Comparison between theory and simulation for the two-level decoupled Hamming associative memory

Abstract

This paper presents simulations of the capacity and error correction capability of the two-level decoupled Hamming network. The simulation results presented here are compared to the theoretically predicted results derived in a related paper (Ikeda, Watta, and Hassoun, 1998). In this analysis, we study capacity as a function of system dimension, window size, and noise. It is demonstrated that the two-level memory has a large capacity in the case of uniform random fundamental patterns, and that there is close agreement between the theoretical and emperical results.

A Weighted Voting Model of Associative Memory

“…Note that the simple voting memory can be seen as a special case of weighted voting with and all other weights set to zero: . Although there are many possible ways of choosing proper weights, we propose that the weights be set as follows: rank (37) That is, given the fact that we know that a memory pattern is (locally) ranked 1, is the probability that it is, in fact, the target pattern. In noisy environments, the target pattern does not always locally get ranked 1, though; and, given the fact that a memory pattern locally receives a rank of , is the probability that said memory pattern is the target.…”

“…From our assumptions, follows a binomial distribution: (1) where , and is the combination of things taken at a time Similarly, let be a random variable which gives the local distance between the input and one of the nontarget patterns. The distribution for is given by [17], [37] (2) For each , the local window will vote for the target pattern if and , where ranges over all the indices except for the index of the target image. Hence, the probability that a local window will vote for the target pattern is given by…”

“…The two-level decoupled Hamming memory was shown to have a number of advantages over other neural-net-based associative memories [16], [37]. First, it was shown both theoretically and experimentally that the two-level decoupled Hamming memory has high capacity and offers a large amount of error correction.…”