arXiv subjects

Yeow Meng Chee

Publications and source records attributed to Yeow Meng Chee.

At least 19 recordsLinked to original sources

arXiv2026

Chouinard's Conjecture for Graphical t-Designs

A $t$-wise balanced design on the edge set of a complete graph is graphical if its block multiset is invariant under the induced action of the symmetric group on the vertices. Chouinard conjectured that, for each fixed index $\lambda$, there are only finitely many nontrivial simple graphical $t$-wise balanced designs with $t>1$. We prove the conjecture for $t$-designs, which are the $t$-wise balanced designs whose blocks all have the same size. Our theorem does not require simplicity, and we bound all parameters of the designs by explicit polynomials in $\lambda$.

math.CO↗

arXiv2026

On $t$-edge-balanced graphs

A graph $G$ on $n$ vertices with $k$ edges is $t$-edge-balanced if every graph on $n$ vertices with $t$ edges is contained in exactly the same number of subgraphs of $K_n$ isomorphic to $G$. Despite the existence of infinite families of $2$-edge-balanced graphs, no $t$-edge-balanced graphs were known for $t \ge 3$. This paper resolves the existence question for $t \ge 3$ in two directions. For $t = 3$, we derive necessary arithmetic conditions on the parameters $(n,k)$ and use a simulated annealing search to find the first known examples of $3$-edge-balanced graphs. For $t \ge 4$, we prove that no nontrivial $t$-edge-balanced graphs exist.

math.CO↗

arXiv2026

A Mixture of Experts Vision Transformer for High-Fidelity Surface Code Decoding

Quantum error correction is a key ingredient for large scale quantum computation, protecting logical information from physical noise by encoding it into many physical qubits. Topological stabilizer codes are particularly appealing due to their geometric locality and practical relevance. In these codes, stabilizer measurements yield a syndrome that must be decoded into a recovery operation, making decoding a central bottleneck for scalable real time operation. Existing decoders are commonly classified into two categories. Classical algorithmic decoders provide strong and well established baselines, but may incur substantial computational overhead at large code distances or under stringent latency constraints. Machine learning based decoders offer fast GPU inference and flexible function approximation, yet many approaches do not explicitly exploit the lattice geometry and local structure of topological codes, which can limit performance. In this work, we propose QuantumSMoE, a quantum vision transformer based decoder that incorporates code structure through plus shaped embeddings and adaptive masking to capture local interactions and lattice connectivity, and improves scalability via a mixture of experts layer with a novel auxiliary loss. Experiments on the toric code demonstrate that QuantumSMoE outperforms state-of-the-art machine learning decoders as well as widely used classical baselines.

quant-ph↗

arXiv2026

Sequence Reconstruction for Sticky Insertion/Deletion Channels

The sequence reconstruction problem for insertion/deletion channels has attracted significant attention owing to their applications recently in some emerging data storage systems, such as racetrack memories, DNA-based data storage. Our goal is to investigate the reconstruction problem for sticky-insdel channels where both sticky-insertions and sticky-deletions occur. If there are only sticky-insertion errors, the reconstruction problem for sticky-insertion channel is a special case of the reconstruction problem for tandem-duplication channel which has been well-studied. In this work, we consider the $(t, s)$-sticky-insdel channel where there are at most $t$ sticky-insertion errors and $s$ sticky-deletion errors when we transmit a message through the channel. For the reconstruction problem, we are interested in the minimum number of distinct outputs from these channels that are needed to uniquely recover the transmitted vector. We first provide a recursive formula to determine the minimum number of distinct outputs required. Next, we provide an efficient algorithm to reconstruct the transmitted vector from erroneous sequences.

cs.IT↗

arXiv2026

Efficient Approximation of Quantum Channel Fidelity Exploiting Symmetry

Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021] introduced an asymptotically converging semidefinite programming hierarchy of outer bounds for this quantity. However, the size of the semidefinite programs (SDPs) grows exponentially with respect to the level of the hierarchy, thus making their computation unscalable. In this work, by exploiting the symmetries in the SDP, we show that, for a fixed output dimension of the quantum channel, we can compute the SDP in time polynomial with respect to the level of the hierarchy and input dimension. As a direct consequence of our result, the optimal fidelity can be approximated with an accuracy of $ε$ in $\mathrm{poly}(1/ε, \text{input dimension})$ time.

quant-ph↗

arXiv2026

Modeling Concurrency Control as a Learnable Function

Concurrency control (CC) algorithms are important in modern transactional databases, as they enable high performance by executing transactions concurrently while ensuring correctness. However, state-of-the-art CC algorithms struggle to perform well across diverse workloads, and most do not consider workload drifts. In this paper, we propose NeurCC, a novel learned concurrency control algorithm that achieves high performance across diverse workloads. The algorithm is quick to optimize, making it robust against dynamic workloads. It learns a function that captures a large number of design choices from existing CC algorithms. The function is implemented as an efficient in-database lookup table that maps database states to concurrency control actions. The learning process is based on a combination of Bayesian optimization and a novel graph reduction search algorithm, which converges quickly to a function that achieves high transaction throughput. We compare NeurCC against five state-of-the-art CC algorithms and show that it consistently outperforms the baselines both in transaction throughput and in optimization time.

cs.DB↗

arXiv2025

On de Bruijn Array Codes Part II: Linear Codes

An M-sequence generated by a primitive polynomial has many interesting and desirable properties. A pseudo-random array is the two-dimensional generalization of an M-sequence. There are non-primitive polynomials all of whose non-zero sequences have the same period. These polynomials generate \emph{sets} of sequences with properties similar to M-sequences. In this paper, a two-dimensional generalization for such sequences is given. This generalization is for a pseudo-random array code, which is a set of $r_1 \times r_2$ arrays in which each $n_1 \times n_2$ nonzero matrix is contained exactly once as a window in one of the arrays. Moreover, these arrays have the shift-and-add property, i.e., the bitwise addition of two arrays (or a nontrivial shift of such arrays) is another array (or a shift of another array) from the code. All the known arrays can be formed by folding sequences generated from an irreducible polynomial or a reducible polynomial whose factors have the same degree and the same exponent. Two proof techniques are used to prove the constructions are indeed of pseudo-random array codes. The first technique is based on another method, different from folding, for constructing some of these arrays. The second technique is a generalization of a known proof technique. This generalization enables the construction of pseudo-random arrays with parameters not known before, and also provides a variety of pseudo-random array codes which cannot be generated by the first method. The two techniques also suggest two different hierarchies between pseudo-random array codes. Finally, two methods to verify whether a folding of sequences, generated by these polynomials, yields a pseudo-random array or a pseudo-random array code, will be presented.

cs.IT↗

arXiv2025

Constructions of Covering Sequences and Arrays

An $(n,R)$-covering sequence is a cyclic sequence whose consecutive $n$-tuples form a code of length $n$ and covering radius $R$. Using several construction methods improvements of the upper bounds on the length of such sequences for $n \leq 20$ and $1 \leq R \leq 3$, are obtained. The definition is generalized in two directions. An $(n,m,R)$-covering sequence code is a set of cyclic sequences of length $m$ whose consecutive $n$-tuples form a code of length~$n$ and covering radius $R$. The definition is also generalized to arrays in which the $m \times n$ sub-matrices form a covering code with covering radius $R$. We prove that asymptotically there are covering sequences that attain the sphere-covering bound up to a constant factor.

math.CO↗

arXiv2025

Optimal Multi-Objective Best Arm Identification with Fixed Confidence

We consider a multi-armed bandit setting with finitely many arms, in which each arm yields an $M$-dimensional vector reward upon selection. We assume that the reward of each dimension (a.k.a. {\em objective}) is generated independently of the others. The best arm of any given objective is the arm with the largest component of mean corresponding to the objective. The end goal is to identify the best arm of {\em every} objective in the shortest (expected) time subject to an upper bound on the probability of error (i.e., fixed-confidence regime). We establish a problem-dependent lower bound on the limiting growth rate of the expected stopping time, in the limit of vanishing error probabilities. This lower bound, we show, is characterised by a max-min optimisation problem that is computationally expensive to solve at each time step. We propose an algorithm that uses the novel idea of {\em surrogate proportions} to sample the arms at each time step, eliminating the need to solve the max-min optimisation problem at each step. We demonstrate theoretically that our algorithm is asymptotically optimal. In addition, we provide extensive empirical studies to substantiate the efficiency of our algorithm. While existing works on pure exploration with multi-objective multi-armed bandits predominantly focus on {\em Pareto frontier identification}, our work fills the gap in the literature by conducting a formal investigation of the multi-objective best arm identification problem.

cs.LG↗

arXiv2024

Permutation and Multi-permutation Codes Correcting Multiple Deletions

Permutation codes in the Ulam metric, which can correct multiple deletions, have been investigated extensively recently. In this work, we are interested in the maximum size of permutation codes in the Ulam metric and aim to design permutation codes that can correct multiple deletions with efficient decoding algorithms. We first present an improvement on the Gilbert--Varshamov bound of the maximum size of these permutation codes by analyzing the independence number of the auxiliary graph. The idea is widely used in various cases and our contribution in this section is enumerating the number of triangles in the auxiliary graph and showing that it is small enough. Next, we design permutation codes correcting multiple deletions with a decoding algorithm. In particular, the constructed permutation codes can correct $t$ deletions with at most $(3t-1) \log n+o(\log n)$ bits of redundancy where $n$ is the length of the code. Our construction is based on a new mapping which yields a new connection between permutation codes in the Hamming metric and permutation codes in various metrics. Furthermore, we construct permutation codes that correct multiple bursts of deletions using this new mapping. Finally, we extend the new mapping for multi-permutations and construct the best-known multi-permutation codes in Ulam metric.

cs.IT↗

arXiv2024

Maximum Length RLL Sequences in de Bruijn Graph

Free-space quantum key distribution requires to synchronize the transmitted and received signals. A timing and synchronization system for this purpose based on a de Bruijn sequence has been proposed and studied recently for a channel associated with quantum communication that requires reliable synchronization. To avoid a long period of no-pulse in such a system on-off pulses are used to simulate a \emph{zero} and on-on pulses are used to simulate a \emph{one}. However, these sequences have high redundancy and low rate. To reduce the redundancy and increase the rate, run-length limited sequences in the de Bruijn graph are proposed for the same purpose. The maximum length of such sequences in the de Bruijn graph is studied and an efficient algorithm to construct a large set of these sequences is presented. Based on known algorithms and enumeration methods, maximum length sequence for which the position of each window can be computed efficiently is presented and an enumeration on the number of such sequences is given.

cs.IT↗

arXiv2024

Pairs in Nested Steiner Quadruple Systems

Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs. Each pair in such a partition is called a nested design pair and its multiplicity is the number of times it is a pair in this partition. Such a partition of each block is considered as a new block design called a nested Steiner quadruple system. Several related questions on this type of design are considered in this paper: What is the maximum multiplicity of the nested design pair with minimum multiplicity? What is the minimum multiplicity of the nested design pair with maximum multiplicity? Are there nested quadruple systems in which all the nested design pairs have the same multiplicity? Of special interest are nested quadruple systems in which all the $\binom{v}{2}$ pairs are nested design pairs with the same multiplicity. Several constructions of nested quadruple systems are considered and in particular classic constructions of SQS are examined.

math.CO↗

arXiv2024

Repairing Reed-Solomon Codes with Side Information

We generalize the problem of recovering a lost/erased symbol in a Reed-Solomon code to the scenario in which some side information about the lost symbol is known. The side information is represented as a set $S$ of linearly independent combinations of the sub-symbols of the lost symbol. When $S = \varnothing$, this reduces to the standard problem of repairing a single codeword symbol. When $S$ is a set of sub-symbols of the erased one, this becomes the repair problem with partially lost/erased symbol. We first establish that the minimum repair bandwidth depends on $|S|$ and not the content of $S$ and construct a lower bound on the repair bandwidth of a linear repair scheme with side information $S$. We then consider the well-known subspace-polynomial repair schemes and show that their repair bandwidths can be optimized by choosing the right subspaces. Finally, we demonstrate several parameter regimes where the optimal bandwidths can be achieved for full-length Reed-Solomon codes.

cs.IT↗

arXiv2024

On de Bruijn Covering Sequences and Arrays

An $(m,n,R)$-de Bruijn covering array (dBCA) is a doubly periodic $M \times N$ array over an alphabet of size $q$ such that the set of all its $m \times n$ windows form a covering code with radius $R$. An upper bound of the smallest array area of an $(m,n,R)$-dBCA is provided using a probabilistic technique which is similar to the one that was used for an upper bound on the length of a de Bruijn covering sequence. A folding technique to construct a dBCA from a de Bruijn covering sequence or de Bruijn covering sequences code is presented. Several new constructions that yield shorter de Bruijn covering sequences and $(m,n,R)$-dBCAs with smaller areas are also provided. These constructions are mainly based on sequences derived from cyclic codes, self-dual sequences, primitive polynomials, an interleaving technique, folding, and mutual shifts of sequences with the same covering radius. Finally, constructions of de Bruijn covering sequences codes are also discussed.

cs.IT↗

arXiv2024

Efficient designs for threshold group testing without gap

Given $d$ defective items in a population of $n$ items with $d \ll n$, in threshold group testing without gap, the outcome of a test on a subset of items is positive if the subset has at least $u$ defective items and negative otherwise, where $1 \leq u \leq d$. The basic goal of threshold group testing is to quickly identify the defective items via a small number of tests. In non-adaptive design, all tests are designed independently and can be performed in parallel. The decoding time in the non-adaptive state-of-the-art work is a polynomial of $(d/u)^u (d/(d-u))^{d - u}, d$, and $\log{n}$. In this work, we present a novel design that significantly reduces the number of tests and the decoding time to polynomials of $\min\{u^u, (d - u)^{d - u}\}, d$, and $\log{n}$. In particular, when $u$ is a constant, the number of tests and the decoding time are $O(d^3 (\log^2{n}) \log{(n/d)} )$ and $O\big(d^3 (\log^2{n}) \log{(n/d)} + d^2 (\log{n}) \log^3{(n/d)} \big)$, respectively. For a special case when $u = 2$, with non-adaptive design, the number of tests and the decoding time are $O(d^3 (\log{n}) \log{(n/d)} )$ and $O(d^2 (\log{n} + \log^2{(n/d)}) )$, respectively. Moreover, with 2-stage design, the number of tests and the decoding time are $O(d^2 \log^2{(n/d)} )$.

cs.IT↗

arXiv2024

Repairing with Zero Skip Cost

To measure repair latency at helper nodes, we introduce a new metric called skip cost that quantifies the number of contiguous sections accessed on a disk. We provide explicit constructions of zigzag codes and fractional repetition codes that incur zero skip cost

cs.IT↗

arXiv2024

Recovery Sets of Subspaces from a Simplex Code

Recovery sets for vectors and subspaces are important in the construction of distributed storage system codes. These concepts are also interesting in their own right. In this paper, we consider the following very basic recovery question: what is the maximum number of possible pairwise disjoint recovery sets for each recovered element? The recovered elements in this work are d-dimensional subspaces of a $k$-dimensional vector space over GF(q). Each server stores one representative for each distinct one-dimensional subspace of the k-dimensional vector space, or equivalently a distinct point of PG(k-1,q). As column vectors, the associated vectors of the stored one-dimensional subspaces form the generator matrix of the $[(q^k -1)/(q-1),k,q^{k-1}]$ simplex code over GF(q). Lower bounds and upper bounds on the maximum number of such recovery sets are provided. It is shown that generally, these bounds are either tight or very close to being tight.

cs.IT↗

arXiv2024

On the Asymptotic Nonnegative Rank of Matrices and its Applications in Information Theory

In this paper, we study the asymptotic nonnegative rank of matrices, which characterizes the asymptotic growth of the nonnegative rank of fixed nonnegative matrices under the Kronecker product. This quantity is important since it governs several notions in information theory such as the so-called exact Rényi common information and the amortized communication complexity. By using the theory of asymptotic spectra of V. Strassen (J. Reine Angew. Math. 1988), we define formally the asymptotic spectrum of nonnegative matrices and give a dual characterization of the asymptotic nonnegative rank. As a complementary of the nonnegative rank, we introduce the notion of the subrank of a nonnegative matrix and show that it is exactly equal to the size of the maximum induced matching of the bipartite graph defined on the support of the matrix (therefore, independent of the value of entries). Finally, we show that two matrix parameters, namely rank and fractional cover number, belong to the asymptotic spectrum of nonnegative matrices.

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