TL;DR
This paper introduces a polynomial-time dynamic programming algorithm for reserved-length prefix coding, enabling optimal lossless encoding with length restrictions, and extends to quasiarithmetic and g-length constrained codes.
Contribution
The paper presents a novel polynomial-time algorithm for reserved-length prefix coding and its extensions, improving encoding efficiency under length constraints.
Findings
Efficient optimal codes for reserved-length constraints
Extension to quasiarithmetic prefix coding
Method for codes with a fixed number of codeword lengths
Abstract
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).
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Taxonomy
TopicsAlgorithms and Data Compression · Error Correcting Code Techniques · Advanced Wireless Communication Techniques