We introduce an average case analysis of the search primitive operations (equality and thresholding) in associative memories. We provide a general framework for analysis, using as parameters the word space distribution and the CAM size parameters:m(number of memory words) andn(memory word length). Using this framework, we calculate the probability that the whole CAM memory responds to a search primitive operation after comparing up tokmost significant bits (1≤k≤n) in each word; furthermore, we provide a closed formula for the average value ofkand the probability that there exists at least one memory word that equals the centrally broadcast word. Additionally, we derive results for the cases of uniform and exponential distribution of word spaces. We prove that in both cases the average value ofkdepends strongly on lgm, whenn>lgm: for the case of uniform distribution, the average value is practically independent ofn, while in the exponential depends weakly on the difference between the sample space size 2nand the CAM sizem. Furthermore, in both cases, the averagekis approximatelynwhenn≤lgm. Verification of our theoretical results through massive simulations on a parallel machine is presented. One of the main results of this work, that the average value ofkcan be much smaller than n or even practically independent ofnin some cases, has an important practical effect: associative memories can be designed with fast execution times of threshold primitives and low implementation complexity, leading to high performance associative memories that can scale up to sizes larger than previous designs at a low cost.
ASJC Scopus subject areas
- Theoretical Computer Science
- Hardware and Architecture
- Computer Networks and Communications
- Artificial Intelligence