Efficient and Compact Representations of Some Non-Canonical Prefix-Free Codes
Antonio Fari\~na, Travis Gagie, Szymon Grabowski, Giovanni Manzini,, Gonzalo Navarro, Alberto Ord\'o\~nez

TL;DR
This paper introduces efficient, compact data structures for storing and processing various types of prefix-free codes, enabling fast encoding and decoding with minimal space, applicable in the word-RAM computational model.
Contribution
It presents novel space-efficient representations for optimal and nearly optimal prefix-free codes, including alphabetic and lexicographically ordered variants, with improved encoding and decoding times.
Findings
Optimal alphabetic prefix-free code stored in O(σ log L) bits
Encoding and decoding in O(min(ℓ, log L)) time
Nearly optimal alphabetic code stored in o(σ) bits with constant-time operations
Abstract
For many kinds of prefix-free codes there are efficient and compact alternatives to the traditional tree-based representation. Since these put the codes into canonical form, however, they can only be used when we can choose the order in which codewords are assigned to symbols. In this paper we first show how, given a probability distribution over an alphabet of symbols, we can store an optimal alphabetic prefix-free code in bits such that we can encode and decode any codeword of length in time, where is the maximum codeword length. With further bits, for any constant , we can encode and decode time. We then show how to store a nearly optimal alphabetic prefix-free code in \(o (\sigma)\) bits such that we can encode and decode in constant time. We also consider a kind of…
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Taxonomy
TopicsAlgorithms and Data Compression · DNA and Biological Computing · semigroups and automata theory
