3,536 research outputs found
Block synchronization for quantum information
Locating the boundaries of consecutive blocks of quantum information is a
fundamental building block for advanced quantum computation and quantum
communication systems. We develop a coding theoretic method for properly
locating boundaries of quantum information without relying on external
synchronization when block synchronization is lost. The method also protects
qubits from decoherence in a manner similar to conventional quantum
error-correcting codes, seamlessly achieving synchronization recovery and error
correction. A family of quantum codes that are simultaneously synchronizable
and error-correcting is given through this approach.Comment: 7 pages, no figures, final accepted version for publication in
Physical Review
Algebraic techniques in designing quantum synchronizable codes
Quantum synchronizable codes are quantum error-correcting codes that can
correct the effects of quantum noise as well as block synchronization errors.
We improve the previously known general framework for designing quantum
synchronizable codes through more extensive use of the theory of finite fields.
This makes it possible to widen the range of tolerable magnitude of block
synchronization errors while giving mathematical insight into the algebraic
mechanism of synchronization recovery. Also given are families of quantum
synchronizable codes based on punctured Reed-Muller codes and their ambient
spaces.Comment: 9 pages, no figures. The framework presented in this article
supersedes the one given in arXiv:1206.0260 by the first autho
An Architecture for High Data Rate Very Low Frequency Communication
Very low frequency (VLF) communication is used for long range shore-to-ship broadcasting applications. This paper proposes an architecture for high data rate VLF communication using Gaussian minimum shift keying (GMSK) modulation and low delay parity check (LDPC) channel coding. Non-data aided techniques are designed and used for carrier phase synchronization, symbol timing recovery, and LDPC code frame synchronization. These require the estimation of the operative Eb/N0 for which a kurtosis based algorithm is used. Also, a method for modeling the probability density function of the received signal under the bit condition is presented in this regard. The modeling of atmospheric radio noise (ARN) that corrupts VLF signals is described and an algorithm for signal enhancement in the presence of ARN in given. The BER performance of the communication system is evaluated for bit rates of 400 bps, 600 bps, and 800 bps for communication bandwidth of ~200 Hz.Defence Science Journal, 2013, 63(1), pp.25-33, DOI:http://dx.doi.org/10.14429/dsj.63.376
Codes for protection from synchronization loss and additive errors
Codes for protection from synchronization loss and additive error
A Unified Approach to Synchronization Problems over Subgroups of the Orthogonal Group
Given a group , the problem of synchronization over the group
is a constrained estimation problem where a collection of group
elements are estimated based on noisy
observations of pairwise ratios for an incomplete set of
index pairs . This problem has gained much attention recently and finds
lots of applications due to its appearance in a wide range of scientific and
engineering areas. In this paper, we consider the class of synchronization
problems over a closed subgroup of the orthogonal group, which covers many
instances of group synchronization problems that arise in practice. Our
contributions are threefold. First, we propose a unified approach to solve this
class of group synchronization problems, which consists of a suitable
initialization and an iterative refinement procedure via the generalized power
method. Second, we derive a master theorem on the performance guarantee of the
proposed approach. Under certain conditions on the subgroup, the measurement
model, the noise model and the initialization, the estimation error of the
iterates of our approach decreases geometrically. As our third contribution, we
study concrete examples of the subgroup (including the orthogonal group, the
special orthogonal group, the permutation group and the cyclic group), the
measurement model, the noise model and the initialization. The validity of the
related conditions in the master theorem are proved for these specific
examples. Numerical experiments are also presented. Experiment results show
that our approach outperforms existing approaches in terms of computational
speed, scalability and estimation error
Quantum Synchronizable Codes From Finite Geometries
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that, in principle, such a code can be constructed through a combination of a classical linear code and its subcode if the two are both cyclic and dual-containing. However, finding such classical codes that lead to promising quantum synchronizable error-correcting codes is not a trivial task. In fact, although there are two families of classical codes that are proved to produce quantum synchronizable codes with good minimum distances and highest possible tolerance against misalignment, their code lengths have been restricted to primes and Mersenne numbers. In this paper, examining the incidence vectors of projective spaces over the finite fields of characteristic 2, we give quantum synchronizable codes from cyclic codes whose lengths are not primes or Mersenne numbers. These projective geometric codes achieve good performance in quantum error correction and possess the best possible ability to recover synchronization, thereby enriching the variety of good quantum synchronizable codes. We also extend the current knowledge of cyclic codes in classical coding theory by explicitly giving generator polynomials of the finite geometric codes and completely characterizing the minimum weight nonzero codewords. In addition to the codes based on projective spaces, we carry out a similar analysis on the well-known cyclic codes from Euclidean spaces that are known to be majority logic decodable and determine their exact minimum distances
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