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 $W$ microstates of the famous Boltzmann-Planck entropy formula $S=k \log(W)$ 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

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

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