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The effects of randomization on finite-memory decision schemes

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1 Author(s)

This paper is concerned with the differences between deterministic and randomized finite-memory decision rules. It is shown that for any hypothesis-testing problem there exists a b < \infty such that, for any B , the optimal deterministic rule with B + b bits in memory has a lower error probability than the optimal randomized rule with B bits in memory. Suboptimal deterministic rules with this property are demonstrated. These deterministic rules lose at most b bits. Thus for large memories the fraction of memory, measured in bits, lost by deterministic rules is negligible.

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Information Theory, IEEE Transactions on  (Volume:18 ,  Issue: 4 )