# Optimal Compression for Two-Field Entries in Fixed-Width Memories

## TL;DR

This paper addresses the challenge of optimally compressing two-field entries in fixed-width memory systems, providing efficient algorithms and demonstrating superior success probabilities over existing methods.

## Contribution

It introduces an optimal code design algorithm for two-field fixed-width memory compression, including a constrained single-code variant, with proven decompositions and empirical validation.

## Key findings

- Optimal codes significantly improve success probabilities.
- Efficient dynamic programming algorithms are developed.
- Empirical results show superiority over existing algorithms.

## Abstract

Data compression is a well-studied (and well-solved) problem in the setup of long coding blocks. But important emerging applications need to compress data to memory words of small fixed widths. This new setup is the subject of this paper. In the problem we consider we have two sources with known discrete distributions, and we wish to find codes that maximize the success probability that the two source outputs are represented in $L$ bits or less. A good practical use for this problem is a table with two-field entries that is stored in a memory of a fixed width $L$. Such tables of very large sizes drive the core functionalities of network switches and routers. After defining the problem formally, we solve it optimally with an efficient code-design algorithm. We also solve the problem in the more constrained case where a single code is used in both fields (to save space for storing code dictionaries). For both code-design problems we find decompositions that yield efficient dynamic-programming algorithms. With an empirical study we show the success probabilities of the optimal codes for different distributions and memory widths. In particular, the study demonstrates the superiority of the new codes over existing compression algorithms.