Optimal delayed decoding of predictively encoded sources

Predictive coding eliminates redundancy due to correlations between the current and past signal samples, so that only the innovation, or prediction residual, needs to be encoded. However, the decoder may, in principle, also exploit correlations with future samples. Prior decoder enhancement work mainly applied a non-causal filter to smooth the regular decoder reconstruction. In this work we broaden the scope to pose the problem: Given an allowed decoding delay, what is the optimal decoding algorithm for predictively encoded sources? To exploit all information available to the decoder, the proposed algorithm recursively estimates conditional probability densities, given both past and available future information, and computes the optimal reconstruction via conditional expectation. We further derive a near-optimal low complexity approximation to the optimal decoder, which employs a time-invariant lookup table or codebook approach. Simulations indicate that the latter method closely approximates the optimal delayed decoder, and that both considerably outperform the competition.