Related papers: Code Construction and Decoding Algorithms for Semi…
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such…
Motivated by applications in spatial genomics, we revisit group testing (Dorfman~1943) and propose the class of $\lambda$-{\sf ADD}-codes, studying such codes with certain distance $d$ and codelength $n$. When $d$ is constant, we provide…
Constrained clustering has been well-studied in the unsupervised learning society. However, how to encode constraints into community structure detection, within complex networks, remains a challenging problem. In this paper, we propose a…
In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic…
This paper considers a new secure gradient coding problem with uncoded groupwise keys, formalized as a (K, N, N_r, M, S) secure gradient coding model, where a user aims to compute the sum of the gradients from K datasets with the assistance…
Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the…
Quantization has been an effective technology in ANN (approximate nearest neighbour) search due to its high accuracy and fast search speed. To meet the requirement of different applications, there is always a trade-off between retrieval…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
Quantum Tanner codes are a recently developed family of quantum error-correcting codes characterized by favorable asymptotic performance characteristics. Despite their theoretical potential, practical decoding algorithms that effectively…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
One of the main weakness of the family of centralizer codes is that its length is always $n^2$. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form $nk$.…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
A multi-party quantum key distribution protocol based on repetitive code is designed for the first time in this paper. First we establish a classical (t, n) threshold protocol which can authenticate the identity of the participants, and…
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding…
Quantum reading provides a general framework where to formulate the statistical discrimination of quantum channels. Several paths have been taken for such a problem. However, there is much to be done in the avenue of optimizing channel…
Similarity-based clustering and semi-supervised learning methods separate the data into clusters or classes according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper,…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
To alleviate the suboptimal performance of belief propagation (BP) decoding of short low-density parity-check (LDPC) codes, a plethora of improved decoding algorithms has been proposed over the last two decades. Many of these methods can be…