352 research outputs found
Dynamics of continued fractions and distribution of modular symbols
We formulate a thermodynamical approach to the study of distribution of
modular symbols, motivated by the work of Baladi-Vall\'ee. We introduce the
modular partitions of continued fractions and observe that the statistics for
modular symbols follow from the behavior of modular partitions. We prove the
limit Gaussian distribution and residual equidistribution for modular
partitions as a vector-valued random variable on the set of rationals whose
denominators are up to a fixed positive integer by studying the spectral
properties of transfer operator associated to the underlying dynamics. The
approach leads to a few applications. We show an average version of conjectures
of Mazur-Rubin on statistics for the period integrals of an elliptic newform.
We further observe that the equidistribution of mod values of modular
symbols leads to mod non-vanishing results for special modular -values
twisted by a Dirichlet character.Comment: 42 page
Outage-based ergodic link adaptation for fading channels with delayed CSIT
Link adaptation in which the transmission data rate is dynamically adjusted
according to channel variation is often used to deal with time-varying nature
of wireless channel. When channel state information at the transmitter (CSIT)
is delayed by more than channel coherence time due to feedback delay, however,
the effect of link adaptation can possibly be taken away if this delay is not
taken into account. One way to deal with such delay is to predict current
channel quality given available observation, but this would inevitably result
in prediction error. In this paper, an algorithm with different view point is
proposed. By using conditional cdf of current channel given observation, outage
probability can be computed for each value of transmission rate . By
assuming that the transmission block error rate (BLER) is dominated by outage
probability, the expected throughput can also be computed, and can be
determined to maximize it. The proposed scheme is designed to be optimal if
channel has ergodicity, and it is shown to considerably outperform conventional
schemes in certain Rayleigh fading channel model
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