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Quantization of Multiple Sources Using Nonnegative Integer Bit Allocation

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2 Author(s)
Farber, B. ; Fair Isaac Corp., San Diego, CA ; Zeger, K.

Asymptotically optimal real-valued bit allocation among a set of quantizers for a finite collection of sources was derived in 1963 by Huang and Schultheiss, and an algorithm for obtaining an optimal nonnegative integer-valued bit allocation was given by Fox in 1966. We prove that, for a given bit budget, the set of optimal nonnegative integer-valued bit allocations is equal to the set of nonnegative integer-valued bit allocation vectors which minimize the Euclidean distance to the optimal real-valued bit-allocation vector of Huang and Schultheiss. We also give an algorithm for finding optimal nonnegative integer-valued bit allocations. The algorithm has lower computational complexity than Fox's algorithm, as the bit budget grows. Finally, we compare the performance of the Huang-Schultheiss solution to that of an optimal integer-valued bit allocation. Specifically, we derive upper and lower bounds on the deviation of the mean-squared error (MSE) using optimal integer-valued bit allocation from the MSE using optimal real-valued bit allocation. It is shown that, for asymptotically large transmission rates, optimal integer-valued bit allocations do not necessarily achieve the same performance as that predicted by Huang-Schultheiss for optimal real-valued bit allocations

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Information Theory, IEEE Transactions on  (Volume:52 ,  Issue: 11 )