arXiv subjects

Hanwen Yao

Publications and source records attributed to Hanwen Yao.

13 recordsLinked to original sources

arXiv2026

Towards Scalable Quaternary Message-Passing Decoding for Quantum Error Correction

The scalability and interpretability of message-passing (MP) decoding, such as (quaternary) Belief Propagation, remain open challenges in quantum error correction. Even for surface codes, arguably the first testbed for decoding methods, studies of improved MP decoders have mostly been restricted to small distances ($d \lesssim 19$). Moreover, the mismatch with established message-passing theory limits the decoder's interpretability, making it unclear whether MP decoding can sustain its effectiveness at large system sizes. This work takes a step toward a more principled and interpretable MP decoding framework, with the goal of making MP-based decoding more reliable and bridging theory and practice. We introduce a dilution method, which allows a quaternary Min-Sum (MS) decoder to exhibit an apparent depolarizing threshold of $16\%$ up to distance $20$, outperforming Minimum-Weight Perfect Matching in finite-length regimes. Notably, for $X$-noise, the standard MS decoder under dilution has worst-case complexity $O(N \log^2 d)$ and outperforms BP-OSD at $d=65$. The observed $\sim 9\%$ threshold may correspond to a true asymptotic threshold. Finally, we give a graph-dilution argument that interprets the success of the dilution method and offers insight into when MP algorithms can genuinely scale. Taken together, these results provide encouraging progress toward scalable and interpretable MP decoding in quantum error correction.

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arXiv2026

Stabilizer-Assisted Inactivation Decoding of Quantum Error-Correcting Codes with Erasures

In this work, we develop a reduced complexity maximum likelihood (ML) decoder for quantum low-density parity-check (QLDPC) codes over erasures. Our decoder combines classical inactivation decoding, which integrates peeling with symbolic guessing, with a new dual peeling procedure. In the dual peeling stage, we perform row operations on the stabilizer matrix to efficiently reveal stabilizer generators and their linear combinations whose support lies entirely on the erased set. Each such stabilizer identified allows us to freely fix a bit in its support without affecting the logical state of the decoded result. This removes one degree of freedom that would otherwise require a symbolic guess, reducing the number of inactivated variables and decreasing the size of the final linear system that must be solved. We further show that dual peeling combined with standard peeling alone, without inactivation, is sufficient to achieve ML for erasure decoding of surface codes. Simulations across several QLDPC code families confirm that our decoder matches ML logical failure performance while significantly reducing the complexity of inactivation decoding, including more than a 20% reduction in symbolic guesses for the B1 lifted product code at high erasure rates.

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arXiv2025

QUITS: A modular Qldpc code circUIT Simulator

To achieve quantum fault tolerance with lower overhead, quantum low-density parity-check (QLDPC) codes have emerged as a promising alternative to topological codes such as the surface code, offering higher code rates. To support their study, an end-to-end framework for simulating QLDPC codes at the circuit level is needed. In this work, we present QUITS, a modular and flexible circuit-level simulator for QLDPC codes. Its design allows users to freely combine LDPC code constructions, syndrome extraction circuits, decoding algorithms, and noise models, enabling comprehensive and customizable studies of the performance of QLDPC codes under circuit-level noise. QUITS supports several leading QLDPC families, including hypergraph product codes, lifted product codes, and balanced product codes. As part of the framework, we introduce a syndrome extraction circuit improved from Tremblay, Delfosse, and Beverland [Phys. Rev. Lett. 129, 050504 (2022)] that applies to all three code families. In particular, for a small hypergraph product code, our circuit achieves lower depth than the conventional method, resulting in improved logical performance. Using QUITS, we evaluate the performance of state-of-the-art QLDPC codes and decoders under various settings, revealing trade-offs between the decoding runtime and the logical failure rate. The source code of QUITS is available online.

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arXiv2024

Cluster Decomposition for Improved Erasure Decoding of Quantum LDPC Codes

We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connelly et al. in 2022. Like the VH decoder, the idea is to first run the peeling decoder and then post-process the resulting stopping set. The cluster decoder breaks the stopping set into a tree of clusters which can be solved sequentially via Gaussian Elimination (GE). By allowing clusters of unconstrained size, this decoder achieves maximum-likelihood (ML) performance with reduced complexity compared with full GE. When GE is applied only to clusters whose sizes are less than a constant, the performance is degraded but the complexity becomes linear in the block length. Our simulation results show that, for hypergraph product codes, the cluster decoder with constant cluster size achieves near-ML performance similar to VH decoding in the low-erasure-rate regime. For the general quantum LDPC codes we studied, the cluster decoder can be used to estimate the ML performance curve with reduced complexity over a wide range of erasure rates.

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arXiv2024

Erasure Decoding for Quantum LDPC Codes via Belief Propagation with Guided Decimation

Quantum low-density parity-check (LDPC) codes are a promising family of quantum error-correcting codes for fault tolerant quantum computing with low overhead. Decoding quantum LDPC codes on quantum erasure channels has received more attention recently due to advances in erasure conversion for various types of qubits including neutral atoms, trapped ions, and superconducting qubits. Belief propagation with guided decimation (BPGD) decoding of quantum LDPC codes has demonstrated good performance in bit-flip and depolarizing noise. In this work, we apply BPGD decoding to quantum erasure channels. Using a natural modification, we show that BPGD offers competitive performance on quantum erasure channels for multiple families of quantum LDPC codes. Furthermore, we show that the performance of BPGD decoding on erasure channels can sometimes be improved significantly by either adding damping or adjusting the initial channel log-likelihood ratio for bits that are not erased. More generally, our results demonstrate BPGD is an effective general-purpose solution for erasure decoding across the quantum LDPC landscape.

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arXiv2024

Belief Propagation Decoding of Quantum LDPC Codes with Guided Decimation

Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction. A variety of decoders have been proposed for QLDPC codes and many of them utilize belief propagation (BP) decoding in some fashion. However, the use of BP decoding for degenerate QLDPC codes is known to have issues with convergence. These issues are typically attributed to short cycles in the Tanner graph and code degeneracy (i.e. multiple error patterns with the same syndrome). Although various methods have been proposed to mitigate the non-convergence issue, such as BP with ordered statistics decoding (BP-OSD) and BP with stabilizer inactivation (BP-SI), achieving better performance with lower complexity remains an active area of research. In this work, we propose a decoder for QLDPC codes based on BP guided decimation (BPGD), which has been previously studied for constraint satisfaction and lossy compression problems. The decimation process is applicable to both binary and quaternary BP and it involves sequentially fixing the value of the most reliable qubits to encourage BP convergence. Despite its simplicity, We find that BPGD significantly reduces the BP failure rate due to non-convergence, achieving performance on par with BP with ordered statistics decoding and BP with stabilizer inactivation, without the need to solve systems of linear equations.

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arXiv2023

Design, Performance, and Complexity of CRC-Aided List Decoding of Convolutional and Polar Codes for Short Messages

Motivated by the need to communicate short control messages in 5G and beyond, this paper carefully designs codes for cyclic redundancy check (CRC)-aided list decoding of tail-biting convolutional codes (TBCCs) and polar codes. Both codes send a 32-bit message using an 11-bit CRC and 512 transmitted bits. We aim to provide a careful, fair comparison of the error performance and decoding complexity of polar and TBCC techniques for a specific case. Specifically, a TBCC is designed to match the rate of a (512, 43) polar code, and optimal 11-bit CRCs for both codes are designed. The paper examines the distance spectra of the polar and TBCC codes, illuminating the different distance structures for the two code types. We consider both adaptive and non-adaptive CRC-aided list decoding schemes. For polar codes, an adaptive decoder must start with a larger list size to avoid an error floor. For rate-32/512 codes with an 11-bit CRC, the optimized CRC-TBCC design achieves a lower total failure rate than the optimized CRC-polar design. Simulations showed that the optimized CRC-TBCC design achieved significantly higher throughput than the optimized CRC-polar design, so that the TBCC solution achieved a lower total failure rate while requiring less computational complexity.

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arXiv2023

A Deterministic Algorithm for Computing the Weight Distribution of Polar Codes

In this work, we present a deterministic algorithm for computing the entire weight distribution of polar codes. As the first step, we derive an efficient recursive procedure to compute the weight distribution that arises in successive cancellation decoding of polar codes along any decoding path. This solves the open problem recently posed by Polyanskaya, Davletshin, and Polyanskii. Using this recursive procedure, at code length n, we can compute the weight distribution of any polar cosets in time O(n^2). We show that any polar code can be represented as a disjoint union of such polar cosets; moreover, this representation extends to polar codes with dynamically frozen bits. However, the number of polar cosets in such representation scales exponentially with a parameter introduced herein, which we call the mixing factor. To upper bound the complexity of our algorithm for polar codes being decreasing monomial codes, we study the range of their mixing factors. We prove that among all decreasing monomial codes with rates at most 1/2, self-dual Reed-Muller codes have the largest mixing factors. To further reduce the complexity of our algorithm, we make use of the fact that, as decreasing monomial codes, polar codes have a large automorphism group. That automorphism group includes the block lower-triangular affine group (BLTA), which in turn contains the lower-triangular affine group (LTA). We prove that a subgroup of LTA acts transitively on certain subsets of decreasing monomial codes, thereby drastically reducing the number of polar cosets that we need to evaluate. This complexity reduction makes it possible to compute the weight distribution of polar codes at length n = 128.

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arXiv2022

Efficient Algorithms for the Bee-Identification Problem

The bee-identification problem, formally defined by Tandon, Tan and Varshney (2019), requires the receiver to identify "bees" using a set of unordered noisy measurements. In this previous work, Tandon, Tan, and Varshney studied error exponents and showed that decoding the measurements jointly results in a significantly smaller error exponent. In this work, we study algorithms related to this joint decoder. First, we demonstrate how to perform joint decoding efficiently. By reducing to the problem of finding perfect matching and minimum-cost matchings, we obtain joint decoders that run in time quadratic and cubic in the number of "bees" for the binary erasure (BEC) and binary symmetric channels (BSC), respectively. Next, by studying the matching algorithms in the context of channel coding, we further reduce the running times by using classical tools like peeling decoders and list-decoders. In particular, we show that our identifier algorithms when used with Reed-Muller codes terminate in almost linear and quadratic time for BEC and BSC, respectively. Finally, for explicit codebooks, we study when these joint decoders fail to identify the "bees" correctly. Specifically, we provide practical methods of estimating the probability of erroneous identification for given codebooks.

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arXiv2022

Polar Coded Modulation via Hybrid Bit Labeling

Bit-interleaved coded modulation (BICM) and multilevel coded modulation (MLC) are commonly used to combine polar codes with high order modulation. While BICM benefits from simple design and the separation of coding and modulation, MLC shows better performance under successive-cancellation decoding. In this paper we propose a hybrid polar coded modulation scheme that lies between BICM and MLC, wherein a fraction of bits are assigned to set-partition (SP) labeling and the remaining bits are assigned for Gray labeling. The SP labeled bits undergo sequential demodulation, using iterative demodulation and polar decoding similar to MLC, whereas the Gray labeled bits are first demodulated in parallel and then sent for decoding similar to BICM. Either polar codes or other channel codes (such as LDPC codes) can be used for the Gray labeled bits. For length 2048 rate 1/2 polar code on 256-QAM, the performance gap between BICM (Gray labeling only) and MLC (SP labeling only) can be almost fully closed by the hybrid scheme. Notably, the hybrid scheme has a significant latency advantage over MLC. These performance gains make the proposed scheme attractive for future communication systems such as 6G.

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arXiv2021

Computing Permanents on a Trellis

The problem of computing the permanent of a matrix has attracted interest since the work of Ryser(1963) and Valiant(1979). On the other hand, trellises were extensively studied in coding theory since the 1960s. In this work, we establish a connection between the two domains. We introduce the canonical trellis $T_n$ that represents all permutations, and show that the permanent of a $n$ by $n$ matrix $A$ can be computed as a flow on this trellis. Under certain normalization, the trellis-based method invokes slightly less operations than best known exact methods. Moreover, if $A$ has structure, then $T_n$ becomes amenable to vertex merging, thereby significantly reducing its complexity. - Repeated rows: Suppose $A$ has only $t<n$ distinct rows. The best known method to compute $per(A)$, due to Clifford and Clifford (2020), has complexity $O(n^{t+1})$. Merging vertices in $T_n$, we obtain a reduced trellis that has complexity $O(n^t)$. - Order statistics: Using trellises, we compute the joint distribution of $t$ order statistics of $n$ independent, but not identically distributed, random variables in time $O(n^{t+1})$. Previously, polynomial-time methods were known only when the variables are drawn from two non-identical distributions. - Sparse matrices: Suppose each entry in $A$ is nonzero with probability $d/n$ with $d$ is constant. We show that $T_n$ can be pruned to exponentially fewer vertices, resulting in complexity $O(ϕ^n)$ with $ϕ<2$. - TSP: Intersecting $T_n$ with another trellis that represents walks, we obtain a trellis that represents circular permutations. Using the latter trellis to solve the traveling salesperson problem recovers the well-known Held-Karp algorithm. Notably, in all cases, the reduced trellis are obtained using known techniques in trellis theory. We expect other trellis-theoretic results to apply to other structured matrices.

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arXiv2020

List Decoding of Arikan's PAC Codes

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short block lengths is far from optimal. Arikan has recently presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. Such PAC codes provide dramatic improvement in performance as compared to both standard successive-cancellation decoding as well as CRC-aided list decoding. Arikan's PAC codes are based primarily upon the following ideas: replacing CRC precoding with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. His simulations show that PAC codes, resulting from the combination of these ideas, are close to finite-length bounds on the performance of any code under ML decoding. One of our main goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size $L$ is moderately large (say, $L \ge 128$). List decoding has distinct advantages over sequential decoding is certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, using these estimates to approximate the union bound on their performance under ML decoding. These results indicate that PAC codes are superior to both polar codes and Reed-Muller codes, and suggest that the goal of rate-profiling may be to optimize the weight distribution at low weights.

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arXiv2019

Explicit Polar Codes with Small Scaling Exponent

Herein, we focus on explicit constructions of $\ell\times\ell$ binary kernels with small scaling exponent for $\ell \le 64$. In particular, we exhibit a sequence of binary linear codes that approaches capacity on the BEC with quasi-linear complexity and scaling exponent $μ< 3$. To the best of our knowledge, such a sequence of codes was not previously known to exist. The principal challenges in establishing our results are twofold: how to construct such kernels and how to evaluate their scaling exponent. In a single polarization step, an $\ell\times\ell$ kernel $K_\ell$ transforms an underlying BEC into $\ell$ bit-channels $W_1,W_2,\ldots,W_\ell$. The erasure probabilities of $W_1,W_2,\ldots,W_\ell$, known as the polarization behavior of $K_\ell$, determine the resulting scaling exponent $μ(K_\ell)$. We first introduce a class of self-dual binary kernels and prove that their polarization behavior satisfies a strong symmetry property. This reduces the problem of constructing $K_\ell$ to that of producing a certain nested chain of only $\ell/2$ self-orthogonal codes. We use nested cyclic codes, whose distance is as high as possible subject to the orthogonality constraint, to construct the kernels $K_{32}$ and $K_{64}$. In order to evaluate the polarization behavior of $K_{32}$ and $K_{64}$, two alternative trellis representations (which may be of independent interest) are proposed. Using the resulting trellises, we show that $μ(K_{32})=3.122$ and explicitly compute over half of the polarization behavior coefficients for $K_{64}$, at which point the complexity becomes prohibitive. To complete the computation, we introduce a Monte-Carlo interpolation method, which produces the estimate $μ(K_{64})\simeq 2.87$. We augment this estimate with a rigorous proof that $μ(K_{64})<2.97$.

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