Reduction of Sufficient Number of Code Tables of $k$-Bit Delay Decodable Codes

TL;DR

This paper introduces a method to significantly reduce the number of code tables needed for $k$-bit delay decodable codes, improving efficiency in analysis, construction, and implementation.

Contribution

The paper presents a novel approach to drastically decrease the number of code tables required for optimal $k$-bit delay decodable codes.

Findings

Reduces the number of code tables from exponential to a smaller set.

Enables more efficient code analysis and construction.

Maintains optimal average codeword length with fewer code tables.

Abstract

A $k$-bit delay decodable code-tuple is a lossless source code that can achieve a smaller average codeword length than Huffman codes by using a finite number of code tables and allowing at most $k$-bit delay for decoding. It is known that there exists a $k$-bit delay decodable code-tuple with at most $2^{(2^k)}$ code tables that attains the optimal average codeword length among all the $k$-bit delay decodable code-tuples for any given i.i.d. source distribution. Namely, it suffices to consider only the code-tuples with at most $2^{(2^k)}$ code tables to accomplish optimality. In this paper, we propose a method to dramatically reduce the number of code tables to be considered in the theoretical analysis, code construction, and coding process.