9,490 research outputs found
On the Combinatorial Version of the Slepian-Wolf Problem
We study the following combinatorial version of the Slepian-Wolf coding
scheme. Two isolated Senders are given binary strings and respectively;
the length of each string is equal to , and the Hamming distance between the
strings is at most . The Senders compress their strings and
communicate the results to the Receiver. Then the Receiver must reconstruct
both strings and . The aim is to minimise the lengths of the transmitted
messages.
For an asymmetric variant of this problem (where one of the Senders transmits
the input string to the Receiver without compression) with deterministic
encoding a nontrivial lower bound was found by A.Orlitsky and K.Viswanathany.
In our paper we prove a new lower bound for the schemes with syndrome coding,
where at least one of the Senders uses linear encoding of the input string.
For the combinatorial Slepian-Wolf problem with randomized encoding the
theoretical optimum of communication complexity was recently found by the first
author, though effective protocols with optimal lengths of messages remained
unknown. We close this gap and present a polynomial time randomized protocol
that achieves the optimal communication complexity.Comment: 20 pages, 14 figures. Accepted to IEEE Transactions on Information
Theory (June 2018
Numerical and analytical bounds on threshold error rates for hypergraph-product codes
We study analytically and numerically decoding properties of finite rate
hypergraph-product quantum LDPC codes obtained from random (3,4)-regular
Gallager codes, with a simple model of independent X and Z errors. Several
non-trival lower and upper bounds for the decodable region are constructed
analytically by analyzing the properties of the homological difference, equal
minus the logarithm of the maximum-likelihood decoding probability for a given
syndrome. Numerical results include an upper bound for the decodable region
from specific heat calculations in associated Ising models, and a minimum
weight decoding threshold of approximately 7%.Comment: 14 pages, 5 figure
Information-theoretic Physical Layer Security for Satellite Channels
Shannon introduced the classic model of a cryptosystem in 1949, where Eve has
access to an identical copy of the cyphertext that Alice sends to Bob. Shannon
defined perfect secrecy to be the case when the mutual information between the
plaintext and the cyphertext is zero. Perfect secrecy is motivated by
error-free transmission and requires that Bob and Alice share a secret key.
Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the
Shannon model assuming that the channels are noisy and proved that secrecy can
be achieved without sharing a secret key. This model is called wiretap channel
model and secrecy capacity is known when Eve's channel is noisier than Bob's
channel.
In this paper we review the concept of wiretap coding from the satellite
channel viewpoint. We also review subsequently introduced stronger secrecy
levels which can be numerically quantified and are keyless unconditionally
secure under certain assumptions. We introduce the general construction of
wiretap coding and analyse its applicability for a typical satellite channel.
From our analysis we discuss the potential of keyless information theoretic
physical layer security for satellite channels based on wiretap coding. We also
identify system design implications for enabling simultaneous operation with
additional information theoretic security protocols
A Survey on Metric Learning for Feature Vectors and Structured Data
The need for appropriate ways to measure the distance or similarity between
data is ubiquitous in machine learning, pattern recognition and data mining,
but handcrafting such good metrics for specific problems is generally
difficult. This has led to the emergence of metric learning, which aims at
automatically learning a metric from data and has attracted a lot of interest
in machine learning and related fields for the past ten years. This survey
paper proposes a systematic review of the metric learning literature,
highlighting the pros and cons of each approach. We pay particular attention to
Mahalanobis distance metric learning, a well-studied and successful framework,
but additionally present a wide range of methods that have recently emerged as
powerful alternatives, including nonlinear metric learning, similarity learning
and local metric learning. Recent trends and extensions, such as
semi-supervised metric learning, metric learning for histogram data and the
derivation of generalization guarantees, are also covered. Finally, this survey
addresses metric learning for structured data, in particular edit distance
learning, and attempts to give an overview of the remaining challenges in
metric learning for the years to come.Comment: Technical report, 59 pages. Changes in v2: fixed typos and improved
presentation. Changes in v3: fixed typos. Changes in v4: fixed typos and new
method
A reliable order-statistics-based approximate nearest neighbor search algorithm
We propose a new algorithm for fast approximate nearest neighbor search based
on the properties of ordered vectors. Data vectors are classified based on the
index and sign of their largest components, thereby partitioning the space in a
number of cones centered in the origin. The query is itself classified, and the
search starts from the selected cone and proceeds to neighboring ones. Overall,
the proposed algorithm corresponds to locality sensitive hashing in the space
of directions, with hashing based on the order of components. Thanks to the
statistical features emerging through ordering, it deals very well with the
challenging case of unstructured data, and is a valuable building block for
more complex techniques dealing with structured data. Experiments on both
simulated and real-world data prove the proposed algorithm to provide a
state-of-the-art performance
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