# Your search: "author:Jafar, Syed Ali"

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## Scholarly Works (6 results)

The problem of weakly-private information retrieval, is a variant of private information

retrieval, where the user wants to retrieve 1 out of K messages from a distributed storage

system with N servers that stores all K messages, and is willing to leak some information

of the identity of the desired message. In this work, we study the problem of weakly-private

information retrieval. A novel information leakage metric is proposed, and the capacity for

the setting of N = 2 servers, and arbitrary number of messages K is characterized. In

particular, in the capacity achieving scheme, designing the distribution of the non-uniformly

distributed noise Z turns out to be the key to achieve the capacity.

We investigate the optimality of linear interference

alignment (allowing symbol extensions) for Â 3-user

$M_T\times M_R$ MIMO interference channel where $M_T$ and $M_R$

denote the number of antennas at each transmitter and each receiver,

respectively, and the \emph{channel coefficients are held constant}. Recently, Wang et al. have conjectured that interference alignment based on linear beamforming using only proper Gaussian codebooks and possibly with symbol extensions, is sufficient to achieve the information theoretic DoF outer bound for all $M_T, M_R$ values except

if $|M_T-M_R|=1$, $\min(M_T,M_R)\geq 2$. A partial proof of the conjecture is provided by Wang et al. for arbitrary $M_T, M_R$ values subject to a final numerical evaluation step that needs to be performed for each $M_T, M_R$ setting to complete the proof. The numerical evaluation step is also carried out explicitly by Wang et al. to settle the conjecture for all Â $M_T, M_R$ values up to 10. For $|M_T-M_R|=1$, $\min(M_T,M_R)\geq 2$, Wang et al. show that interference alignment schemes based on linear beamforming with proper Gaussian signaling and symbol extensions are not sufficient to achieve the information-theoretic DoF outer bonds. In contrast, in this note we show, for all $M_T, M_R$ values up to 10, that interference alignment schemes based on linear beamforming over symbol extensions are enough to achieve the information theoretic DoF outer bounds for constant channels, if \emph{asymmetric complex signaling} is utilized. Based on this new insight, we conjecture that linear interference alignment is optimal for achieving the information theoretic DoF outer bounds for all $M_T, M_R$ values in the 3 user $M_T\times M_R$ MIMO interference channel with constant channel coefficients, except for the case $M_T=M_R=1$ where it is known that either time/frequency-varying channels or non-linear (e.g., rational alignment) schemes are required.

We characterize the degrees of freedom (DoF) of MIMO interference networks with rank-

deficient channel matrices. For the 2-user rank deficient MIMO interference channel, we prove

the optimality of previously known achievable DoF in the symmetric case and generalize the re-

sult to fully asymmetric settings. For the K-user rank deficient interference channel, we improve

the previously known achievable DoF and provide a tight outer bound to establish optimality

in symmetric settings. In particular, we show that for the K-user rank deficient interference

channel, when all nodes have M antennas, all direct channels have rank D0, all cross chan-

nels are of rank D, and the channels are otherwise generic, the optimal DoF value per user is

min(D0, M −min(M,(K−1)D)). For 2-user and 3-user rank deficient channels, achievable schemes2

are for both constant and time-varying channels, while for K-user rank deficient channels, we present schemes for time-varying channels and note that the insights would act as stepping stones for constant channels. Notably for interference channels, the rank-deficiency of direct channels does not help and the rank-deficiency of cross-channels does not hurt. The main technical challenge is to account for the spatial dependencies introduced by rank deficiencies in the interference alignment schemes that typically rely on the independence of channel coefficients.