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arXiv · 2605.05132

A Factor-Graph Formulation of CSS Syndrome Decoding: Joint BP and Four-State BP

Kenta Kasai
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Abstract

For CSS syndrome decoding, the two check matrices impose binary parity-check constraints on the two Pauli error components. The posterior can therefore be written as a binary factor graph with two Tanner graphs coupled by the local joint prior at each qubit. We call the sum-product algorithm on this factorization joint belief propagation (joint BP). Joint BP retains the local channel correlation between the two Pauli components. This note compares joint BP with the four-state Pauli-label factor graph used for four-state BP. The two algorithms are shown to have the same posterior weights, messages, and beliefs after relabeling the four local Pauli states and marginalizing the irrelevant binary component.

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Kenta Kasai. 2026-05-06. A Factor-Graph Formulation of CSS Syndrome Decoding: Joint BP and Four-State BP. https://arxiv.org/abs/2605.05132

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