Color-Rule-Function Encoding for Combinatorial Memory

Abstract: 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.