Efficient Soft-Output Guessing for Enhanced Quantum Tanner Code Decoding

Abstract

We introduce a generalized low-density parity-check decoding framework for quantum Tanner codes utilizing soft-output guessing random additive noise decoding (SOGRAND). By soft-output decoding entire component codes, we mitigate trapping sets and cycles, resulting in improved convergence. SOGRAND, combined with ordered statistic decoding (OSD) post-processing, outperforms the standard belief propagation plus OSD baseline by up to three orders of magnitude in logical error rate, providing a way forward for scalable decoding of the emerging class of Tanner-code-based quantum codes.

Figures (2)

• Figure 1: Overview SOGRAND decoding on GLDPC codes. VN CN. Decoding is performed through iterative message passing on the classical Tanner code (left). During the CN update (right), SOGRAND decodes the incoming LLR $\bm{L_\mathrm{A}^j}$ and computes extrinsic LLR $\bm{L_\mathrm{E}^j}$. Within this process, SOGRAND identifies a list of likely error patterns that satisfy the local syndrome condition, as well as a likelihood that the correct error pattern has not been identified, from which soft-output is extracted.
• Figure 2: Decoding performance for $[[250, 10, 15]]$ and $[[200, 10, 10]]$ quantum Tanner codes (a), (b) Logical block error rate (BLER) under depolarizing noise. SOGRAND decoding (circles) significantly outperforms standard BP (squares). The addition of OSD post-processing (blue) further suppresses errors, with the correlation-aware decoding SOGRAND+OSD* (green) providing the best performance. (c) Convergence of the pseudothreshold $p_\mathrm{th}$ (top) and logical BLER at $p=10^{-3}$ (bottom) as a function of the maximum decoding iterations $N_\mathrm{iter}$.