Given a database, the private information retrieval (PIR) protocol allows user to make queries several servers and retrieve certain item of database via feedbacks without revealing identity specific any single server. Classic k-server PIR protocols work on replicated databases, i.e., each k stores whole copy database. Recently, new models were proposed with coding techniques arising from distributed storage system. In these models, server only fraction 1/s where s > 1 is given rational...

Limited-magnitude errors modify a transmitted integer vector in at most $t$ entries, where each entry can increase by $\kp$ or decrease $\km$. This channel model is particularly relevant to applications such as flash memories and DNA storage. A perfect code for this equivalent tiling of $\Z^n$ asymmetric limited-magnitude balls $\cB(n,t,\kp,\km)$. In paper, we focus on the case $t=2$ $\km=\kp-1$, derive necessary conditions $m$ $n$ existence lattice $\cB(n,2,m,m-1)$. Specifically, prove that...

To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit constructions of error-correcting codes that are suitable as primer addresses efficient encoding algorithms. Specifically, our take cyclic or linear inputs produce sets similar capabilities. Using classes BCH codes, we obtain infinite families length n, minimum...

Given a database, the private information retrieval (PIR) protocol allows user to make queries several servers and retrieve certain item of database via feedbacks, without revealing privacy specific any single server. Classical models PIR protocols require that each server stores whole copy database. Recently new are proposed with coding techniques arising from distributed storage system. In these only fraction $1/s$ where $s>1$ is given rational number. array codes recently by Fazeli, Vardy...

Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, bounds MCWCs and constructions optimal are studied. First, we derive three different types upper which Johnson-type given by Chee <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> for some parameters. The asymptotic lower bound is also examined. Then, obtain existence two...

We construct permutation codes capable of correcting bursts stable deletions. For a single burst exactly s deletions, our code has size sn!/((2s)!n) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , while the upper bound n!/s!(n - + 1). also for cases up to and b at most deletions each.

Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of vector-matrix multiplication on resistive crossbars. Prior work has concentrated locating a single error and, in this work, several classes presented handle multiple errors. It is first shown that one known constructions, based spherical codes, fact A second family then with 0–1 paritycheck matrices sparse and disjunct; such have been used other...

Abstract Nonuniform group divisible designs (GDDs) have been studied by numerous researchers for the past two decades due to their essential role in constructions other types of designs. In this paper, we investigate existence problem ‐GDDs type . First, determine completely spectrum and Furthermore, general cases, show that each , a ‐GDD exists if only except possibly

Non-uniform group divisible designs (GDDs) and non-uniform Kirkman frames are useful in the constructions for other types of designs. In this paper, we consider existence problems K1(3)-GDDs type gum1 with K1(3)={k:k≡1mod3} hum1. First, determine completely spectrum uniform gu. Then, entire problem m>0. We show that, each given g, up to a small number undetermined cases u, necessary conditions on (u,m) K1(3)-GDD also sufficient, except possibly when u≡2mod4 g≡3mod6 u≡6mod12 g≡1,5mod6....

Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces corrupted version the set, including sequence loss, symbol substitution, insertion/deletion, limited-magnitude errors in symbols. Various parameter regimes New bounds on code parameters provided, which improve upon known bounds. constructed, at times matching up lower-order terms or small constant factors.

Permutation codes and multipermutation are widely studied due to various applications in information theory. Designing correcting deletion errors has been the main subject of works literature best our knowledge, there exist only optimal capable a single permutation. In this paper, we construct several classes permutation that burst length s ≥ 2, for both stable unstable models. Efficient error decoders provided show correctness constructions.

We construct integer error-correcting codes and covering for the limited-magnitude error channel with more than one error. The are lattices that pack or cover space appropriate ball. Some of constructions attain an asymptotic packing/covering density is constant. results obtained via various methods, including use in Hamming metric, modular B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> -sequences, 2-fold Sidon sets, sets avoiding...

To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit constructions of error-correcting codes that are suitable as primer addresses efficient encoding algorithms. Specifically, our take cyclic or linear inputs produce sets similar capabilities. Using classes BCH codes, we obtain infinite families length n, minimum...

A robust positioning pattern is a large array that allows mobile device to locate its position by reading possibly corrupted small window around it. In this paper, we provide constructions of binary patterns, equipped with efficient locating algorithms, are constant number errors and have redundancy within factor optimality. Furthermore, modify our correct rank obtain patterns any less than number. Additionally, construct $q$-ary sequences errors, some which length attaining the upper bound....

Abstract A triple system is a collection of b blocks, each size three, on set v points. It j ‐balanced when every two ‐sets points appear in numbers blocks that are as nearly equal possible, and well balanced it for . Well‐balanced systems arise the minimization variance file availability distributed systems. shown 2‐balanced 3‐balanced exists, so does one balanced. Using known new results variants group divisible designs, constructions well‐balanced developed. these, spectrum pairs which...

To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit constructions of error-correcting codes that are suitable as primer addresses efficient encoding algorithms. Specifically, our take cyclic or linear inputs produce sets similar capabilities. Using classes BCH codes, we obtain infinite families length $n$, minimum...

In a bus with n wires, each wire has two states, `0' or `1', representing one bit of information. Whenever the state transitions from to `1' `0', joule heating causes temperature rise, and high temperatures have adverse effects on on-chip performance. Recently, class low-power cooling (LPC) codes was proposed control such during transmission. As suggested in earlier work, LPC may be used simultaneously both peak average power consumption buses. Specifically, an (n, t, w)-LPC code is coding...

Abstract A G ‐design of order n is a decomposition the complete graph on vertices into edge‐disjoint subgraphs isomorphic to . Grooming uniform all‐to‐all traffic in optical ring networks with grooming ratio C requires determination decompositions each having at most edges. The drop cost such total number nonzero degree these subgraphs, and optimal when minimum. existence spectrum problem ‐designs for five‐vertex graphs long standing posed by Bermond, Huang, Rosa Sotteau 1980, which closely...

We study generalized covering radii, a fundamental property of linear codes that characterizes the trade-off between storage, latency, and access in data-query protocols such as PIR. prove lower upper bounds on radii Reed-Muller codes, well finding their exact value certain extreme cases. With application to mind, we also construct algorithm gets input set points space, find corresponding codewords from code are jointly not farther away than bound radius code. runs time is polynomial parameters.