  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 upto 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>=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.
