Efficient on-line schemes for encoding individual sequences with side information at the decoder

We present adaptive on-line schemes for lossy encoding of individual sequences, under the conditions of the Wyner-Ziv (WZ) problem. In the first part of this paper, a set of fixed-rate scalar source codes with zero delay is presented. We propose a randomized on-line coding scheme, which achieves asymptotically (and with high probability), the performance of the best source code in the set, uniformly over all source sequences. Efficient algorithms for implementing this scheme for small and large sets of encoders are presented. In the second part of this work, we generalize our results to the case of variable-rate coding. A set of variable-rate scalar source codes is presented. This time, the performance is measured by the Lagrangian Cost (LC), which is defined as a weighted sum of the distortion and the length of the encoded sequence. Efficient algorithms for implementing the generalized on-line coding scheme are presented. We then consider the special case of lossless variable-rate coding. An on-line scheme which uses Huffman codes is presented. We show that this scheme can be implemented efficiently using the same graphic methods from the first part. Finally, combining the results from former sections, we build a generalized efficient algorithm for a structured set of variable-rate encoders.