It has been shown that a neural network model recently proposed to describe basic memory performance is based on a ternary/binary coding/decoding algorithm which leads to a new neural network assembly memory model (NNAMM) providing maximum-likelihood recall/recognition properties and implying a new memory unit architecture with Hopfield two-layer network, N-channel time gate, auxiliary reference memory, and two nested feedback loops. For the data coding used, conditions are found under which a version of Hopfied network implements maximum-likelihood convolutional decoding algorithm and, simultaneously, linear statistical classifier of arbitrary binary vectors with respect to Hamming distance between vector analyzed and reference vector given. In addition to basic memory performance and etc, the model explicitly describes the dependence on time of memory trace retrieval, gives a possibility of one-trial learning, metamemory simulation, generalized knowledge representation, and distinct description of conscious and unconscious mental processes. It has been shown that an assembly memory unit may be viewed as a model of a smallest inseparable part or an 'atom' of consciousness. Some nontraditional neurobiological backgrounds (dynamic spatiotemporal synchrony, properties of time dependent and error detector neurons, early precise spike firing, etc) and the model's application to solve some interdisciplinary problems from different scientific fields are discussed.