Predictive-State Communication: Innovation Coding and Reconciliation under Delay

TL;DR

Predictive-State Communication (PSC) reframes interactive, delay-dominated communication as state synchronization rather than verbatim symbol transport. By maintaining a shared predictive state and transmitting primarily innovations, PSC ties the required channel load to cross-entropy under model mismatch, yielding a perception–capacity band that jointly depends on predictive quality, delay $L$, and capacity: $r_{\min}(L,\cdot) \le r \le \min\{ r_{\max}(L,\cdot), \frac{C_{\mathrm{innov}}}{\bar{h}} \}$. The paper introduces architectural primitives—StateID, anchors, bounded rollback, and patch-based reconciliation—and mismatch signals to operationalize PSC, then illustrates the feasibility band with a stylized example using cross-entropy proxies. It also outlines open research directions in state standardization, patch coding, delay-aware control, security, and evaluation methodologies, highlighting PSC’s potential for more efficient, responsive interactions in AI-assisted communication systems where predictive priors are strong and delay is significant.

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 large language models 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.

Figures (2)

• Figure 1: System architecture; the physical channel carries only innovation bits.
• Figure 2: Illustration of PSC. (A) Innovation load versus token rate for three predictors against a fixed link budget; better prediction lowers innovation load. (B) Operating interval for the learned predictor between starvation floor and capacity/delay ceiling; shaded region shows feasible rates. (C) Operation schematic: receiver speculates for continuity; sender transmits compact patch to restore agreement without full retransmission.