Predictive-State Communication: Innovation Coding and Reconciliation under Delay

Abstract: Shannon theory models communication as the reliable transfer of symbol sequences, with performance governed by capacity and rate-distortion limits. When both endpoints possess strong predictors -- as in modern LLMs and related generative priors -- literal symbol transport is no longer the only operational regime. We propose predictive-state communication (PSC), in which the transmitter and receiver maintain an explicit shared predictive state, and the physical channel is used primarily to convey innovations, i.e., corrective information that reconciles the receiver's provisional trajectory with the transmitter's realized trajectory. This viewpoint replaces entropy-rate accounting by cross-entropy accounting under model mismatch, and it introduces feasibility constraints that depend jointly on capacity, delay, and perceptual continuity requirements; the resulting operating set is typically a bounded perception-capacity band rather than a one-sided threshold. We outline the protocol and architectural implications (state identifiers, anchors, bounded rollback, and patch-based updates) and provide a stylized illustrative example to visualize the induced feasibility region and its dependence on predictive quality.