The analytical formulation of crosstalk due to superposition, which is an essential concept of associative memory based on the outer product algorithm, is presented in terms of Hamming distance between the memorized keys and the input key. The formulated result of crosstalk becomes similar to the Krawtchouk polynomial. Some 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 a smaller number of high-order correlation cross products rather than the conventional one. The architecture proposed completely removes crosstalk due to the memorized keys having an odd number Hamming distance from the input key. A relatively large part of the remaining crosstalk due to the memorized keys having an even number Hamming distance from the input key is removed by utilizing the coding technique, which constructs a simple error-correcting Hamming code introducing little redundancy.
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