10,517 research outputs found
Combinatorial channels from partially ordered sets
A central task of coding theory is the design of schemes to reliably transmit data though space, via communication systems, or through time, via storage systems. Our goal is to identify and exploit structural properties common to a wide variety of coding problems, classical and modern, using the framework of partially ordered sets. We represent adversarial error models as combinatorial channels, form combinatorial channels from posets, identify a structural property of posets that leads to families of channels with the same codes, and bound the size of codes by optimizing over a family of equivalent channels. A large number of previously studied coding problems that fit into this framework. This leads to a new upper bound on the size of s-deletion correcting codes. We use a linear programming framework to obtain sphere-packing upper bounds when there is little underlying symmetry in the coding problem. Finally, we introduce and investigate a strong notion of poset homomorphism: locally bijective cover preserving maps. We look for maps of this type to and from the subsequence partial order on q-ary strings
Observation of the decay
The first observation of the decay is reported. The
study is based on a sample of proton-proton collisions corresponding to
of integrated luminosity collected with the LHCb detector. The
significance of the signal is standard deviations. The branching fraction
is measured to be , where the third uncertainty comes from the
branching fraction that is used as a normalisation.
In addition, the charge asymmetries of and
, which are control channels, are measured to be and , respectively. All results are consistent with
theoretical expectations
Optimality of Treating Interference as Noise: A Combinatorial Perspective
For single-antenna Gaussian interference channels, we re-formulate the
problem of determining the Generalized Degrees of Freedom (GDoF) region
achievable by treating interference as Gaussian noise (TIN) derived in [3] from
a combinatorial perspective. We show that the TIN power control problem can be
cast into an assignment problem, such that the globally optimal power
allocation variables can be obtained by well-known polynomial time algorithms.
Furthermore, the expression of the TIN-Achievable GDoF region (TINA region) can
be substantially simplified with the aid of maximum weighted matchings. We also
provide conditions under which the TINA region is a convex polytope that relax
those in [3]. For these new conditions, together with a channel connectivity
(i.e., interference topology) condition, we show TIN optimality for a new class
of interference networks that is not included, nor includes, the class found in
[3].
Building on the above insights, we consider the problem of joint link
scheduling and power control in wireless networks, which has been widely
studied as a basic physical layer mechanism for device-to-device (D2D)
communications. Inspired by the relaxed TIN channel strength condition as well
as the assignment-based power allocation, we propose a low-complexity
GDoF-based distributed link scheduling and power control mechanism (ITLinQ+)
that improves upon the ITLinQ scheme proposed in [4] and further improves over
the heuristic approach known as FlashLinQ. It is demonstrated by simulation
that ITLinQ+ provides significant average network throughput gains over both
ITLinQ and FlashLinQ, and yet still maintains the same level of implementation
complexity. More notably, the energy efficiency of the newly proposed ITLinQ+
is substantially larger than that of ITLinQ and FlashLinQ, which is desirable
for D2D networks formed by battery-powered devices.Comment: A short version has been presented at IEEE International Symposium on
Information Theory (ISIT 2015), Hong Kon
Oblivious channels
Let C = {x_1,...,x_N} \subset {0,1}^n be an [n,N] binary error correcting
code (not necessarily linear). Let e \in {0,1}^n be an error vector. A codeword
x in C is said to be "disturbed" by the error e if the closest codeword to x +
e is no longer x. Let A_e be the subset of codewords in C that are disturbed by
e. In this work we study the size of A_e in random codes C (i.e. codes in which
each codeword x_i is chosen uniformly and independently at random from
{0,1}^n). Using recent results of Vu [Random Structures and Algorithms 20(3)]
on the concentration of non-Lipschitz functions, we show that |A_e| is strongly
concentrated for a wide range of values of N and ||e||.
We apply this result in the study of communication channels we refer to as
"oblivious". Roughly speaking, a channel W(y|x) is said to be oblivious if the
error distribution imposed by the channel is independent of the transmitted
codeword x. For example, the well studied Binary Symmetric Channel is an
oblivious channel.
In this work, we define oblivious and partially oblivious channels and
present lower bounds on their capacity. The oblivious channels we define have
connections to Arbitrarily Varying Channels with state constraints.Comment: Submitted to the IEEE International Symposium on Information Theory
(ISIT) 200
Conformal blocks of W_N Minimal Models and AGT correspondence
We study the AGT correspondence between four-dimensional supersymmetric gauge
field theory and two-dimensional conformal field theories in the context of W_N
minimal models. The origin of the AGT correspondence is in a special integrable
structure which appears in the properly extended conformal theory. One of the
basic manifestations of this integrability is the special orthogonal basis
which arises in the extended theory. We propose modification of the AGT
representation for the W_N conformal blocks in the minimal models. The
necessary modification is related to the reduction of the orthogonal basis.
This leads to the explicit combinatorial representation for the conformal
blocks of minimal models and employs the sum over N-tupels of Young diagrams
with additional restrictions.Comment: 16 pages; v2: typos removed, more comments, references added; v3:
minor corrections, references added, JHEP versio
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