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Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
Arithmetic coding is an essential class of coding techniques. One key issue of arithmetic encoding method is to predict the probability of the current coding symbol from its context, i.e., the preceding encoded symbols, which usually can be…
The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and…
For $q$ a prime power, the discrete logarithm problem (DLP) in $\mathbb{F}_{q}$ consists in finding, for any $g \in \mathbb{F}_{q}^{\times}$ and $h \in \langle g \rangle$, an integer $x$ such that $g^x = h$. We present an algorithm for…
Efficient and scalable decoding of quantum codes is essential for high-performance quantum error correction. In this work, we introduce Reliable Subset Reduction (RSR), a reliability-driven preprocessing framework that leverages belief…
In this paper, we study the discrete logarithm problem in the finite fields $\F_{q^n}$ where $n|q-1$. The field is called a Kummer field or a Kummer extension of $\F_q$. It plays an important role in improving the AKS primality proving…
Since the elliptic curve discrete logarithms problem (ECDLP) was proposed, it has been widely used in cryptosystem because of its strong security. Although the proposal of the extended Shor's algorithm offers hope for cracking ECDLP, it is…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
Gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs). Motivated by the fact that existing ODEs do not distinguish between two fundamentally different…
Under polynomial time reduction, the maximum likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
Different quantum error correction schemes trade off overhead, error suppression, and hardware connectivity. Code concatenation can relax these tradeoffs by using an outer code whose non-local connectivity is supplied by logical operations…
The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques,…
$\newcommand{\NP}{\mathsf{NP}}\newcommand{\GapSVP}{\textrm{GapSVP}}$We give a simple proof that the (approximate, decisional) Shortest Vector Problem is $\NP$-hard under a randomized reduction. Specifically, we show that for any $p \geq 1$…
Real quantum computers will be subject to complicated, qubit-dependent noise, instead of simple noise such as depolarizing noise with the same strength for all qubits. We can do quantum error correction more effectively if our decoding…
In this paper, we provide a theoretical analysis of the recently introduced weakly adversarial networks (WAN) method, used to approximate partial differential equations in high dimensions. We address the existence and stability of the…
To improve the quality of computation experience for mobile devices, mobile-edge computing (MEC) is a promising paradigm by providing computing capabilities in close proximity within a sliced radio access network (RAN), which supports both…
The Slepian-Wolf (SW) coding system is a source coding system with two encoders and a decoder, where these encoders independently encode source sequences from two correlated sources into codewords, and the decoder reconstructs both source…