Related papers: Decoding Frequency Permutation Arrays under Infini…
List decoding of insertions and deletions in the Levenshtein metric is considered. The Levenshtein distance between two sequences is the minimum number of insertions and deletions needed to turn one of the sequences into the other. In this…
We define sequence patterns of length $n$ and level $\ell$ to be equivalence classes of sequences that have $n$ elements from the set of $\ell$ integer symbols $\{1,2,\ldots,\ell\}$ with no restriction on repetition, where the equivalence…
We present a new approach to the problem of alternating signs for fermionic many body Monte Carlo simulations. We demonstrate that the exchange of identical fermions is typically short-ranged even when the underlying physics is dominated by…
We show that for any permutation $\pi$ there exists an integer $k_{\pi}$ such that every permutation avoiding $\pi$ as a pattern is a product of at most $k_{\pi}$ separable permutations. In other words, every strict class $\mathcal C$ of…
We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for…
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
We bound the number of electromagnetic signals which may be observed over a frequency range $2W$ for a time $T$ within a region of space enclosed by a radius $R$. Our result implies that broadband fields in space cannot be arbitrarily…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…
A deterministic finite-state automaton (FSA) is an abstract sequential machine that reads the symbols comprising an input word one at a time. An FSA is symmetric if its output is independent of the order in which the input symbols are read,…
Advanced millimeter-wave software-defined array (SDA) platforms, or testbeds at affordable costs and high performance are essential for the wireless community. In this paper, we present a low-cost, portable, and programmable SDA that allows…
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or…
In almost 30 years of operation, the Very Large Array (VLA) has proved to be a remarkably flexible and productive radio telescope. However, the basic capabilities of the VLA have changed little since it was designed. A major expansion…
The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…
A permutation code is a nonlinear code whose codewords are permutation of a set of symbols. We consider the use of permutation code in the deletion channel, and consider the symbol-invariant error model, meaning that the values of the…
The permutation language $P_n$ consists of all words that are permutations of a fixed alphabet of size $n$. Using divide-and-conquer, we construct a regular expression $R_n$ that specifies $P_n$. We then give explicit bounds for the length…
Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate the construction…
The frequency diverse array (FDA) based directional modulation (DM) technology plays an important role in the implementation of the physical-layer security (PLS) transmission of 5G and beyond communication system. In order to meet the…
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…