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Spatial complementary code keying modulation (SCCKM) is proposed as a novel block coding modulation scheme. An input binary sequence is modulated based on the different lengths of complementary code keying (CCK) modulation and then spread…
We present a new explicit construction of onesided bipartite lossless expanders of constant degree, with arbitrary constant ratio between the sizes of the two vertex sets. Our construction is simpler to state and analyze than the only prior…
Multi-dimensional coherent spectroscopy (MDCS)1,2 is a powerful method for optical spectroscopy that has become an important tool for studying ultrafast dynamics in a wide range of systems. It is an optical analog of multidimensional…
In the research of next-generation wireless communication technologies, orthogonal time frequency space (OTFS) modulation is emerging as a promising technique for high-speed mobile environments due to its superior efficiency and robustness…
Zero correlation zone (ZCZ) sequences and Golay sequences are two kinds of sequences with different preferable correlation properties. It was shown by Gong \textit{et al.} and Chen \textit{et al.} that some Golay sequences also possess a…
Orthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is…
Exponential, de Vaucouleurs, and S\'ersic profiles are simple and successful models for fitting two-dimensional images of galaxies. One numerical issue encountered in this kind of fitting is the pixel rendering and convolution (or…
Spatially-coupled (SC) codes are constructed by coupling many regular low-density parity-check codes in a chain. The decoding chain of SC codes stops when facing burst erasures. This problem can not be overcome by increasing coupling…
One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) =…
Several new constructions of 3-dimensional optical orthogonal codes are presented here. In each case the codes have ideal autocorrelation $\mathbf{ \lambda_a=0} $, and in all but one case a cross correlation of $ \mathbf{\lambda_c=1} $. All…
We compute out-of-time-order correlators (OTOCs) in two-dimensional holographic conformal field theories (CFTs) with different left- and right-moving temperatures. Depending on whether the CFT lives on a spatial line or circle, the dual…
Certain applications require the use of signals that combine both the capability to operate with low signal-to-noise ratios and the ability to support multiple users without interference. In the case where many users have very different…
Controlling and engineering continuous spectral modes of entangled photons represents one of the promising approaches toward secure quantum communications. By using the telecom bandwidth generated from a cascade-emitted biphoton in atomic…
Orthogonal Time Frequency Space (OTFS) is a $\text{2-D}$ modulation technique that has the potential to overcome the challenges faced by orthogonal frequency division multiplexing (OFDM) in high Doppler environments. The performance of OTFS…
Hypercontractivity is one of the most powerful tools in Boolean function analysis. Originally studied over the discrete hypercube, recent years have seen increasing interest in extensions to settings like the $p$-biased cube, slice, or…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
The agents within a multi-agent system (MAS) operating in marine environments often need to utilize task payloads and avoid collisions in coordination, necessitating adherence to a set of relative-pose constraints, which may include…
Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, based on a new concept of mixed sets defined as function images of symbol type domains, a compositional…
A novel code construction algorithm is presented to find all the possible code families for code reconfiguration in an OCDMA system. The algorithm is developed through searching all the complete subgraphs of a constructed graph. The…
Exponents and logarithms are fundamental components in many important applications such as logistic regression, maximum likelihood, relative entropy, and so on. Since the exponential cone can be viewed as the epigraph of perspective of the…