175 research outputs found
DECODING OF MULTIPOINT ALGEBRAIC GEOMETRY CODES VIA LISTS
Algebraic geometry codes have been studied greatly since their introduction by Goppa . Early study had focused on algebraic geometry codes CL(D;G) where G was taken to be a multiple of a single point. However, it has been shown that if we allow G to be supported by more points, then the associated code may have better parameters. We call such a code a multipoint code and if G is supported by m points, then we call it an m-point code. In this dissertation, we wish to develop a decoding algorithm for multipoint codes. We show how we can embed a multipoint algebraic geometry code into a one-point supercode so that we can perform list decoding in the supercode. From the output list, we determine which of the elements is a codeword in the multipoint code. In this way we have unique decoding up to the minimum distance for multipoint algebraic geometry codes, provided the parameters of the list decoding algorithm are set appropriately
List Decoding Algorithm based on Voting in Groebner Bases for General One-Point AG Codes
We generalize the unique decoding algorithm for one-point AG codes over the
Miura-Kamiya Cab curves proposed by Lee, Bras-Amor\'os and O'Sullivan (2012) to
general one-point AG codes, without any assumption. We also extend their unique
decoding algorithm to list decoding, modify it so that it can be used with the
Feng-Rao improved code construction, prove equality between its error
correcting capability and half the minimum distance lower bound by Andersen and
Geil (2008) that has not been done in the original proposal except for
one-point Hermitian codes, remove the unnecessary computational steps so that
it can run faster, and analyze its computational complexity in terms of
multiplications and divisions in the finite field. As a unique decoding
algorithm, the proposed one is empirically and theoretically as fast as the BMS
algorithm for one-point Hermitian codes. As a list decoding algorithm,
extensive experiments suggest that it can be much faster for many moderate
size/usual inputs than the algorithm by Beelen and Brander (2010). It should be
noted that as a list decoding algorithm the proposed method seems to have
exponential worst-case computational complexity while the previous proposals
(Beelen and Brander, 2010; Guruswami and Sudan, 1999) have polynomial ones, and
that the proposed method is expected to be slower than the previous proposals
for very large/special inputs.Comment: Accepted for publication in J. Symbolic Computation. LaTeX2e
article.cls, 42 pages, 4 tables, no figures. Ver. 6 added an illustrative
example of the algorithm executio
Computational Aspects of Retrieving a Representation of an Algebraic Geometry Code
Producción CientíficaCode-based cryptography is an interesting alternative to classic number-theoretic public key cryptosystem since it is conjectured to be secure against quantum computer attacks. Many families of codes have been proposed for these cryptosystems such as algebraic geometry codes. In [Designs, Codes and Cryptography, pages 1-16, 2012] -for so called very strong algebraic geometry codes , where is an algebraic curve over , is an -tuple of mutually distinct -rational points of and is a divisor of with disjoint support from --- it was shown that an equivalent representation can be found. The -tuple of points is obtained directly from a generator matrix of , where the columns are viewed as homogeneous coordinates of these points. The curve is given by , the homogeneous elements of degree of the vanishing ideal . Furthermore, it was shown that can be computed efficiently as the kernel of certain linear map. What was not shown was how to get the divisor and how to obtain efficiently an adequate decoding algorithm for the new representation. The main result of this paper is an efficient computational approach to the first problem, that is getting . The security status of the McEliece public key cryptosystem using algebraic geometry codes is still not completely settled and is left as an open problemThis research was partly supported by the Danish National Research Foundation and the National Science Foundation of China (Grant No.\ 11061130539) for the Danish-Chinese Center for Applications of Algebraic Geometry in Coding Theory and Cryptography and by Spanish grants MTM2007-64704, MTM2010-21580-C02-02 and MTM2012-36917-C03-03. Part of the research of the second author is also funded by the Vernon Wilson Endowed Chair at Eastern Kentucky University during his sabbatical leave
Analysis and Design of Multiple-Antenna Cognitive Radios with Multiple Primary User Signals
We consider multiple-antenna signal detection of primary user transmission
signals by a secondary user receiver in cognitive radio networks. The optimal
detector is analyzed for the scenario where the number of primary user signals
is no less than the number of receive antennas at the secondary user. We first
derive exact expressions for the moments of the generalized likelihood ratio
test (GLRT) statistic, yielding approximations for the false alarm and
detection probabilities. We then show that the normalized GLRT statistic
converges in distribution to a Gaussian random variable when the number of
antennas and observations grow large at the same rate. Further, using results
from large random matrix theory, we derive expressions to compute the detection
probability without explicit knowledge of the channel, and then particularize
these expressions for two scenarios of practical interest: 1) a single primary
user sending spatially multiplexed signals, and 2) multiple spatially
distributed primary users. Our analytical results are finally used to obtain
simple design rules for the signal detection threshold.Comment: Revised version (14 pages). Change in titl
Técnicas de pré-codificação para sistemas multicelulares coordenados
Doutoramento em TelecomunicaçõesCoordenação Multicélula é um tópico de investigação em rápido
crescimento e uma solução promissora para controlar a interferência entre
células em sistemas celulares, melhorando a equidade do sistema e
aumentando a sua capacidade. Esta tecnologia já está em estudo no LTEAdvanced
sob o conceito de coordenação multiponto (COMP). Existem
várias abordagens sobre coordenação multicélula, dependendo da
quantidade e do tipo de informação partilhada pelas estações base, através
da rede de suporte (backhaul network), e do local onde essa informação é
processada, i.e., numa unidade de processamento central ou de uma forma
distribuída em cada estação base.
Nesta tese, são propostas técnicas de pré-codificação e alocação de
potência considerando várias estratégias: centralizada, todo o
processamento é feito na unidade de processamento central; semidistribuída,
neste caso apenas parte do processamento é executado na
unidade de processamento central, nomeadamente a potência alocada a
cada utilizador servido por cada estação base; e distribuída em que o
processamento é feito localmente em cada estação base. Os esquemas
propostos são projectados em duas fases: primeiro são propostas soluções
de pré-codificação para mitigar ou eliminar a interferência entre células,
de seguida o sistema é melhorado através do desenvolvimento de vários
esquemas de alocação de potência. São propostas três esquemas de
alocação de potência centralizada condicionada a cada estação base e com
diferentes relações entre desempenho e complexidade. São também
derivados esquemas de alocação distribuídos, assumindo que um sistema
multicelular pode ser visto como a sobreposição de vários sistemas com
uma única célula. Com base neste conceito foi definido uma taxa de erro
média virtual para cada um desses sistemas de célula única que compõem
o sistema multicelular, permitindo assim projectar esquemas de alocação
de potência completamente distribuídos.
Todos os esquemas propostos foram avaliados em cenários realistas,
bastante próximos dos considerados no LTE. Os resultados mostram que
os esquemas propostos são eficientes a remover a interferência entre
células e que o desempenho das técnicas de alocação de potência
propostas é claramente superior ao caso de não alocação de potência. O
desempenho dos sistemas completamente distribuídos é inferior aos
baseados num processamento centralizado, mas em contrapartida podem
ser usados em sistemas em que a rede de suporte não permita a troca de
grandes quantidades de informação.Multicell coordination is a promising solution for cellular wireless systems
to mitigate inter-cell interference, improving system fairness and
increasing capacity and thus is already under study in LTE-A under the
coordinated multipoint (CoMP) concept. There are several coordinated
transmission approaches depending on the amount of information shared
by the transmitters through the backhaul network and where the
processing takes place i.e. in a central processing unit or in a distributed
way on each base station.
In this thesis, we propose joint precoding and power allocation techniques
considering different strategies: Full-centralized, where all the processing
takes place at the central unit; Semi-distributed, in this case only some
process related with power allocation is done at the central unit; and Fulldistributed,
where all the processing is done locally at each base station.
The methods are designed in two phases: first the inter-cell interference is
removed by applying a set of centralized or distributed precoding vectors;
then the system is further optimized by centralized or distributed power
allocation schemes. Three centralized power allocation algorithms with
per-BS power constraint and different complexity tradeoffs are proposed.
Also distributed power allocation schemes are proposed by considering
the multicell system as superposition of single cell systems, where we
define the average virtual bit error rate (BER) of interference-free single
cell system, allowing us to compute the power allocation coefficients in a
distributed manner at each BS.
All proposed schemes are evaluated in realistic scenarios considering LTE
specifications. The numerical evaluations show that the proposed schemes
are efficient in removing inter-cell interference and improve system
performance comparing to equal power allocation. Furthermore, fulldistributed
schemes can be used when the amounts of information to be
exchanged over the backhaul is restricted, although system performance is
slightly degraded from semi-distributed and full-centralized schemes, but
the complexity is considerably lower. Besides that for high degrees of
freedom distributed schemes show similar behaviour to centralized ones
Impact of antenna correlation on the performance of partial relay selection
Antenna correlation is generally viewed as an obstacle to realize the desired performance of a wireless system. In this article, we investigate the performance of partial relay selection in the presence of antenna correlation. We consider both channel state information (csi)-assisted and fixed gain amplify-and-forward (AF) relay schemes. The source and the destination are equipped with multiple antennas communicating via the best first hop signal-to-noise ratio (SNR) relay. We derived the closed form expression for outage probability, average symbol error rate (SER) for both schemes. Further, an exact expression is derived for the ergodic capacity in the csi-assisted relay case and an approximated expression is considered for the fixed gain case. Moreover, we provide simple asymptotic results and show that the diversity order of the system remains unchanged with the effect of antenna correlation for both types of relay schemes
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Performance evaluation of fixed WiMax physical layer under high fading channels
This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.A radio channel characteristic modelling is essential in every network planning. This project deals with the performance of WiMax networks in an outdoor environment while using fading channel models. The radio channels characteristics are analyzed by simulations have been done using Matlab programming. Stanford University Interim(SUI) Channels set was proposed to simulate the fixed broadband wireless access channel environments where IEEE 802.16d is to be deployed. It has six channel models that are grouped into three categories according to three typical different outdoor Terrains, in order to give a comprehensive study of fading channels on the overall performance of the system, WiMax system has been tested under SUI channels that modified into account for 30o directional antennas, with 90% cell coverage and with 99.9% reliability in its geographical covered area. Furthermore, in order to combat the fading which occurs in urban areas and improve the capacity and the throughput of the system, multiples antennas at both ends of communication link are used, the transmission gain obtained when using multiple antennas instead of only a single antenna. Space-time coding and maximum ratio combining for more than one transmit and receive antenna is implemented to allow performance investigations in various MIMO scenarios. It has been concluded that uses multiple antennas at the receiver offers a significant improvement of 3 dB of gain in the channel SNR. This thesis also contain implementation of all compulsory features of the WiMax OFDM physical layer specified in IEEE 802.16-2004 using Matlab coding. In order to combat the temporal variations in quality on a multipath fading channel, an adaptive modulation technique is used. This technique employs multiple modulation schemes to instantaneously adapt to the variations in the channel SNR, thus maximizing the system throughput and improving BER performance. WiMax transceiver has been tested with and without encoding and studied the effect of encoding on multipath channel. Testing the system with flexible channel bandwidth has been part of this thesis. Finally it has been explained in this thesis the affect of increasing the size of cyclic prefix on overall performance of WiMax system
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