Ali Bereyhi

Empirical coordination in a triangular multiterminal network

In this paper, we investigate the problem of the empirical coordination in a triangular multiterminal network. A triangular multiterminal network consists of three terminals where two terminals observe two external i.i.d correlated sequences. The third terminal wishes to generate a sequence with desired empirical joint distribution. For this problem, we derive inner and outer bounds on the empirical coordination capacity region. It is shown that the capacity region of the degraded source network and the inner and outer bounds on the capacity region of the cascade multiterminal network can be directly obtained from our inner and outer bounds. For a cipher system, we establish key distribution over a network with a reliable terminal, using the results of the empirical coordination. As another example, the problem of rate distortion in the triangular multiterminal network is discussed in which a distributed doubly symmetric binary source is available.

RSB decoupling property of MAP estimators

The large-system decoupling property of a MAP estimator is studied when it estimates the i.i.d. vector x from the observation y = Ax + z with A being chosen from a wide range of matrix ensembles, and the noise vector z being i.i.d. and Gaussian. Using the replica method, we show that the marginal joint distribution of any two corresponding input and output symbols converges to a deterministic distribution which describes the input-output distribution of a single user system followed by a MAP estimator. Under the bRSB assumption, the single user system is a scalar channel with additive noise where the noise term is given by the sum of an independent Gaussian random variable and b correlated interference terms. As the bRSB assumption reduces to RS, the interference terms vanish which results in the formerly studied RS decoupling principle.

Asymptotics of transmit antenna selection: Impact of multiple receive antennas

Consider a fading Gaussian MIMO channel with Nt transmit and Nr receive antennas. The transmitter selects Lt antennas corresponding to the strongest channels. For this setup, we study the distribution of the input-output mutual information when Nt grows large. We show that, for any Nr and Lt, the distribution of the input-output mutual information is accurately approximated by a Gaussian distribution whose mean grows large and whose variance converges to zero. Our analysis depicts that, in the large limit, the gap between the expectation of the mutual information and its corresponding upper bound, derived by applying Jensens inequality, converges to a constant which only depends on Nr and Lt. The result extends the scope of channel hardening to the general case of antenna selection with multiple receive and selected transmit antennas. Although the analyses are given for the large-system limit, our numerical investigations indicate the robustness of the approximated distribution even when the number of antennas is not large.

Asymptotics of nonlinear LSE precoders with applications to transmit antenna selection

This paper studies the large-system performance of Least Square Error (LSE) precoders which minimize the input-output distortion over an arbitrary support subject to a general penalty function. The asymptotics are determined via the replica method in a general form which encloses the Replica Symmetric (RS) and Replica Symmetry Breaking (RSB) ansätze. As a result, the “marginal decoupling property” of LSE precoders for b-steps of RSB is derived. The generality of the studied setup enables us to address special cases in which the number of active transmit antennas are constrained. Our numerical investigations depict that the computationally efficient forms of LSE precoders based on “li-norm” minimization perform close to the cases with “zero-norm” penalty function which have a considerable improvements compared to the random antenna selection. For the case with BPSK signals and restricted number of active antennas, the results show that RS fails to predict the performance while the RSB ansatz is consistent with theoretical bounds.

Replica symmetry breaking in compressive sensing

For noisy compressive sensing systems, the asymptotic distortion with respect to an arbitrary distortion function is determined when a general class of least-square based reconstruction schemes is employed. The sampling matrix is considered to belong to a large ensemble of random matrices including i.i.d. and projector matrices, and the source vector is assumed to be i.i.d. with a desired distribution. We take a statistical mechanical approach by representing the asymptotic distortion as a macroscopic parameter of a spin glass and employing the replica method for the large-system analysis. In contrast to earlier studies, we evaluate the general replica ansatz which includes the RS ansatz as well as RSB. The generality of the solution enables us to study the impact of symmetry breaking. Our numerical investigations depict that for the reconstruction scheme with the “zero-norm” penalty function, the RS fails to predict the asymptotic distortion for relatively large compression rates; however, the one-step RSB ansatz gives a valid prediction of the performance within a larger regime of compression rates.

A new class of nonlinear precoders for hardware efficient massive MIMO systems

A general class of nonlinear Least Square Error (LSE) precoders in multi-user multiple-input multiple-output systems is analyzed using the replica method from statistical mechanics. A single cell downlink channel with N transmit antennas at the base station and K single-antenna users is considered. The data symbols are assumed to be iid Gaussian and the precoded symbols on each transmit antenna are restricted to be chosen from a predefined set X. The set X encloses several well-known constraints in wireless communications including signals with peak power, constant envelope signals and finite constellations such as Phase Shift Keying (PSK). We determine the asymptotic distortion of the LSE precoder under both the Replica Symmetry (RS) and the one step Replica Symmetry Breaking (1-RSB) assumptions. For the case of peak power constraint on each transmit antenna, our analyses under the RS assumption show that the LSE precoder can reduce the peak to average power ratio to 3dB without any significant performance loss. For PSK constellations, as N/K grows, the RS assumption fails to predict the performance accurately and therefore, investigations under the 1-RSB assumption are further considered. The results show that the 1-RSB assumption is more accurate.

Key agreement over a state-dependent 3-receiver broadcast channel

In this paper, we consider the problem of secret key agreement in state-dependent 3-receiver broadcast channels. In the proposed model, there are two legitimate receivers, an eavesdropper and a transmitter where the channel state information is non-causally available at the transmitter. We consider two setups. In the first setup, the transmitter tries to agree on a common key with the legitimate receivers while keeping it concealed from the eavesdropper. Simultaneously, the transmitter agrees on a private key with each of the legitimate receivers that needs to be kept secret from the other legitimate receiver and the eavesdropper. For this setup, we derive inner and outer bounds on the secret key capacity region. In the second setup, we assume that a backward public channel is available among the receivers and the transmitter. Each legitimate receiver wishes to share a private key with the transmitter. For this setup, an inner bound on the private key capacity region is found. Furthermore, the capacity region of the secret key in the state-dependent wiretap channel can be deduced from our inner and outer bounds.