Related papers: Systematic Codes for Rank Modulation
We develop a framework for constructing quantum error-correcting codes and logical gates for three types of spaces -- composite permutation-invariant spaces of many qubits or qudits, composite constant-excitation Fock-state spaces of many…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions.…
We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum…
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
The accurate specification of the number of factors is critical to the validity of factor models and the topic almost occupies the central position in factor analysis. Plenty of estimators are available under the restrictive condition that…
In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this…
Systematic polar codes are shown to outperform non-systematic polar codes in terms of the bit-error-rate (BER) performance. However theoretically the mechanism behind the better performance of systematic polar codes is not yet clear. In…
Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…
Rank-1 modifications in k-times (k > 1) often are performed to achieve rank-k modification. We propose a rank- k modification for enhancing computational efficiency. As the first step towards a rank- k modification, an algorithm to perform…
In this paper, for any fixed positive integers $t$ and $q>2$, we construct $q$-ary codes correcting a burst of at most $t$ deletions with redundancy $\log n+8\log\log n+o(\log\log n)+\gamma_{q,t}$ bits and near-linear encoding/decoding…
Typically, forward error correction (FEC) codes are designed based on the minimization of the error rate for a given code rate. However, for applications that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive…
This paper describes our submission to the First Workshop on Reordering for Statistical Machine Translation. We have decided to build a reordering system based on tree-to-string model, using only publicly available tools to accomplish this…
Recent advances have shown that statistical tests for the rank of cross-covariance matrices play an important role in causal discovery. These rank tests include partial correlation tests as special cases and provide further graphical…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH)…
Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and complemented copy of a substring of length $k$ adjacent to its…
Pairwise association measure is an important operation in data analytics. Kendall's tau coefficient is one widely used correlation coefficient identifying non-linear relationships between ordinal variables. In this paper, we investigated a…
Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for unique string…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…