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Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…
We consider a transmitter that encodes data packets using network coding and broadcasts coded packets. A receiver employing network decoding recovers the data packets if a sufficient number of error-free coded packets are gathered. The…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies of algebraic soft-decision decoding with infinite cost are first studied…
Unsupervised hashing methods have attracted widespread attention with the explosive growth of large-scale data, which can greatly reduce storage and computation by learning compact binary codes. Existing unsupervised hashing methods attempt…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
As one of the three main pillars of fine-grained complexity theory, the 3SUM problem explains the hardness of many diverse polynomial-time problems via fine-grained reductions. Many of these reductions are either directly based on or…
A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is proposed, referred to as tree-based Chase-type algorithm}. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns,…
We generalize the leverage score sampling sketch for $\ell_2$-subspace embeddings, to accommodate sampling subsets of the transformed data, so that the sketching approach is appropriate for distributed settings. This is then used to derive…
This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. The proposed method is applicable to various channels and ensembles. The focus is on both…
This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with…
We provide a geometric characterization of $k$-dimensional $\mathbb{F}_{q^m}$-linear sum-rank metric codes as tuples of $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^k$. We then use this characterization to study one-weight codes in the…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Constraint programming is a family of techniques for solving combinatorial problems, where the problem is modelled as a set of decision variables (typically with finite domains) and a set of constraints that express relations among the…
Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of $q$-ary linear codes under some certain conditions, where $q$ is a power…
This paper is concerned with the ordered statistic decoding with local constraints (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly…
We consider the problem of distributedly computing a general class of functions, referred to as gradient-type computation, while maintaining the privacy of the input dataset. Gradient-type computation evaluates the sum of some `partial…
Optimal modulation (OM) schemes for Gaussian channels with peak and average power constraints are known to require nonuniform probability distributions over signal points, which presents practical challenges. An established way to map…
We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…
Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to…