Near-Optimal Depth-Constrained Codes
P. Gupta, B. Prabhakar, and S. Boyd
IEEE Transactions on Information Theory, 50(12):3294-3298, December 2004.
This note considers an -letter alphabet in which the th letter is accessed with probability . The problem is to design efficient algorithm for constructing near-optimal, depth-constrained Huffman and alphabetic codes. We recast the problem as one of determining a probability vector in an appropriate convex set , so as to minimize the relative entropy over all . Methods from convex optimization give an explicit solution for in terms of . We show that the Huffman and alphabetic codes so constructed are within 1 and 2 bits of the corresponding optimal depth-constrained codes.