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Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…
The notion of generalized rank invariant in the context of multiparameter persistence has become an important ingredient for defining interesting homological structures such as generalized persistence diagrams. Naturally, computing these…
We study the problem of channel resolvability for fixed i.i.d. input distributions and discrete memoryless channels (DMCs), and derive the strong converse theorem for any DMCs that are not necessarily full rank. We also derive the optimal…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic…
Duadic group algebra codes are a generalization of quadratic residue codes. This paper settles an open problem raised by Zhu concerning the existence of duadic group algebra codes. These codes can be used to construct degenerate quantum…
It has been shown that $1$-parameter persistence modules have a very simple classification, namely there is a discrete invariant called a barcode that completely characterizes $1$-parameter persistence modules up to isomorphism. In…
Maximally Recoverable Local Reconstruction Codes (LRCs) are codes designed for distributed storage to provide maximum resilience to failures for a given amount of storage redundancy and locality. An $(n,r,h,a,g)$-MR LRC has $n$ coordinates…
A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics…
Locally repairable codes (LRCs) are considered with equal or unequal localities, local distances and local field sizes. An explicit two-layer architecture with a sum-rank outer code is obtained, having disjoint local groups and achieving…
We propose an easy-to-implement hard-decision majority-logic decoding algorithm for Reed-Muller codes RM(r,m) with m >= 3, m/2 >= r >= 1. The presented algorithm outperforms the best known majority-logic decoding algorithms and offers…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Massive multiple-input multiple-output (M-MIMO) technique brings better energy efficiency and coverage but higher computational complexity than small-scale MIMO. For linear detections such as minimum mean square error (MMSE), prohibitive…
The paper proposes to decode Reed-Muller (RM) codes by projecting onto only a few subspaces such that the number of projections is significantly reduced. It reveals that the probability that error pairs are canceled simultaneously in two…
A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
This paper focuses on robust transceiver design for throughput enhancement on the interference channel (IC), under imperfect channel state information (CSI). In this paper, two algorithms are proposed to improve the throughput of the…
Multi-criteria Chinese word segmentation (MCCWS) aims to exploit the relations among the multiple heterogeneous segmentation criteria and further improve the performance of each single criterion. Previous work usually regards MCCWS as…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…