By Topic

Causal coding of stationary sources and individual sequences with high resolution

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
T. Linder ; Dept. of Math. & Stat., Queen's Univ., Kingston, Ont., Canada ; R. Zamir

In a causal source coding system, the reconstruction of the present source sample is restricted to be a function of the present and past source samples, while the code stream itself may be noncausal and have variable rate. Neuhoff and Gilbert showed that for memoryless sources, optimum performance among all causal source codes is achieved by time-sharing at most two memoryless codes (quantizers) followed by entropy coding. In this work, we extend Neuhoff and Gilbert's result in the limit of small distortion (high resolution) to two new settings. First, we show that at high resolution, an optimal causal code for a stationary source with finite differential entropy rate consists of a uniform quantizer followed by a (sequence) entropy coder. This implies that the price of causality at high resolution is approximately 0.254 bit, i.e., the space-filling loss of the uniform quantizer. Then, we consider individual sequences and introduce a deterministic analogue of differential entropy, which we call "Lempel-Ziv differential entropy." We show that for any bounded individual sequence with finite Lempel-Ziv differential entropy, optimum high-resolution performance among all finite-memory variable-rate causal codes is achieved by dithered scalar uniform quantization followed by Lempel-Ziv coding. As a by-product, we also prove an individual-sequence version of the Shannon lower bound.

Published in:

IEEE Transactions on Information Theory  (Volume:52 ,  Issue: 2 )