[Paper Review] Fast Recursive Coding Based on Grouping of Symbols

Nikolay Ponomarenko, Vladimir Lukin+3 more|ArXiv.org|Aug 21, 2007

Algorithms and Data Compression11 references3 citations

TL;DR

This paper proposes a multiplication-free, integer-only recursive coding technique that groups symbols to achieve compression efficiency comparable to arithmetic coding, with code lengths up to 20–30% shorter for large alphabets and only 1–3% worse in the worst case. The method uses recursive partitioning of symbol groups based on cumulative probabilities, enabling fast, low-complexity encoding and decoding without floating-point operations.

ABSTRACT

A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very large alphabets. The code length for the proposed technique can be up to 20-30% less than for arithmetic coding and, in the worst case it is only by 1-3% larger.

Motivation & Objective

• To develop a fast, low-complexity coding method suitable for large alphabets.
• To eliminate multiplication and floating-point arithmetic in compression algorithms.
• To achieve coding efficiency close to or better than arithmetic coding.
• To enable practical implementation in embedded or real-time systems with limited computational resources.

Proposed method

• The algorithm groups symbols into blocks based on their cumulative probabilities to reduce the number of recursive steps.
• It uses recursive partitioning of symbol groups, where each partition is encoded using integer arithmetic only.
• The method operates exclusively with 8-bit integers, avoiding 32-bit or floating-point operations.
• Symbol probabilities are updated recursively within each group, maintaining compression efficiency.
• The recursion is structured to minimize the number of encoding steps while preserving high coding gain.
• The algorithm is designed for both encoding and decoding with low computational overhead.

Experimental results

Research questions

• RQ1 Can a recursive coding method achieve compression efficiency close to arithmetic coding without using multiplication or floating-point operations?
• RQ2 How effective is symbol grouping in reducing the number of recursive steps for large alphabets?
• RQ3 What is the maximum achievable compression gain using integer-only recursive encoding with grouped symbols?
• RQ4 How does the method perform in the worst-case scenario compared to arithmetic coding?
• RQ5 Can the method be implemented efficiently in hardware or embedded systems with minimal computational resources?

Key findings

• The proposed method achieves code lengths up to 20–30% shorter than arithmetic coding for large alphabets.
• In the worst-case scenario, the code length is only 1–3% longer than arithmetic coding.
• The algorithm is multiplication-free and uses only 8-bit integer operations, enabling efficient implementation.
• The recursive structure ensures high compression efficiency even for symbols with highly skewed probabilities.
• The method maintains low computational complexity, making it suitable for real-time or embedded applications.
• The technique demonstrates strong performance across diverse symbol distributions, particularly benefiting from large alphabet sizes.