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Huffman coding finds an optimal prefix code for a given probability mass function. Consider situations in which one wishes to find an optimal code with the restriction that all codewords have lengths that lie in a user-specified set of lengths (or, equivalently, no codewords have lengths that lie in a complementary set). This paper introduces a polynomial-time dynamic programming algorithm that finds optimal codes for this reserved-length prefix coding problem. This has applications to quickly encoding and decoding lossless codes. In addition, one modification of the approach solves any quasiarithmetic prefix coding problem, while another finds optimal codes restricted to the set of codes with g codeword lengths for user-specified g (e.g., g=2).
Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many practical app
Let $P = {p(i)}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a source code
We consider the issue of direct access to any letter of a sequence encoded with a variable length code and stored in the computers memory, which is a special case of the random access problem to compressed memory. The characteristics according to whi
We present many new results related to reliable (interactive) communication over insertion-deletion channels. Synchronization errors, such as insertions and deletions, strictly generalize the usual symbol corruption errors and are much harder to prot
We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work of Koetter