[Paper Review] Results on the Fundamental Gain of Memory-Assisted Universal Source Coding

Ahmad Beirami, Mohsen Sardari+1 more|arXiv (Cornell University)|May 19, 2012

Algorithms and Data Compression11 references4 citations

TL;DR

This paper proposes memory-assisted universal source coding that leverages previously memorized sequences to reduce redundancy in finite-length data compression. By combining context memorization with MDL-based clustering for compound sources, the method achieves up to 6-fold improvement over conventional universal compression, especially for short to moderate sequence lengths.

ABSTRACT

Many applications require data processing to be performed on individual pieces of data which are of finite sizes, e.g., files in cloud storage units and packets in data networks. However, traditional universal compression solutions would not perform well over the finite-length sequences. Recently, we proposed a framework called memory-assisted universal compression that holds a significant promise for reducing the amount of redundant data from the finite-length sequences. The proposed compression scheme is based on the observation that it is possible to learn source statistics (by memorizing previous sequences from the source) at some intermediate entities and then leverage the memorized context to reduce redundancy of the universal compression of finite-length sequences. We first present the fundamental gain of the proposed memory-assisted universal source coding over conventional universal compression (without memorization) for a single parametric source. Then, we extend and investigate the benefits of the memory-assisted universal source coding when the data sequences are generated by a compound source which is a mixture of parametric sources. We further develop a clustering technique within the memory-assisted compression framework to better utilize the memory by classifying the observed data sequences from a mixture of parametric sources. Finally, we demonstrate through computer simulations that the proposed joint memorization and clustering technique can achieve up to 6-fold improvement over the traditional universal compression technique when a mixture of non-binary Markov sources is considered.

Motivation & Objective

• Address the fundamental performance gap in universal compression of finite-length sequences due to inherent redundancy.
• Investigate whether memorizing source statistics at intermediate nodes can yield a fundamental gain over conventional universal compression.
• Develop a clustering technique to effectively utilize memory when sources are mixtures of parametric models (compound sources).
• Characterize the theoretical and practical gains of joint memorization and clustering in memory-assisted compression.
• Demonstrate the effectiveness of a fast MDL-based clustering algorithm for improving compression efficiency in finite-length scenarios.

Proposed method

• Propose a memory-assisted universal source coding framework where intermediate nodes memorize past sequences to inform compression of new sequences.
• Model the source as a compound mixture of parametric sources (e.g., Markov sources) to reflect real-world content generators.
• Introduce a clustering algorithm based on Minimum Description Length (MDL) principle to group similar sequences in memory for efficient context learning.
• Use iterative swapping of sequences between clusters to minimize total description length, improving compression efficiency.
• Apply Context Tree Weighting (CTW) for universal compression and evaluate performance across multiple runs.
• Derive theoretical lower bounds on memorization gain for compound sources and validate them via simulations.

Experimental results

Research questions

• RQ1 Can memorization of past sequences from the same source provide a fundamental gain in universal compression of finite-length sequences?
• RQ2 How does the memorization gain vary with sequence length $n$ and memory size $m$?
• RQ3 What is the performance improvement of joint memorization and clustering compared to memorization without clustering for compound sources?
• RQ4 How can clustering be effectively realized to maximize compression gain in memory-assisted source coding?
• RQ5 To what extent does MDL-based clustering approximate the optimal joint memorization and clustering gain?

Key findings

• For a single parametric source, memorization achieves a significant gain, with over 50% improvement in compression rate for $n = 128$ kB and $m = 8$ MB.
• Theoretical analysis shows that memorization gain diminishes as $n \to \infty$, approaching zero, as expected in the asymptotic regime.
• For a compound source with $\mathcal{K} = 10$ non-binary Markov sources, joint memorization and clustering achieve up to 6-fold improvement over traditional universal compression.
• MDL-based clustering closely approximates the optimal joint memorization and clustering gain, with $g_{\text{MDL}}$ within 0.94–0.998 of $g_{\text{CM}}$ across tested sequence lengths.
• Without clustering, memory-assisted compression can perform worse than conventional universal compression, validating the necessity of clustering for compound sources.
• Simulation results show that $g_{\text{MDL}}$ reaches 1.8862 for $n = 100$ KB and $m = 10$ MB, indicating substantial performance gains even at moderate sequence lengths.