A stack algorithm for source coding with a fidelity criterion

A new scheme for encoding source information with respect to a fidelity criterion by tree codes is analyzed. Taking its design from earlier stack sequential decoders for channels, the algorithm keeps a stack of code tree paths of variable lengths ordered by a metric. It repeatedly extends the topmost path and reorders, until the topmost rises above a given metric . The analysis uses difference equations, both linear and nonlinear; a commonly occurring nonlinear equation is solved asymptotically for the first time. The distribution of the worst metric to appear at the stack top is found to fall off faster than exponentially below a specifiable metric, whenever the encoder performance lies above the rate-distortion limit. Next, development of the top path is found to follow asymptotically a certain trajectory in the length-metric plane; this leads to a tight bound on path length released at termination. Finally, difference equations are written to bound the nodes searched. The work concludes with numerical calculations and simulations for the binary lid source with Hamming distortion measure. Comparison is made to other algorithms.