Variable Length Compression of Codeword Indices for Lossy Compression

Many problems in information theory feature an index into a random codebook being encoded with a fixed length scheme. We propose to purposefully select the index in a manner that skews its distribution, thus making variable length entropy coding of the index more attractive. In an application to lossy compression of a Bernoulli source, we illustrate that variable length coding yields a reduction in the rate over fixed length coding, and allows to reach a requisite rate distortion performance level using a smaller codebook.