Related papers: Sequence Folding, Lattice Tiling, and Multidimensi…
Network coding is a new technique to transmit data through a network by letting the intermediate nodes combine the packets they receive. Given a network, the network coding solvability problem decides whether all the packets requested by…
Constant dimension codes (CDCs) are essential for error correction in random network coding. A fundamental problem of CDCs is to determine their maximal possible size for given parameters. Inserting construction and multilevel construction…
This paper introduces a novel framework for constructing algebraic lattices based on Construction-D, leveraging nested linear codes and prime ideals from algebraic number fields. We focus on the application of these lattices in block-fading…
Linear integer constraints are one of the most important constraints in combinatorial problems since they are commonly found in many practical applications. Typically, encodings to Boolean satisfiability (SAT) format of conjunctive normal…
A space-filling curve (SFC) maps points in a multi-dimensional space to one-dimensional points by discretizing the multi-dimensional space into cells and imposing a linear order on the cells. This way, an SFC enables the indexing of…
Aperiodic tiling --- a form of complex global geometric structure arising through locally checkable, constant-time matching rules --- has long been closely tied to a wide range of physical, information-theoretic, and foundational…
A new achievable rate region is given for the Gaussian cognitive many-to-one interference channel. The proposed novel coding scheme is based on the compute-and-forward approach with lattice codes. Using the idea of decoding sums of…
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
Spatially coupled low-density parity-check (SC-LDPC) codes are a class of capacity approaching LDPC codes with low message recovery latency when a sliding window decoding is used. In this paper, we first present a new method for the…
Two-dimensional lattices provide the arena for many physics problems of essential importance, a non-trivial symmetry in such lattices will help to reveal the underlying physics. Whether there is a directional scaling for the 2D lattices is…
This work addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. In contrast to the standard approach in the literature which employs random…
While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learnt how to extract this information so as to predict the detailed, biological active, three-dimensional structure of…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
Benders' decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be…
The tiling problem has been a famous problem that has appeared in many Mathematics problems. Many of its solutions are rooted in high-level Mathematics. Thus we hope to tackle this problem using more elementary Mathematics concepts. In this…
We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a…
We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from…
We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…
Proving capacity for networks without feedback or cooperation usually involves two fundamental random coding techniques: superposition coding and binning. Although conceptually very different, these two techniques often achieve the same…