Real-Time Coding With Limited Lookahead

IEEE Transactions on Information Theory (Impact Factor: 2.33). 05/2011; 59(6). DOI: 10.1109/Allerton.2011.6120150
Source: arXiv


A real time coding system with lookahead consists of a memoryless source, a
memoryless channel, an encoder, which encodes the source symbols sequentially
with knowledge of future source symbols upto a fixed finite lookahead, d, with
or without feedback of the past channel output symbols and a decoder, which
sequentially constructs the source symbols using the channel output. The
objective is to minimize the expected per-symbol distortion. For a fixed finite
lookahead d>=1 we invoke the theory of controlled markov chains to obtain an
average cost optimality equation (ACOE), the solution of which, denoted by
D(d), is the minimum expected per-symbol distortion. With increasing d, D(d)
bridges the gap between causal encoding, d=0, where symbol by symbol
encoding-decoding is optimal and the infinite lookahead case, d=\infty, where
Shannon Theoretic arguments show that separation is optimal. We extend the
analysis to a system with finite state decoders, with or without noise-free
feedback. For a Bernoulli source and binary symmetric channel, under hamming
loss, we compute the optimal distortion for various source and channel
parameters, and thus obtain computable bounds on D(d). We also identify regions
of source and channel parameters where symbol by symbol encoding-decoding is
suboptimal. Finally, we demonstrate the wide applicability of our approach by
applying it in additional coding scenarios, such as the case where the
sequential decoder can take cost constrained actions affecting the quality or
availability of side information about the source.

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    • "For optimal vector quantization in a multi-stage problem, Borkar et al. [6] investigated existence results. Recently [2] considered the average cost optimality equation for causal coding of i.i.d. sources with finite lookahead. "
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    ABSTRACT: For a vector Markov source driven by additive Gaussian noise, we study the existence and structure of optimal quantization policies. The quantizers allowed are the ones which have convex codecells. For the finite horizon problem and bounded cost, we show that an optimal zero-delay quantization policy exists. Then the linear quadratic Gaussian problem is considered as an important extension of the bounded cost assumption for the finite horizon setting. For the infinite horizon setup, the existence of an optimal stationary policy is established among the class of Markov coding policies.
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    ABSTRACT: The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate. Structure theorems, pertaining to the encoder and next-state functions are derived for every given finite-state decoder, which can have access to side information.
    Full-text · Article · Aug 2011 · IEEE Transactions on Information Theory
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    ABSTRACT: Source coding with a side information "vending machine" is a recently proposed framework in which the statistical relationship between the side information and the source, instead of being given and fixed as in the classical Wyner-Ziv problem, can be controlled by the decoder. This control action is selected by the decoder based on the message encoded by the source node. Unlike conventional settings, the message can thus carry not only information about the source to be reproduced at the decoder, but also control information aimed at improving the quality of the side information. In this paper, the analysis of the trade-offs between rate, distortion and cost associated with the control actions is extended from the previously studied point-to-point set-up to two basic multiterminal models. First, a distributed source coding model is studied, in which two encoders communicate over rate-limited links to a decoder, whose side information can be controlled. The control actions are selected by the decoder based on the messages encoded by both source nodes. For this set-up, inner bounds are derived on the rate-distortion-cost region for both cases in which the side information is available causally and non-causally at the decoder. These bounds are shown to be tight under specific assumptions, including the scenario in which the sequence observed by one of the nodes is a function of the source observed by the other and the side information is available causally at the decoder. Then, a cascade scenario in which three nodes are connected in a cascade and the last node has controllable side information, is also investigated. For this model, the rate-distortion-cost region is derived for general distortion requirements and under the assumption of causal availability of side information at the last node.
    Full-text · Article · Sep 2011 · IEEE Transactions on Information Theory
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