DocumentCode :
2256900
Title :
A vector version of witsenhausen’s counterexample: A convergence of control, communication and computation
Author :
Grover, Pulkit ; Sahai, Anant
Author_Institution :
Dept. of EECS, Univ. of California at Berkeley, Berkeley, CA, USA
fYear :
2008
fDate :
9-11 Dec. 2008
Firstpage :
1636
Lastpage :
1641
Abstract :
We argue that Witsenhausen´s counterexample provides a useful conceptual bridge between distributed control, communication and computation. Inspired by the utility of studying long block-lengths in information theory, we formulate a vector version of the counterexample. Information-theoretic arguments are then used to derive bounds on the minimum cost for the vector problem. Restricted to the scalar case, the lower bounds are a strict improvement over Witsenhausen´s lower bound for some parameter values. The upper bounds are based on two strategies that can asymptotically outperform optimal linear and nonlinear scalar strategies. To investigate the computational aspects of such problems, we then consider a simpler problem of lossless source coding. From a distributed control perspective, the computations required for encoding and decoding can be viewed as internal communication between virtually distributed agents. We derive new lower bounds that establish a tradeoff between the computation, communication and distortion costs for lossless source coding.
Keywords :
source coding; telecommunication control; Witsenhausen´s counterexample; decoding; distributed control; encoding; information theory; lossless source coding; lower bounds; nonlinear scalar strategies; optimal linear strategies; vector problem; virtually distributed agents; Bridges; Communication system control; Convergence; Costs; Distributed computing; Distributed control; Information theory; Source coding; Upper bound; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on
Conference_Location :
Cancun
ISSN :
0191-2216
Print_ISBN :
978-1-4244-3123-6
Electronic_ISBN :
0191-2216
Type :
conf
DOI :
10.1109/CDC.2008.4739477
Filename :
4739477
Link To Document :
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