Bit Recycling with Prefix Codes

This paper presents a technique that aims at reducing the expansion of the compressed files that is caused by the multiplicity of equivalent messages. It does not try to eliminate multiplicity. Instead, it takes advantage of multiplicity by converting it into useful information, which we choose to describe parts of the compressed file itself. We call this technique bit recycling. On the decompressor side, when a message M is received, the set M of messages equivalent to M is determined, and the particular choice (M Sigma M) made by the compressor is perceived as a hint, which translates into a bit sequence. Such a bit sequence is said to be recycled and the bits it contains can be omitted from the compressed file. On the compressor side, the task is more complicated because the message that is currently selected among the set of equivalent ones carries information about the following messages. To make these far- reaching selections, the compressor may use non-deterministic choices but we propose a resolution algorithm along with a greedy version that allows the compressor to proceed in a stream-like fashion. We propose two ways to obtain recycled bit sequences: flat recycling, where a constant number of bits (about log2 M) is recovered for any selection of M Sigma M; and proportional recycling, where the number of bits that is recovered for the selection of M Sigma M grows with the cost of encoding M. In a 2006 paper, Dube and Beaudoin showed that they obtained the best experimental results using proportional recycling. We believe this recycling method to be close to optimal.