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

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

Reduced complexity sequence detection

The paper deals with the design of suboptimal receivers for data transmission over frequency selective channels. The complexity of the optimum detector, that is the maximum likelihood sequence detector (MLSD), turns out be exponential in the channel memory. Hence, when dealing with channels with long memory, suboptimal receiver structures must be considered. Among suboptimal methods, a technique that allows reduction of the complexity is the delayed decision feedback sequence detector (DDFSD). This receiver is based on a Viterbi processor where the channel memory is truncated. The memory truncation is compensated by a per-survivor decision feedback equalizer. In order to achieve good performance, it is crucial to operate an appropriate prefiltering of the received sequence before the DDFSD. Our contribution is to extend the principles of MLSD and DDFSD to the case where the prefilter is the feedforward filter of a minimum mean-square error decision feedback equalizer (MMSE-DFE). Moreover performance evaluation of the MMSE prefiltered DDFSD is addressed. The union upper bound is used to evaluate the probability of first-event error. Simulation results show that our proposed design of the MMSE-DDFSD gives substantial benefits when a severe frequency selective channel is considered

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

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