TCD: Time-Conditioned Diffusion Decoding for Binary Short Block Codes

Abstract

Neural channel decoders have attracted growing attention as promising routes for high-performance decoding of short block codes. A recent milestone is denoising diffusion error correction codes (DDECC), which fuses diffusion probabilistic models with a Transformer-based denoiser and outperforms earlier neural approaches. Yet its customized line-search update lacks formal convergence guarantees, and its convergence speed and decoding accuracy can still be improved. To overcome these limitations, we propose time-conditioned diffusion (TCD) decoder, a continuous-time neural decoder built upon stochastic differential equation (SDE) theory. TCD leverages high-order diffusion samplers to achieve theoretically-grounded, fast convergence. It further introduces 1) a time-conditioned Transformer-based denoiser with continuous embeddings, 2) an initialization that maps received signals to valid diffusion states, and 3) an early-stopping rule tailored for decoding. Moreover, we derive three analytically driven, low-complexity guidance schemes—likelihood-gradient, posterior-mean, and their hybrid—conditioned on the received signal to further enhance decoding accuracy. Simulations on BCH, LDPC, Polar codes show that guided TCD outperforms DDECC across nearly all settings while markedly reducing computational cost. Against other universal neural decoders, TCD achieves state-of-the-art performance, further closing the gap to maximum-likelihood decoding.