61 research outputs found
The Shannon-McMillan Theorem Proves Convergence to Equiprobability of Boltzmann's Microstates
The paper shows that, for large number of particles and for distinguishable
and non-interacting identical particles, convergence to equiprobability of the
microstates of the famous Boltzmann-Planck entropy formula is
proved by the Shannon-McMillan theorem, a cornerstone of information theory.
This result further strengthens the link between information theory and
statistical mechanics.Comment: 5 page
Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory
The paper analyzes the entropy of a system composed by an arbitrary number of
indistinguishable particles at the equilibrium, defining entropy as a function
of the quantum state of the system, not of its phase space representation. Our
crucial observation is that the entropy of the system is the Shannon entropy of
the random occupancy numbers of the quantum states allowed to system's
particles. We consider the information-theoretic approach, which is based on
Jaynes' maximum entropy principle, and the empirical approach, which leads to
canonical typicality in modern quantum thermodynamics. In the
information-theoretic approach, the occupancy numbers of particles' quantum
states are multinomially distributed, while in the empirical approach their
distribution is multivariate hypergeometric. As the number of samples of the
empirical probability tends to infinity, the multivariate hypergeometric
distribution tends to the multinomial distribution. This reconciles, at least
in the limit, the two approaches. When regarded from the perspective of quantum
measurement, our analysis suggests the existence of another kind of
subjectivism than the well-known subjectivism that characterizes the maximum
entropy approach. This form of subjectivity is responsible for the collapse of
entropy to zero after the quantum measurement, both in the
information-theoretic and in the empirical approaches
Tight Upper and Lower Bounds to the Information Rate of the Phase Noise Channel
Numerical upper and lower bounds to the information rate transferred through
the additive white Gaussian noise channel affected by discrete-time
multiplicative autoregressive moving-average (ARMA) phase noise are proposed in
the paper. The state space of the ARMA model being multidimensional, the
problem cannot be approached by the conventional trellis-based methods that
assume a first-order model for phase noise and quantization of the phase space,
because the number of state of the trellis would be enormous. The proposed
lower and upper bounds are based on particle filtering and Kalman filtering.
Simulation results show that the upper and lower bounds are so close to each
other that we can claim of having numerically computed the actual information
rate of the multiplicative ARMA phase noise channel, at least in the cases
studied in the paper. Moreover, the lower bound, which is virtually
capacity-achieving, is obtained by demodulation of the incoming signal based on
a Kalman filter aided by past data. Thus we can claim of having found the
virtually optimal demodulator for the multiplicative phase noise channel, at
least for the cases considered in the paper.Comment: 5 pages, 2 figures. Accepted for presentation at ISIT 201
Wiener's loop filter for PLL-based carrier recovery of OQPSK and MSK-type modulations
This letter considers carrier recovery for offset quadrature phase shift keying (OQPSK) and minimum shift keying-type (MSK-type) modulations based on phase-lock loop (PLL). The concern of the letter is the optimization of the loop filter of the PLL. The optimization is worked out in the light of Wiener's theory taking into account the phase noise affecting the incoming carrier, the additive white Gaussian noise that is present on the channel, and the self-noise produced by the phase detector. Delay in the loop, which may affect the numerical implementation of the PLL, is also considered. Closed-form expressions for the loop filter and for the mean-square error are given for the case where the phase noise is characterized as a first-order process
Optimal filtering in pilot-aided carrier recovery
The paper deals with carrier recovery based on pilot symbols in single-carrier systems. Wiener's method is used to determine the optimal unconstrained filter in estimation of phase noise assuming that a sequence of equally spaced pilot symbols is available. Our analysis allows to capture two effects that are not considered in the existing literature: the impact of aliasing due to sampling of the phase noise sequence at the pilot rate and the cyclostationary nature of the estimate hence of its performance. Experimental results are derived also for the case, where the filter is constrained to the cascade of two moving averages. These results show that, in the considered example, the mean-square phase error of the constrained filter is within 0.35 dB from the MSE of the optimal filter
Design of Short, High-Rate DVB-S2-Like Semi-Regular LDPC Codes
This work focuses on high-rate () moderate-length () low-density parity-check codes. High-rate codes allow to maintain good quality of the preliminary decisions that are used in carrier recovery, while a moderate code length allows to keep the latency low. The interleaver of the LDPC matrix that we consider is inspired to the DVB-S2 standard one. A novel approach for avoiding short cycles is analyzed. A modified BP decoding algorithm is applied in order to deal with longer cycles. Simulations and results for the AWGN channel are presented, both for BPSK signalling and for coded modulation based on the partition
Techniques for Efficient Spectrum Sensing in Heterogeneous Wireless Networks
Spectrum sensing is one of the most challenging and complex task in cognitive radio and it should be often performed by mobile devices with a limited battery life. So the development of efficient techniques for advanced spectrum sensing in heterogeneous, ad hoc environments, such as those in emergency situations, is of crucial importance. In this context spectrum sensing can be completed by the determination of the spatial coordinates of the devices in order to achieve the full potential of ad hoc networks management.
In this work we present two techniques for improving the efficiency of mobile devices involved in spatial spectrum sensing: design of efficacious frequency synthesizers and hybrid localization for saving energy in the tracking process.
Among the different frequency synthesis techniques, we focus on the phase-locked loop (PLL) approach and we consider the optimization of the loop filter for the PLL in the light of Wiener theory by taking into account the phase
noise affecting the incoming carrier, the additive white Gaussian noise and the self-noise produced by the phase detector. Then we show an approach for improving the trade-off between energy consumption and performance in a localization tracking process, realized mixing active signal transmissions as well as passive signal reflections
Pilot-Aided Equalization with a Constrained Noise-Estimation Filter
In this paper we focus on a single carrier pilotassisted
transmission scheme where one pilot symbol is periodically
inserted in the transmitted sequence on a time-division
multiplexing basis. A new equalization scheme, where the knowledge
of pilot symbols is exploited by the equalizer to generate
an estimate of the noise affecting the symbol to be detected,
is introduced and analyzed. The criterion used to compute the
equalizer coefficients is the minimization of the mean-square
error (MSE). The main new result of our analysis is that the
optimal pilot aided equalizer (PAE) can be decomposed as the
cascade of an unconstrained minimum MSE (MMSE) linear
equalizer (LE) and a data-aided noise estimation filter. This
result completes and extends the noise-predictive view of decision
feedback equalization to general data-aided equalization. The
PAE is compared here to the MMSE-LE and to the MSE decision
feedback equalizer on two frequency selective wireless channels
Lower Bound Based on Kalman Carrier Recovery below the Information Rate of Wiener Phase Noise Channel
A new lower bound below the information rate
transferred through the Additive White Gaussian Noise (AWGN)
channel affected by discrete-time multiplicative Wiener’s phase
noise is proposed in the paper. The proposed lower bound is based
on the Kalman approach to data-aided carrier phase recovery,
and is less computationally demanding than known methods
based on phase quantization and trellis representation of phase
memory. Simulation results show that the lower bound is close
to the actual channel capacity, especially at low-to-intermediate
signal-to-noise ratio
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