A Generic Top-Down Dynamic-Programming Approach to Prefix-Free Coding

Abstract

Given a probability distribution over a set of n words to be transmitted, the Huffman Coding problem is to find a minimal-cost prefix free code for transmitting those words. The basic Huffman coding problem can be solved in O(n log n) time but variations are more difficult. One of the standard techniques for solving these variations utilizes a top-down dynamic programming approach.In this paper we show that this approach is amenable to dynamic programming speedup techniques, permitting a speedup of an order of magnitude for many algorithms in the literature for such variations as mixed radix, reserved length and one-ended coding. These speedups are immediate implications of a general structural property that permits batching together the calculation of many DP entries.

Modular non-repeating codes for DNA storage

“…For mixed-radix output, in the special case where the radices at each position are fully specified, the relevant cousin of the Huffman code is the mixed-radix Huffman code, for the discovery of which optimal dynamic programming strate-gies have been presented [47,48]. However, taking this approach in our situation would require a different mixed-radix Huffman code for every possible combination of radices, and so is not particularly convenient for the situation when the number of available coding nucleotides varies from site to site (as in the repeat-avoiding code).…”