Variable-length Splittable Codes with Multiple Delimiters

TL;DR

This paper introduces variable-length splittable codes with multiple delimiters, demonstrating their theoretical properties, efficient encoding/decoding algorithms, and superior compression performance over Fibonacci codes.

Contribution

It defines and analyzes multi-delimiter splittable codes, proving their completeness, universality, and providing a fast byte-aligned decoding algorithm.

Findings

Multi-delimiter codes are splittable and complete.

Multi-delimiter codes outperform Fibonacci codes in compression.

A fast byte-aligned decoding algorithm is developed for these codes.

Abstract

Variable-length splittable codes are derived from encoding sequences of ordered integer pairs, where one of the pair's components is upper bounded by some constant, and the other one is any positive integer. Each pair is encoded by the concatenation of two fixed independent prefix encoding functions applied to the corresponding components of a pair. The codeword of such a sequence of pairs consists of the sequential concatenation of corresponding pair's encodings. We call such codes splittable. We show that Fibonacci codes of higher orders and codes with multiple delimiters of the form 011...10 are splittable. Completeness and universality of multi-delimiter codes are proved. Encoding of integers by multi-delimiter codes is considered in detail. For these codes, a fast byte aligned decoding algorithm is constructed. The comparative compression performance of Fibonacci codes and different multi-delimiter codes is presented. By many useful properties, multi-delimiter codes are superior to Fibonacci codes.