A "follow the perturbed leader"-type algorithm for zero-delay quantization of individual sequences

Zero-delay lossy source coding schemes are considered for individual sequences. Performance is measured by the distortion redundancy, defined as the difference between the normalized cumulative mean squared distortion of the scheme and the normalized cumulative distortion of the best scalar quantizer of the same rate which is matched to the entire sequence to be encoded. Recently, Weissman and Merhav constructed a randomized scheme which, for any bounded individual sequence of length n, achieves a distortion redundancy O(n^-13/logn). However, this scheme has prohibitive complexity (both space and time) which makes practical implementation infeasible. In this paper, we present an efficiently computable algorithm based on a "follow the perturbed leader"-type prediction method by Kalai and Vempala. Our algorithm achieves distortion redundancy O(n^-14/ logn), which is somewhat worse than that of the scheme by Merhav and Weissman, but it has computational complexity that is linear in the sequence length n, and requires O(n¹4/) storage capacity.