without feedback of the past channel output symbols and a decoder, which sequentially constructs the source symbols using the channel output. The objective is to minimize the expected per-symbol distortion. For a fixed finite lookahead d\geq 1 , we invoke the theory of controlled Markov chains to obtain an average cost optimality equation (ACOE), the solution of which, denoted by D(d) , is the minimum expected per-symbol distortion. With increasing d , D(d) bridges the gap between causal encoding, d=0 , where symbol-by-symbol encoding-decoding is optimal and the infinite lookahead case, d=\infty , where Shannon Theoretic arguments show that separation is optimal. We extend the analysis to a system with finite-state decoders, with or without noise-free feedback. For a Bernoulli source and binary symmetric channel, under Hamming loss, we compute the optimal distortion for various source and channel parameters, and thus obtain computable bounds on D(d) . We also identify regions of source and channel parameters where symbol-by-symbol encoding-decoding is suboptimal. Finally, we demonstrate the wide applicability of our approach by applying it in additional coding scenarios, such as the case where the sequential decoder can take cost-constrained actions affecting the quality or availability of side information about the source.