Benjamin Farber

Dr. Benjamin Farber

Fair Isaac Corp.

San Diego, CA

Wednesday, July 13, 2005
3:00 - 4:00 P.M.
Room 1005 EECS

Quantization of Multiple Sources Using Nonnegative Integer Bit Allocation

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 using optimal integer-valued bit allocation from the mean-squared error 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.

Benjamin Farber earned his bachelors in Electrical Engineering from Cornell University in 1999. He completed his PhD in Electrical and Computer Engineering from the University of California, San Diego, in 2005 under the supervision of Professor Kenneth Zeger. His research is focused on scalar quantization over noisy channels and the bit allocation problem for a finite set of quantizers.

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