A Universal Random Coding Ensemble for Sample-Wise Lossy Compression

Area of Science:

• Information Theory
• Data Compression
• Computer Science

Background:

• Rate-distortion theory is fundamental to lossy data compression.
• Lempel-Ziv (LZ) algorithms are widely used for lossless data compression.
• Optimizing code selection is crucial for efficient compression performance.

Purpose of the Study:

• To propose a universal ensemble for random selection of rate-distortion codes.
• To demonstrate the asymptotic optimality of the proposed coding scheme.
• To compare the new scheme against existing methods.

Main Methods:

• Random selection of reproduction vectors based on probability proportional to 2-LZ(x^).
• Analysis using the 1978 Lempel-Ziv (LZ) algorithm for code length.
• Mathematical proofs for asymptotic optimality and converse theorems.

Main Results:

• The proposed ensemble yields an asymptotically optimal variable-rate lossy compression scheme.
• A converse theorem confirms the scheme's performance cannot be essentially improved.
• The new coding scheme demonstrates superior performance compared to shortest LZ code selection.

Conclusions:

• The universal ensemble offers a theoretically sound and practically superior approach to rate-distortion coding.
• This method advances the field of lossy data compression through optimized code selection.
• The findings have implications for designing more efficient compression algorithms.