14 research outputs found
The Capacity of Some P\'olya String Models
We study random string-duplication systems, which we call P\'olya string
models. These are motivated by DNA storage in living organisms, and certain
random mutation processes that affect their genome. Unlike previous works that
study the combinatorial capacity of string-duplication systems, or various
string statistics, this work provides exact capacity or bounds on it, for
several probabilistic models. In particular, we study the capacity of noisy
string-duplication systems, including the tandem-duplication, end-duplication,
and interspersed-duplication systems. Interesting connections are drawn between
some systems and the signature of random permutations, as well as to the beta
distribution common in population genetics
Bounds and Constructions for Generalized Batch Codes
Private information retrieval (PIR) codes and batch codes are two important
types of codes that are designed for coded distributed storage systems and
private information retrieval protocols. These codes have been the focus of
much attention in recent years, as they enable efficient and secure storage and
retrieval of data in distributed systems.
In this paper, we introduce a new class of codes called \emph{-batch
codes}. These codes are a type of storage codes that can handle any multi-set
of requests, comprised of distinct information symbols. Importantly,
PIR codes and batch codes are special cases of -batch codes.
The main goal of this paper is to explore the relationship between the number
of redundancy symbols and the -batch code property. Specifically, we
establish a lower bound on the number of redundancy symbols required and
present several constructions of -batch codes. Furthermore, we extend
this property to the case where each request is a linear combination of
information symbols, which we refer to as \emph{functional -batch
codes}. Specifically, we demonstrate that simplex codes are asymptotically
optimal functional -batch codes, in terms of the number of redundancy
symbols required, under certain parameter regime.Comment: 25 page
The capacity of some Pólya string models
We study random string-duplication systems, called Pólya string models, motivated by certain random mutation processes in the genome of living organisms. Unlike previous works that study the combinatorial capacity of string-duplication systems, or peripheral properties such as symbol frequency, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we give the exact capacity of the random tandem-duplication system, and the end-duplication system, and bound the capacity of the complement tandem-duplication system. Interesting connections are drawn between the former and the beta distribution common to population genetics, as well as between the latter system and signatures of random permutations
Repeat-Free Codes
In this paper we consider the problem of encoding data into repeat-free
sequences in which sequences are imposed to contain any -tuple at most once
(for predefined ). First, the capacity and redundancy of the repeat-free
constraint are calculated. Then, an efficient algorithm, which uses a single
bit of redundancy, is presented to encode length- sequences for . This algorithm is then improved to support any value of of the form
, for , while its redundancy is . We also calculate the
capacity of repeat-free sequences when combined with local constraints which
are given by a constrained system, and the capacity of multi-dimensional
repeat-free codes.Comment: 18 page
Binary -Deletion--Insertion-Burst Correcting Codes and Codes Correcting a Burst of Deletions
We first give a construction of binary -deletion--insertion-burst
correcting codes with redundancy at most ,
where . Then we give an improved construction of binary codes
capable of correcting a burst of non-consecutive deletions, whose
redundancy is reduced from to
. Lastly, by connecting non-binary
-burst-deletion correcting codes with binary
-deletion--insertion-burst correcting codes, we give a new construction
of non-binary -burst-deletion correcting codes with redundancy at most
. This construction is different from previous
results.Comment: Results are covered by others' wor
Throughput and Delay Analysis for Coded ARQ
© 2019 IFIP. We propose a Coded selective-repeat ARQ protocol with cumulative feedback, by building on the uncoded baseline scheme for ARQ, developed by Ausavapattanakun and Nosratinia. Our method leverages discrete-time queuing and coding theory to analyze the performance of the proposed data transmission method. We incorporate forward error-correction (FEC) to reduce in-order delivery delay, and exploit a matrix signal-flow graph approach to analyze the throughput and delay. We demonstrate and contrast the performance of the Coded ARQ protocol with that of the uncoded ARQ scheme, with minimum coding, i.e., with a sliding window of size 2. Coded ARQ can provide gains up to about 40% in terms of throughput. It also provides delay guarantees, and is robust to various challenges such as imperfect and delayed feedback, burst erasures, and round-trip time fluctuations.United States. Defense Advanced Research Projects Agency (Prime Award HR0011-17-C-0050)Intel Corporatio