Multi-Pattern Real-Valued Spectral Associative Memories

A multi-pattern encoding and decoding scheme is presented that extends the family of spectral associative memories (SAMs) to include gray-level, or analog patterns. SAMs are frequency-domain formulations of associative memory that combine the extrinsic redundancy of neural networks with the in-phase, quadrature, and complex modulation schemes of communications. Considerable coding gain occurs at the level of modulation and these networks may be regarded as multi-channel, multi-carrier generalizations of amplitude modulation. Unlike multi-pattern bipolar SAMs, which are exclusively content-addressable, real-valued SAMs also have an address-addressable mode in which the recall of a particular memory may be forced. Band structures and anti-aliasing constraints are presented along with a probabilistic formulation in which virtual entanglement is a natural feature. Simulations are presented that demonstrate dual-memory recall for 6x6 gray-level patterns.