The extrinsic information transfer (EXIT) and generalized EXIT (GEXIT) area theorems provide fundamental conservation laws that connect the rate of classical codes to the performance of maximum-a-posteriori decoding on binary memoryless channels. In this work, we generalize these area theorems to quantum error correcti...
Avijit Mandal, Mert Gökduman, Henry D. Pfister· 0 citations
We introduce a diffusion framework for neural decoding of error-correcting codes (ECCs). We interpret decoding as a conditional diffusion process that progressively predicts codeword bits while treating the physical channel observation as fixed side information. At each stage, a neural model estimates bitwise posterior...
While the ultimate limits on the rate of quantum communication over noisy channels are well-established, very few efficient coding schemes achieving these limits are known. This contrasts sharply with transmitting classical data over classical channels, where polar codes and low-density parity-check codes both efficien...
Avijit Mandal, C. Piveteau, Henry D. Pfister et al.· 0 citations
The results justify the use of BPQM in the decoding step of DQI and of coding-theoretic algorithms based on Regev's reduction whenever the code is drawn from one of the random LDPC ensembles analyzed here and the induced memoryless symmetric pure-state channel lies in the BPQM success region.
Avijit Mandal, C. Piveteau, J. Renes et al.· 3 citations
While autoregressive models optimize the exact data likelihood via the chain rule, diffusion models are typically trained with denoising objectives. We develop conservation laws based on generalized extrinsic information transfer (GEXIT) functions for a broad class of memoryless noise processes, showing that the data--...
Ziv Aharoni, Henry D. Pfister· arXiv.org· 0 citations
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