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On the use of diverse arguments to increase confidence in dependability claims
The Necessity of Relay Selection
We determine necessary conditions on the structure of symbol error rate (SER)
optimal quantizers for limited feedback beamforming in wireless networks with
one transmitter-receiver pair and R parallel amplify-and-forward relays. We
call a quantizer codebook "small" if its cardinality is less than R, and
"large" otherwise. A "d-codebook" depends on the power constraints and can be
optimized accordingly, while an "i-codebook" remains fixed. It was previously
shown that any i-codebook that contains the single-relay selection (SRS)
codebook achieves the full-diversity order, R. We prove the following:
Every full-diversity i-codebook contains the SRS codebook, and thus is
necessarily large. In general, as the power constraints grow to infinity, the
limit of an optimal large d-codebook contains an SRS codebook, provided that it
exists. For small codebooks, the maximal diversity is equal to the codebook
cardinality. Every diversity-optimal small i-codebook is an orthogonal
multiple-relay selection (OMRS) codebook. Moreover, the limit of an optimal
small d-codebook is an OMRS codebook.
We observe that SRS is nothing but a special case of OMRS for codebooks with
cardinality equal to R. As a result, we call OMRS as "the universal necessary
condition" for codebook optimality. Finally, we confirm our analytical findings
through simulations.Comment: 29 pages, 4 figure
Recommended from our members
The use of proofs in diversity arguments
The limits to the reliability that can be claimed for a design-diverse fault-tolerant system are mainly determined by the dependence that must be expected in the failure behaviours of the different versions: claims for independence between version failure processes are not believable. In this note we examine a different approach, in which a simple secondary system is used as a back-up to a more complex primary. The secondary system is sufficiently simple that claims for its perfection (with respect to design faults) are possible, but there is not complete certainty about such perfection. It is shown that assessment of the reliability of the overall fault-tolerant system in this case may take advantage of claims for independence that are more plausible than those involved in design diversity
Exit, Voice, and Disloyalty
Innomhuspositioneringssystem kan med fördel användas i många olika tillämpningar, allt från sjukhus till shoppingcenter. Denna rapport behandlar olika tekniker och lösningar för att designa ett positioneringssystem. Rapporten tar även upp i detalj hur ett system kan konstrueras av ZigBee kombinerat med dödräkning
Exit, Voice, and Disloyalty
This Lecture begins with a puzzle about Albert Hirschman’s famous work Exit, Voice, and Loyalty: Why do we make much of exit and voice but utterly neglect loyalty? It’s a question that goes well beyond Hirschman’s book. For example, much of constitutional theory is preoccupied with a single question: What doesademocracy owe its minorities? And most of the answers to this question fit naturally into the two categories Hirschman made famous: voice and exit. On both the rights side and the structural side of constitutional theory, scholars worry about providing minorities with an adequate level of influence. And the solutions they propose almost inevitably offer minorities a chance at voice or exit, ] as if no other option exists. The First Amendment, for instance, offers minorities the right to free speech (voice) and private association (exit). Similarly, structural arrangements give minorities the chance to vote in national elections (voice) and in state elections (exit)
On the Diversity-Multiplexing Tradeoff of Unconstrained Multiple-Access Channels
In this work the optimal diversity-multiplexing tradeoff (DMT) is
investigated for the multiple-input multiple-output fading multiple-access
channels with no power constraints (infinite constellations). For K users
(K>1), M transmit antennas for each user, and N receive antennas, infinite
constellations in general and lattices in particular are shown to attain the
optimal DMT of finite constellations for the case N equals or greater than
(K+1)M-1, i.e., user limited regime. On the other hand for N<(K+1)M-1 it is
shown that infinite constellations can not attain the optimal DMT. This is in
contrast to the point-to-point case in which infinite constellations are DMT
optimal for any M and N. In general, this work shows that when the network is
heavily loaded, i.e. K>max(1,(N-M+1)/M), taking into account the shaping region
in the decoding process plays a crucial role in pursuing the optimal DMT. By
investigating the cases where infinite constellations are optimal and
suboptimal, this work also gives a geometrical interpretation to the DMT of
infinite constellations in multiple-access channels
Processor Verification Using Efficient Reductions of the Logic of Uninterpreted Functions to Propositional Logic
The logic of equality with uninterpreted functions (EUF) provides a means of
abstracting the manipulation of data by a processor when verifying the
correctness of its control logic. By reducing formulas in this logic to
propositional formulas, we can apply Boolean methods such as Ordered Binary
Decision Diagrams (BDDs) and Boolean satisfiability checkers to perform the
verification.
We can exploit characteristics of the formulas describing the verification
conditions to greatly simplify the propositional formulas generated. In
particular, we exploit the property that many equations appear only in positive
form. We can therefore reduce the set of interpretations of the function
symbols that must be considered to prove that a formula is universally valid to
those that are ``maximally diverse.''
We present experimental results demonstrating the efficiency of this approach
when verifying pipelined processors using the method proposed by Burch and
Dill.Comment: 46 page
MIMO Networks: the Effects of Interference
Multiple-input/multiple-output (MIMO) systems promise enormous capacity
increase and are being considered as one of the key technologies for future
wireless networks. However, the decrease in capacity due to the presence of
interferers in MIMO networks is not well understood. In this paper, we develop
an analytical framework to characterize the capacity of MIMO communication
systems in the presence of multiple MIMO co-channel interferers and noise. We
consider the situation in which transmitters have no information about the
channel and all links undergo Rayleigh fading. We first generalize the known
determinant representation of hypergeometric functions with matrix arguments to
the case when the argument matrices have eigenvalues of arbitrary multiplicity.
This enables the derivation of the distribution of the eigenvalues of Gaussian
quadratic forms and Wishart matrices with arbitrary correlation, with
application to both single user and multiuser MIMO systems. In particular, we
derive the ergodic mutual information for MIMO systems in the presence of
multiple MIMO interferers. Our analysis is valid for any number of interferers,
each with arbitrary number of antennas having possibly unequal power levels.
This framework, therefore, accommodates the study of distributed MIMO systems
and accounts for different positions of the MIMO interferers.Comment: Submitted to IEEE Trans. on Info. Theor
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