We introduce a finite, structure-driven framework for neural population coding based on a fixed additive lattice of 2 × 2 matrices. The model defines a predetermined set of sixteen basis matrices whose admissible linear combinations generate stimulus representations in the real number space R. Information encoding is achieved by selecting lattice combinations that maximize entropy, consistent with efficient coding principles. In this proposal, Population coding is formulated as a probabilistic inference problem governed by a Markov state-space model, where transitions occur over lattice states (distinct matrices in the lattice group), as shown in equation (1). Model parameters are inferred via maximum likelihood estimation. Since the compositional structure of the lattice is fixed a priori, the framework decouples population coding computationalcapacity from stringent network connectivity, enabling a fully computable and classical probabilistic formulation of population coding. Beyond the conventional role of population codes as output representations in [11], the proposed population-coded lattice is conceived as a structured input representation for deeplearning architectures, with cross-entropy optimization serving as an objective for pattern classification. This work demonstrates a direct relation between random analog timed-series data and it’s probability encoding, P(si(t)). This work unifies population coding and information theory within a finite matrix-basedframework, offering a computational reinterpretation of neural representation and inference.