3,928 research outputs found
Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes
In this work, we consider pseudocodewords of (relaxed) linear programming
(LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP
decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo
codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is
proper and -symmetric, and make a connection to finite graph covers of the
3D-TC factor graph. This connection is used to show that the support set of any
pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum
a posteriori constituent decoders on the binary erasure channel. Furthermore,
we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a
finite-length minimum pseudoweight analysis for small cover degrees. Also, an
explicit description of the fundamental cone of the 3D-TC polytope is given.
Finally, we present an extensive numerical study of small-to-medium block
length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the
minimum distance and/or the stopping distance is
high, the minimum pseudoweight (on the additive white Gaussian noise channel)
is strictly smaller than both the and the , and 2)
the minimum pseudoweight grows with the block length, at least for
small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
Preparing quantum states across many qubits is necessary to unlock the full
potential of quantum computers. However, a key challenge is to realize
efficient preparation protocols which are stable to noise and gate
imperfections. Here, using a measurement-based protocol on a 127
superconducting qubit device, we study the generation of the simplest
long-range order -- Ising order, familiar from Greenberger-Horne-Zeilinger
(GHZ) states and the repetition code -- on 54 system qubits. Our efficient
implementation of the constant-depth protocol and classical decoder shows
higher fidelities for GHZ states compared to size-dependent, unitary protocols.
By experimentally tuning coherent and incoherent error rates, we demonstrate
stability of this decoded long-range order in two spatial dimensions, up to a
critical point which corresponds to a transition belonging to the unusual
Nishimori universality class. Although in classical systems Nishimori physics
requires fine-tuning multiple parameters, here it arises as a direct result of
the Born rule for measurement probabilities -- locking the effective
temperature and disorder driving this transition. Our study exemplifies how
measurement-based state preparation can be meaningfully explored on quantum
processors beyond a hundred qubits.Comment: 16 pages, 18 figure
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