Zhou, Hongchao and Bruck, Jehoshua (2012) Efficient Generation of Random Bits From Finite State Markov Chains. IEEE Transactions on Information Theory, 58 (4). pp. 2490-2506. ISSN 0018-9448 http://resolver.caltech.edu/CaltechAUTHORS:20120503-095551724
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The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal efficiency in unbiased random bits generation. Hence, a natural question is what if the sources are correlated? Both Elias and Samuelson proposed methods for generating unbiased random bits in the case of correlated sources (of unknown probability distribution), specifically, they considered finite Markov chains. However, their proposed methods are not efficient or have implementation difficulties. Blum (1986) devised an algorithm for efficiently generating random bits from degree-2 finite Markov chains in expected linear time, however, his beautiful method is still far from optimality on information-efficiency. In this paper, we generalize Blum's algorithm to arbitrary degree finite Markov chains and combine it with Elias's method for efficient generation of unbiased bits. As a result, we provide the first known algorithm that generates unbiased random bits from an arbitrary finite Markov chain, operates in expected linear time and achieves the information-theoretic upper bound on efficiency.
|Additional Information:||© 2012 IEEE. Manuscript received December 23, 2010; revised June 02, 2011; accepted October 04, 2011. This work was supported in part by the National Science Foundation’s Expeditions in Computing Program under Grant CCF-0832824. This paper was presented in part at the 2010 IEEE International Symposium on Information Theory.|
|Subject Keywords:||Markov chain; Random bits generation; Random sequence|
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|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||03 May 2012 18:33|
|Last Modified:||03 May 2012 18:33|
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