Effective Depth in Joint Source-Channel Coding: An Implicit Equilibrium Analysis

A fundamental design question in deep joint source-channel coding (Deep JSCC) remains insufficiently explored: given a channel signal-to-noise ratio (SNR), what effective computation depth is required for semantic reconstruction? Existing Deep JSCC systems typically employ fixed-depth neural architectures selected through empirical hyperparameter tuning, which may lead to unnecessary computation under favorable channel conditions and insufficient refinement under severe channel noise. This paper proposes \emph{Implicit-JSCC}, an implicit equilibrium framework in which semantic encoding and decoding are formulated as fixed-point equilibrium processes. The effective encoder and decoder depths are determined by residual-based solver convergence rather than manually predefined layer numbers, while parameter sharing across equilibrium iterations enables depth-independent parameter complexity. To analyze the resulting effective-depth behavior, we develop a Gaussian-process-inspired kernel evolution framework that models equilibrium iterations as an effective-depth propagation process. Since channel noise is injected between the encoder and decoder, the analysis tracks channel-induced representation perturbations across receiver-side equilibrium iterations and derives a theory-guided depth--SNR relationship. After offline calibration of the system-specific parameters, the resulting model characterizes the required receiver-side refinement depth under different SNRs. Extensive experiments show that Implicit-JSCC achieves competitive reconstruction performance while enabling residual-based adaptive inference and controllable computation--quality tradeoffs. The depth--SNR model further provides a characterization of the SNR-dependent refinement depth required to reach a prescribed perturbation tolerance.