Preposterior analysis for differential encoder design

Abstract

A modified differential encoding structure is proposed and optimized based upon the concept of preposterior analysis from the theory of alphabet-constrained data compression. Using preposterior analysis, the quantizer input sequence is chosen to minimize the expected distortion over a fixed but arbitrary interval, say, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> samples long. By computing the expected distortion over future inputs, preposterior analysis allows future behavior to be modeled, but without an encoding delay as in tree coding. The optimized quantizer input sequence is not simply the prediction error as in classical differential pulse code modulation, but it is a weighted combination of the current prediction error and past encoding errors. The optimization is accomplished using a backward dynamic programming argument.