5 research outputs found
Multi-layer Interference Alignment and GDoF of the K-User Asymmetric Interference Channel
In wireless networks, link strengths are often affected by some topological
factors such as propagation path loss, shadowing and inter-cell interference.
Thus, different users in the network might experience different link strengths.
In this work we consider a K-user asymmetric interference channel, where the
channel gains of the links connected to Receiver k are scaled with P^{\alpha_k
/2}}, k=1,2,...,K, for 0< \alpha_1 \leq \alpha_2 \leq \cdots \leq \alpha_K \leq
1. For this setting, we show that the optimal sum generalized
degrees-of-freedom (GDoF) is characterized as dsum = (\sum_{k=1}^K \alpha_k +
\alpha_K -\alpha_{K-1})/2, which matches the existing result dsum= K/2 when
\alpha_1 = \alpha_2 = ... = \alpha_K =1. The achievability is based on
multi-layer interference alignment, where different interference alignment
sub-schemes are designed in different layers associated with specific power
levels, and successive decoding is applied at the receivers. While the converse
for the symmetric case only requires bounding the sum degrees-of-freedom (DoF)
for selected two users, the converse for this asymmetric case involves bounding
the weighted sum GDoF for selected J+2 users, with corresponding weights
(2^{J}, 2^{J-1}, ... , 2^{2}, 2^{1}), a geometric sequence with common ratio 2,
for the first J users and with corresponding weights (1, 1) for the last two
users, for J \in {1,2, ... , \lceil\log (K/2)\rceil }
The Secrecy Capacity of The Gaussian Wiretap Channel with Rate-Limited Help
The Gaussian wiretap channel with rate-limited help, available at the
legitimate receiver (Rx) or/and transmitter (Tx), is studied under various
channel configurations (degraded, reversely degraded and non-degraded). In the
case of Rx help and all channel configurations, the rate-limited help results
in a secrecy capacity boost equal to the help rate irrespective of whether the
help is secure or not, so that the secrecy of help does not provide any
capacity increase. The secrecy capacity is positive for the reversely-degraded
channel (where the no-help secrecy capacity is zero) and no wiretap coding is
needed to achieve it. More noise at the legitimate receiver can sometimes
result in higher secrecy capacity. The secrecy capacity with Rx help is not
increased even if the helper is aware of the message being transmitted. The
same secrecy capacity boost also holds if non-secure help is available to the
transmitter (encoder), in addition to or instead of the same Rx help, so that,
in the case of the joint Tx/Rx help, one help link can be omitted without
affecting the capacity. If Rx/Tx help links are independent of each other, then
the boost in the secrecy capacity is the sum of help rates and no link can be
omitted without a loss in the capacity. Non-singular correlation of the
receiver and eavesdropper noises does not affect the secrecy capacity and
non-causal help does not bring in any capacity increase over the causal one.Comment: An extended version of the paper presented at the IEEE International
Symposium on Information Theory, Helsinki, Finland, June 26 - July 1, 2022;
submitted to IEEE Trans. Info. Theor
Secure GDoF of the Z-channel with Finite Precision CSIT: How Robust are Structured Codes?
Under the assumption of perfect channel state information at the transmitters
(CSIT), it is known that structured codes offer significant advantages for
secure communication in an interference network, e.g., structured jamming
signals based on lattice codes may allow a receiver to decode the sum of the
jamming signal and the signal being jammed, even though they cannot be
separately resolved due to secrecy constraints, subtract the aggregate jammed
signal, and then proceed to decode desired codewords at lower power levels. To
what extent are such benefits of structured codes fundamentally limited by
uncertainty in CSIT? To answer this question, we explore what is perhaps the
simplest setting where the question presents itself -- a Z interference channel
with secure communication. Using sum-set inequalities based on Aligned Images
bounds we prove that the GDoF benefits of structured codes are lost completely
under finite precision CSIT. The secure GDoF region of the Z interference
channel is obtained as a byproduct of the analysis.Comment: 34 pages, 10 figure