- Low-Delay Error Correction Codes
- Smart Meter Privacy in Electric Grids
- Source Coding for Real-Time Streaming
- Secure MIMO Communication
- Physical-Layer Secret-Key Generation
- Broadcasting over Packet Erasure Channels
- Distributed Interference
Below we list a few topics that the research lab is actively pursuing with the relevant references.MiDAS Codes for Real-Time Streaming Communications
Applications such as live-video streaming, web conferencing, and cloud computing are expected to see a dramatic growth over the next few years. Unlike classical systems, these applications require strict end-to-end delay constraints, real-time processing, and in-order delivery of data packets. Traditional error correction techniques are not designed for such constraints, and can lead to severe playback interruptions due to bursty packet losses over wireless channels. We illustrate such a streaming application in the figure below.
Classical information theory does not account for the streaming nature of applications. It provides little design guidelines. For example:
- Streaming Application such as Skype have been observed to
use overhead that far exceeds the Shannon limit without
- Burst losses cause a very severe performance loss,
as interleaving cannot be used due to the delay constraints.
- MiDAS Codes provide a superior error correction from burst erasures, and are also robust to isolated erasures.
- MiDAS Codes optimize a new distance metric that is
fundamental to streaming applications
- The code parameters can be adjusted on the fly as channel conditions change.
- A. Badr, P. Patil, A. Khisti, W. Tan and J. Apostolopoulos Layered Construction for Low-Delay Streaming Codes IEEE Trans. Inf. Theory, Dec 2016
Smart meters report real-time information of user's energy usage to utility providers. This can leak sensitiv information about the devices being used. For example see the figure below.
We consider the use of a rechargeable battery at user's home to mask information leaked to the utility providers. By determine the optimal charging and discharging policies of the rechargeable battery to mimimize information leakage.
S. Li, A. Khisti and A. Khisti, Information-Theoretic Privacy in Smart Metering Systems with a Rechargeable Battery
Practical techniques for compression of streaming sources
must satisfy two key requirements:
- They must achieve high compression efficiency
- They must be resilient to packet losses
As one would expect these requirements are conflicting in nature. At one extreme, methods such as predictive coding achieve a high compression efficiency, but are sensitive to packet losses. At the other extreme, methods such as still-image coding are not affected by packet losses but do not achieve high compression ratios. We present an information theoretic formulation for characterizing this tradeoff and present a class of coding schemes that achieve a near-optimal tradeoff in certain cases.
F. Etezadi, A. Khisti and M. Trott, Zero-Delay Sequential Transmission of Markov Sources over Burst Erasure Channels, IEEE Trans. Inform. Theory, vol. 60, no. 8, pp. 4584-4613, Aug. 2014
While multiple antennas have been
traditionally used in wireless systems to enhance
throughput and reliability at the physical layer, in
this project we examine their role in enhancing secrecy
against an external eavesdroppers.
When the transmitter uses a multiple
antenna array, it can exploit the directionality of the
channel vectors to create a strong signal gain at the
intended receiver, and a weak signal at other undesired
locations. It can achieve further improvement by sending
noise in the null-space of the intended receiver's channel.
This technique is called artificial noise transmission.
Consider the transmission of a confidential message to
a large number of legitimate receivers. In such a multicast
setup, we cannot use artificial noise transmission. This
is because when the number of receivers exceeds the number of
transmit antennas, we cannot find a null-space simultaneously
for all the channel vectors. We have developed a novel scheme
- artificial noise alignment, where we use an idea from the
interference alignment literature to align noise at the
As shown in the above figure the multiantenna transmitter (with Nt antennas) transmits a superposition of noise and information symbols, such that:
- The noise symbols align at the intended receivers and only
require 1/Nt degrees of freedom
- The noise symbols occupy the full 1 degree of freedom at the eavesdroppers
- The information symbols occupy (1-1/Nt) degrees of
freedom, and can be decoded at the legitimate receivers.
- The information symbols are completely masked by the noise symbols at the eavesdroppers
The above scheme does not require the knowledge of the
eavesdropper's channel for noise alignment, just as in the
original artificial noise transmission scheme. For further
information, please refer to the following papers:
- A. Khisti, and D. Zhang, Artificial-Noise Alignment for Secure Multicast using Multiple Antennas IEEE Comm. Letters, Aug. 2013
- A. Khisti, Interference Alignment for the Multi-Antenna Compound Wiretap Channel IEEE. Trans. Inf. Theory, Special Issue on Interference Networks, March 2011
- A. Khisti and G. W. Wornell, Secure Transmission with Multiple Antennas-II: The MIMOME Wiretap Channel, IEEE. Trans. Inf. Theory, Vol. 56, No. 11, pp. 5515-5532, Nov. 2010
- A. Khisti and G. W. Wornell, Secure Transmission with Multiple Antennas-I: The MISOME Wiretap Channel, IEEE Trans. Inf. Theory, Vol. 56, No. 7, pp. 3088-3104, July 2011
Secret-Key Generation over Fading Channels
Properties of wireless channels such as channel reciprocity and fading can be used to establish a common secret-key between two or more remote terminals. This has become a very active area of research in many different disciplines. Our project focuses on the information theoretic capacity limits of secret-key generation over reciprocal fading channels. Consider the following model:
- Two-way block fading channel
- Reciprocity over the main channel
- Non-Coherent Channel Gains
We have developed a new secret-key
generation scheme for such a system that provides
considerable gains over a training-only scheme. Our
method consists of two-phase where the first phase is
a short training period while the second phase is
source-emulation. We further establish the optimality
of our scheme in the high SNR regime.
developed a new upper bound on
the secret-key capacity (under public discussion) and
established that it is tight in the high SNR regime.
Using this result we show that the training-only
schemes widely used in the literature are far from
There are however very few results on the information theoretic capacity of secret-key generation over wireless fading channels. Such results are important as they provide a theoretical benchmark for the practical systems being developed. However establishing such capacity results can be highly challenging. One should consider a non- coherent channel
To the best of our knowledge
this is the only capacity result on two-way secret-key
generation. It should have impact both on the
theoretical research, as well as on the practical
implementations of physical layer secret-key
Figure: Comparison of secret-key generation schemes as a function of SNR from reference  below. The training-only schemes is far from optimal for a wide-range of SNR values.
- A. Khisti Secret-Key Agreement over Non-Coherent Block Fading Channels with Public Discussion Submitted, IEEE Trans. Inf. Theory, August 2013
- A. Khisti, Interactive
Secret-Key agreement over Fading Channels, Allerton
- M. Andersson, A. Khisti and M. Skoglund, Secure-Key
Agreement over Reciprocal Fading Channels at Low SNR
Broadcasting over Erasure Channels
Broadcast and multicast to devices with different processing capabilities, storage capacities, and screen resolutions is becoming increasingly prevalent in many streaming applications. In point-to-point scenarios, the sender can adjust its transmission/coding rate to avoid packet losses and retransmit lost packets according to the feedback from the receiver through very efficient physical-layer schemes such as HARQ. In contrast, in broadcast/multicast applications, it is costly for the sender to collect and respond to individual receiver feedbacks, and thus HARQ schemes are disabled and packet losses are inevitable. Forward error correction coding provides a natural solution in such applications and is already being standardized in applications such as LTE eMBMS.
In the special case where each receiver must recover all the source packets, rateless codes provide a near optimal solution. However when each receiver is only interested in recovering a certain fraction of source packets they are well known to be sub-optimal. The construction optimal codes in such cases remains an open problem. We have developed a class of practical coding schemes for this setup, inspired by a connection to the joint-source channel coding problem in information theory. Our proposed codes are both simple, yet based on an information theoretic foundation. They can be a promising candidate in future implementations of broadcast/multicast applications.
Y. Li, L. Tan, A. Khisti and E. Soljanin , Successive Segmentation-based Coding for Broadcasting over Erasure Channels International Symposium on Information Theory, Jun 2014, Honolulu, Hawaii
L. Tan, Y. Li, A. Khisti, E. Soljanin, Successive Segmentation-based Coding for Broadcasting over Erasure Channels Submitted, IEEE Trans. Inform. Theory, Aug. 2014
Dirty Interference Cancellation
We have considered distributed interference cancellation based on dirty paper coding. The basic setup is shown in the figure below.
The the interference signal is not known to the transmitter, but known to an external helper. The helper knows the state and wishes to cancel it, but does not known the message. The encoder knows the message but not the state. Interestingly it can be shown that even in such a setup, if the power of the helper exceeds a certain threshold the capacity of this system is same as if the interference did not exist at all. Such a setup is very relevant in current wireless systems. We believe that it can provide an practical alternative to techniques classical coding schemes for the interference channel such as the Han-Koboyashi scheme.
R. Duan, Y. Liang, A. Khisti and S. Shamai (Shitz), “State-Dependent Parallel Gaussian Channelswith a Common Helper in High Power Regime,” International Symposium on Information Theory, Jun 2014, Honolulu, Hawaii
R. Duan, Y. Liang, A. Khisti and S. Shamai (Shitz), “State Dependent Gaussian Z-Channel withMismatched Side Information and Interference,” Information Theory Workshop (ITW), Sep. 2013, Seville, Spain