Combinatorial memory is a class of memory in which information is encoded in the set of paths through a structured mesh. In this work, we introduce a systematic encoding framework, referred to as the Color-Rule-Function (CRF) approach, for representing information in combinatorial memory. The method consists of four key steps: selecting a sequence of paths in the mesh, assigning values (e.g., colors) to each cell, defining a set of rules based on the values encountered along each path, and constructing a Boolean function that determines the state of each path. . The coding procedure is illustrated by several examples. The design space scales of the CRF scale fundamentally faster compared to conventional memory. This apparent advantage arises from the use of rule-based and functional representations but is accompanied by increased hardware complexity. A possible hardware realization of the CRF framework is discussed. Importantly, the hardware overhead can be substantially reduced through the use of customized modules. The examples of the customized design are described in the text. The combination of CRF coding with customized module design may lead to a practical advantage in data storage density. According to the estimates, the data storage density may exceed Exabit per centimeter squared. A key problem that requires further investigation is related to the minimum Hamming distance between an arbitrary target bit sequence and the closest sequence realizable within the CRF framework under fixed hardware constraints.

翻译：组合记忆是一类通过结构化网格中的路径集合来编码信息的记忆方式。本文提出一种名为颜色规则函数（CRF）的系统化编码框架，用于在组合记忆中表示信息。该方法包含四个关键步骤：选择网格中的路径序列、为每个单元格分配数值（如颜色）、根据每条路径上的数值定义一组规则，以及构建确定每条路径状态的布尔函数。通过若干实例阐明了编码过程。相较于传统记忆，CRF的设计空间规模呈指数级更快扩展。这一显著优势源于基于规则和函数的表示方式，但伴随着硬件复杂度的增加。本文讨论了CRF框架的一种可能硬件实现方案。重要的是，通过使用定制化模块可大幅降低硬件开销。文中描述了定制设计的实例。将CRF编码与定制模块设计相结合，可能实现数据存储密度的实际优势。据估计，数据存储密度可能超过每平方厘米百亿亿比特。一个需要进一步研究的关键问题涉及：在固定硬件约束条件下，任意目标比特序列与CRF框架内可实现的最接近序列之间的最小汉明距离。