35,383 research outputs found
Fast decoding of a d(min) = 6 RS code
A method for high speed decoding a d sub min = 6 Reed-Solomon (RS) code is presented. Properties of the two byte error correcting and three byte error detecting RS code are discussed. Decoding using a quadratic equation is shown. Theorems and concomitant proofs are included to substantiate this decoding method
On the undetected error probability of a concatenated coding scheme for error control
Consider a concatenated coding scheme for error control on a binary symmetric channel, called the inner channel. The bit error rate (BER) of the channel is correspondingly called the inner BER, and is denoted by Epsilon (sub i). Two linear block codes, C(sub f) and C(sub b), are used. The inner code C(sub f), called the frame code, is an (n,k) systematic binary block code with minimum distance, d(sub f). The frame code is designed to correct + or fewer errors and simultaneously detect gamma (gamma +) or fewer errors, where + + gamma + 1 = to or d(sub f). The outer code C(sub b) is either an (n(sub b), K(sub b)) binary block with a n(sub b) = mk, or an (n(sub b), k(Sub b) maximum distance separable (MDS) code with symbols from GF(q), where q = 2(b) and the code length n(sub b) satisfies n(sub)(b) = mk. The integerim is the number of frames. The outercode is designed for error detection only
An extended d(min) = 4 RS code
A minimum distance d sub m - 4 extended Reed - Solomon (RS) code over GF (2 to the b power) was constructed. This code is used to correct any single byte error and simultaneously detect any double byte error. Features of the code; including fast encoding and decoding, are presented
Error control for reliable digital data transmission and storage systems
A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. In this paper we present some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative alorithm to find the error locator polynomial. Two codes are considered: (1) a d sub min = 4 single-byte-error-correcting (SBEC), double-byte-error-detecting (DBED) RS code; and (2) a d sub min = 6 double-byte-error-correcting (DBEC), triple-byte-error-detecting (TBED) RS code
Quantum phases of interacting phonons in ion traps
The vibrations of a chain of trapped ions can be considered, under suitable
experimental conditions, as an ensemble of interacting phonons, whose quantum
dynamics is governed by a Bose--Hubbard Hamiltonian. In this work we study the
quantum phases which appear in this system, and show that thermodynamical
properties, such as critical parameters and critical exponents, can be measured
in experiments with a limited number of ions. Besides that, interacting phonons
in trapped ions offer us the possibility to access regimes which are difficult
to study with ultracold bosons in optical lattices, like models with attractive
or site--dependent phonon-phonon interactions.Comment: 10 page
Fast decoding techniques for extended single-and-double-error-correcting Reed Solomon codes
A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots
New Consequences of Induced Transparency in a Double-Lambda scheme: Destructive Interference In Four-wave Mixing
We investigate a four-state system interacting with long and short laser
pulses in a weak probe beam approximation. We show that when all lasers are
tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM)
field is strongly absorbed. The part which is not absorbed has the exact
intensity required to destructively interfere with the excitation pathway
involved in producing the FWM state. We show that with this three-photon
destructive interference, the conversion efficiency can still be as high as
25%. Contrary to common belief,our calculation shows that this process, where
an ideal one-photon electromagnetically induced transparency is established, is
not most suitable for high efficiency conversion. With appropriate
phase-matching and propagation distance, and when the three-photon destructive
interference does not occur, we show that the photon flux conversion efficiency
is independent of probe intensity and can be close to 100%. In addition, we
show clearly that the conversion efficiency is not determined by the maximum
atomic coherence between two lower excited states, as commonly believed. It is
the combination of phase-matching and constructive interference involving the
two terms arising in producing the mixing wave that is the key element for the
optimized FWM generation. Indeed, in this scheme no appreciable excited state
is produced, so that the atomic coherence between states |0> and |2> is always
very small.Comment: Submitted to Phys. Rev. A, 7 pages, 4 figure
Tripartite Graph Clustering for Dynamic Sentiment Analysis on Social Media
The growing popularity of social media (e.g, Twitter) allows users to easily
share information with each other and influence others by expressing their own
sentiments on various subjects. In this work, we propose an unsupervised
\emph{tri-clustering} framework, which analyzes both user-level and tweet-level
sentiments through co-clustering of a tripartite graph. A compelling feature of
the proposed framework is that the quality of sentiment clustering of tweets,
users, and features can be mutually improved by joint clustering. We further
investigate the evolution of user-level sentiments and latent feature vectors
in an online framework and devise an efficient online algorithm to sequentially
update the clustering of tweets, users and features with newly arrived data.
The online framework not only provides better quality of both dynamic
user-level and tweet-level sentiment analysis, but also improves the
computational and storage efficiency. We verified the effectiveness and
efficiency of the proposed approaches on the November 2012 California ballot
Twitter data.Comment: A short version is in Proceeding of the 2014 ACM SIGMOD International
Conference on Management of dat
BCS-BEC crossover in a relativistic boson-fermion model beyond mean field approximation
We investigate the fluctuation effect of the di-fermion field in the
crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein
condensate (BEC) in a relativistic superfluid. We work within the boson-fermion
model obeying a global U(1) symmetry. To go beyond the mean field approximation
we use Cornwall-Jackiw-Tomboulis (CJT) formalism to include higher order
contributions. The quantum fluctuations of the pairing condensate is provided
by bosons in non-zero modes, whose interaction with fermions gives the
two-particle-irreducible (2PI) effective potential. It changes the crossover
property in the BEC regime. With the fluctuations the superfluid phase
transition becomes the first order in grand canonical ensemble. We calculate
the condensate, the critical temperature and particle abundances as
functions of crossover parameter the boson mass.Comment: The model Lagrangian is re-formulated by decomposing the complex
scalar field into its real and imaginary parts. The anomalous propagators of
the complex scalar are then included at tree level. All numerical results are
updated. ReVTex 4, 13 pages, 10 figures, PRD accepted versio
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