22,771 research outputs found
Matched Metrics and Channels
The most common decision criteria for decoding are maximum likelihood
decoding and nearest neighbor decoding. It is well-known that maximum
likelihood decoding coincides with nearest neighbor decoding with respect to
the Hamming metric on the binary symmetric channel. In this work we study
channels and metrics for which those two criteria do and do not coincide for
general codes
Bounds for identifying codes in terms of degree parameters
An identifying code is a subset of vertices of a graph such that each vertex
is uniquely determined by its neighbourhood within the identifying code. If
\M(G) denotes the minimum size of an identifying code of a graph , it was
conjectured by F. Foucaud, R. Klasing, A. Kosowski and A. Raspaud that there
exists a constant such that if a connected graph with vertices and
maximum degree admits an identifying code, then \M(G)\leq
n-\tfrac{n}{d}+c. We use probabilistic tools to show that for any ,
\M(G)\leq n-\tfrac{n}{\Theta(d)} holds for a large class of graphs
containing, among others, all regular graphs and all graphs of bounded clique
number. This settles the conjecture (up to constants) for these classes of
graphs. In the general case, we prove \M(G)\leq n-\tfrac{n}{\Theta(d^{3})}.
In a second part, we prove that in any graph of minimum degree and
girth at least 5, \M(G)\leq(1+o_\delta(1))\tfrac{3\log\delta}{2\delta}n.
Using the former result, we give sharp estimates for the size of the minimum
identifying code of random -regular graphs, which is about
The statistical mechanics of multi-index matching problems with site disorder
We study the statistical mechanics of multi-index matching problems where the
quenched disorder is a geometric site disorder rather than a link disorder. A
recently developed functional formalism is exploited which yields exact results
in the finite temperature thermodynamic limit. Particular attention is paid to
the zero temperature limit of maximal matching problems where the method allows
us to obtain the average value of the optimal match and also sheds light on the
algorithmic heuristics leading to that optimal matchComment: 11 pages 11 figures, RevTe
Graded, Dynamically Routable Information Processing with Synfire-Gated Synfire Chains
Coherent neural spiking and local field potentials are believed to be
signatures of the binding and transfer of information in the brain. Coherent
activity has now been measured experimentally in many regions of mammalian
cortex. Synfire chains are one of the main theoretical constructs that have
been appealed to to describe coherent spiking phenomena. However, for some
time, it has been known that synchronous activity in feedforward networks
asymptotically either approaches an attractor with fixed waveform and
amplitude, or fails to propagate. This has limited their ability to explain
graded neuronal responses. Recently, we have shown that pulse-gated synfire
chains are capable of propagating graded information coded in mean population
current or firing rate amplitudes. In particular, we showed that it is possible
to use one synfire chain to provide gating pulses and a second, pulse-gated
synfire chain to propagate graded information. We called these circuits
synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded
information can rapidly cascade through a neural circuit, and show a
correspondence between this type of transfer and a mean-field model in which
gating pulses overlap in time. We show that SGSCs are robust in the presence of
variability in population size, pulse timing and synaptic strength. Finally, we
demonstrate the computational capabilities of SGSC-based information coding by
implementing a self-contained, spike-based, modular neural circuit that is
triggered by, then reads in streaming input, processes the input, then makes a
decision based on the processed information and shuts itself down
Long-distance quantum communication over noisy networks without long-time quantum memory
The problem of sharing entanglement over large distances is crucial for
implementations of quantum cryptography. A possible scheme for long-distance
entanglement sharing and quantum communication exploits networks whose nodes
share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A
78, 062324 (2008)] the authors put forward an important isomorphism between
storing quantum information in a dimension and transmission of quantum
information in a -dimensional network. We show that it is possible to
obtain long-distance entanglement in a noisy two-dimensional (2D) network, even
when taking into account that encoding and decoding of a state is exposed to an
error. For 3D networks we propose a simple encoding and decoding scheme based
solely on syndrome measurements on 2D Kitaev topological quantum memory. Our
procedure constitutes an alternative scheme of state injection that can be used
for universal quantum computation on 2D Kitaev code. It is shown that the
encoding scheme is equivalent to teleporting the state, from a specific node
into a whole two-dimensional network, through some virtual EPR pair existing
within the rest of network qubits. We present an analytic lower bound on
fidelity of the encoding and decoding procedure, using as our main tool a
modified metric on space-time lattice, deviating from a taxicab metric at the
first and the last time slices.Comment: 15 pages, 10 figures; title modified; appendix included in main text;
section IV extended; minor mistakes remove
Efficient Decoding of Topological Color Codes
Color codes are a class of topological quantum codes with a high error
threshold and large set of transversal encoded gates, and are thus suitable for
fault tolerant quantum computation in two-dimensional architectures. Recently,
computationally efficient decoders for the color codes were proposed. We
describe an alternate efficient iterative decoder for topological color codes,
and apply it to the color code on hexagonal lattice embedded on a torus. In
numerical simulations, we find an error threshold of 7.8% for independent
dephasing and spin flip errors.Comment: 7 pages, LaTe
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