96 research outputs found
Network Coherence Time Matters - Aligned Image Sets and the Degrees of Freedom of Interference Networks with Finite Precision CSIT and Perfect CSIR
This work obtains the first bound that is provably sensitive to network
coherence time, i.e., coherence time in an interference network where all
channels experience the same coherence patterns. This is accomplished by a
novel adaptation of the aligned image sets bound, and settles various open
problems noted previously by Naderi and Avestimehr and by Gou et al. For
example, a necessary and sufficient condition is obtained for the optimality of
1/2 DoF per user in a partially connected interference network where the
channel state information at the receivers (CSIR) is perfect, the channel state
information at the transmitters (CSIT) is instantaneous but limited to finite
precision, and the network coherence time is T_c= 1. The surprising insight
that emerges is that even with perfect CSIR and instantaneous finite precision
CSIT, network coherence time matters, i.e., it has a DoF impact.Comment: 19 pages, 4 figure
Fertility Transition in Pakistan: Evidence from Census
In the absence of an accurate and complete registration system, efforts were made to estimate the levels of vital statistics through sample surveys. The first such effort was made through the Population Growth Estimation (PGE) project conducted from January, 1962 to December 1965. Later on, various demographic surveys were conducted almost at regular intervals and the last effort in the series was Pakistan Reproductive Health and Family Planning Survey (PRHFPS) in the year 2000-01. Although all these efforts were made to ascertain levels and trends of various demographic events, yet the estimates particularly the ones on fertility remained controversial. The first signal of fertility reduction was emanated from the 1975 Pakistan Fertility Survey (PFS) which estimated a Total Fertility Rate (TFR) of 6.3 children from over 7 children estimated earlier from PGE data. However, all hopes of the onset of fertility transition were shattered by the [Retherfordâs, et al. (1987)] study entitled âFertility Trend in Pakistan: The Decline that Wasnâtâ. By using the Own Children Method, they confirmed that the decline in fertility was an artifact of the data. Another study by Shah, Pullum, and Irfan (1986) also termed the fertility decline shown by the PFS data as spurious. The Pakistan Labour Force and Migration Survey, conducted five years later, in 1979-80, estimated a TFR of 6.5 children, thus providing another proof supporting the fact that fertility had not declined to the extent believed.
On the Vector Broadcast Channel with Alternating CSIT: A Topological Perspective
In many wireless networks, link strengths are affected by many topological
factors such as different distances, shadowing and inter-cell interference,
thus resulting in some links being generally stronger than other links. From an
information theoretic point of view, accounting for such topological aspects
has remained largely unexplored, despite strong indications that such aspects
can crucially affect transceiver and feedback design, as well as the overall
performance.
The work here takes a step in exploring this interplay between topology,
feedback and performance. This is done for the two user broadcast channel with
random fading, in the presence of a simple two-state topological setting of
statistically strong vs. weaker links, and in the presence of a practical
ternary feedback setting of alternating channel state information at the
transmitter (alternating CSIT) where for each channel realization, this CSIT
can be perfect, delayed, or not available.
In this setting, the work derives generalized degrees-of-freedom bounds and
exact expressions, that capture performance as a function of feedback
statistics and topology statistics. The results are based on novel topological
signal management (TSM) schemes that account for topology in order to fully
utilize feedback. This is achieved for different classes of feedback mechanisms
of practical importance, from which we identify specific feedback mechanisms
that are best suited for different topologies. This approach offers further
insight on how to split the effort --- of channel learning and feeding back
CSIT --- for the strong versus for the weaker link. Further intuition is
provided on the possible gains from topological spatio-temporal diversity,
where topology changes in time and across users.Comment: Shorter version will be presented at ISIT 201
Quantum Cross Subspace Alignment Codes via the -sum Box Abstraction
Cross-subspace alignment (CSA) codes are used in various private information
retrieval (PIR) schemes (e.g., with secure storage) and in secure distributed
batch matrix multiplication (SDBMM). Using a recently developed -sum box
abstraction of a quantum multiple-access channel (QMAC), we translate CSA
schemes over classical multiple-access channels into efficient quantum CSA
schemes over a QMAC, achieving maximal superdense coding gain. Because of the
-sum box abstraction, the underlying problem of coding to exploit quantum
entanglements for CSA schemes, becomes conceptually equivalent to that of
designing a channel matrix for a MIMO MAC subject to given structural
constraints imposed by the -sum box abstraction, such that the resulting
MIMO MAC is able to implement the functionality of a CSA scheme
(encoding/decoding) over-the-air. Applications include Quantum PIR with secure
and MDS-coded storage, as well as Quantum SDBMM.Comment: arXiv admin note: substantial text overlap with arXiv:2304.0756
Interference Alignment and the Degrees of Freedom for the K User Interference Channel
While the best known outerbound for the K user interference channel states
that there cannot be more than K/2 degrees of freedom, it has been conjectured
that in general the constant interference channel with any number of users has
only one degree of freedom. In this paper, we explore the spatial degrees of
freedom per orthogonal time and frequency dimension for the K user wireless
interference channel where the channel coefficients take distinct values across
frequency slots but are fixed in time. We answer five closely related
questions. First, we show that K/2 degrees of freedom can be achieved by
channel design, i.e. if the nodes are allowed to choose the best constant,
finite and nonzero channel coefficient values. Second, we show that if channel
coefficients can not be controlled by the nodes but are selected by nature,
i.e., randomly drawn from a continuous distribution, the total number of
spatial degrees of freedom for the K user interference channel is almost surely
K/2 per orthogonal time and frequency dimension. Thus, only half the spatial
degrees of freedom are lost due to distributed processing of transmitted and
received signals on the interference channel. Third, we show that interference
alignment and zero forcing suffice to achieve all the degrees of freedom in all
cases. Fourth, we show that the degrees of freedom directly lead to an
capacity characterization of the form
for the multiple access channel, the
broadcast channel, the 2 user interference channel, the 2 user MIMO X channel
and the 3 user interference channel with M>1 antennas at each node. Fifth, we
characterize the degree of freedom benefits from cognitive sharing of messages
on the 3 user interference channel.Comment: 30 pages. Revision extends the 3 user proof to K user
- âŠ