Construction of high-order correlation associative memory with novel retrieval cost performance

Crosstalk due to superposition, which is an essential concept of associative memory based on the outer product algorithm, is explicitly formulated in terms of Hamming distance between the memorized keys and input key. Some noticeable properties of crosstalk, such as symmetricity, linear independency, and cancellation characteristics, are derived by using the Krawtchouk polynomial. These properties are highly useful for reducing crosstalk and make it possible to propose a new architecture of associative memory with fewer high-order correlation cross products than the conventional architecture. The architecture proposed completely removes crosstalk due to the memorized keys having odd number Hamming distance from the input key. In order to remove relatively large parts of the residual crosstalk due to even number Hamming distance from the input key, a coding technique which constructs a simple error correcting Hamming code including relatively little redundancy is introduced