Switch or Stay

One thing that is often reiterated, is that one should keep up to the pace of the world around. If you stay, you will miss somethings, but there is always an advantage in switching. Consider this classical example called the "Monty Hall" problem in probability theory:

The "Monty Hall" problem relates to a popular TV show, where the participant of the game is allowed to win a Bentley (most expensive car!) or has to be satisfied with a goat (most sort after domestic animal!). The problem is stated as a conversation between Monty and the participant Mr. P

Monty : Welcome, Mr P to this game. Before we begin let me explain. You can see 3 closed doors,     behind one of the doors is the most priced Bentley, and behind the others are the useful goats. Choose one and you will be prized with the gift behind the door. You can either go with a shiny, new expensive Bentley or be satisfied with the goat. So are you ready?

Mr. P  : Okay let me choose Door __ .

Monty : Okay let us see if the luck supports you. (Pause) Maybe I can give you another chance. I shall open a second door and see if you want to change the choice.

Monty opens a second door and shows that it is a goat.

Monty :  Do you wish to stay or switch?

Think that you are Mr. P and write your choice... Stay or Switch!

Figure showing the illustration of the Monty Hall Problem. (Drawn using MetaMoji Note App)

Solution : Mr. P would wish to switch in order to win the Bentley. The reasoning is as follows.

We contrast the chance of winning on switching vs the chance of winning on staying with the previous decision

$\mathbb{P} (win|switch) = \mathbb{P}(I = G, III = B) = \frac 23$ and $\mathbb{P} (win|stay) = \mathbb{P}(I = B, III = G) = \frac 13$.

The chances of winning is more while one switches. The solution to the problem seems to be very counter intuitive. Hence this is regarded as a good example problem for learning elementary probability.

Physical Layer Security Using Energy Harvesting Models

This article has appeared in the Technical Article Board of ECE Department, SSET - June 2016

Abstract

A point to point communication with a receiver and a single transmitter is the system under study. We consider the security aspect at the physical layer of the wireless communication transmission in the presence of an eavesdropper. A combination of techniques involving the channel state information(CSI) and energy harvesting information(EHI) is used to ensure the security. The experimentation is performed using the NI USRP 2920 hardware.

Extended Abstract

ireless communication systems consists of a transmitter and many distributed receivers. The eavesdropper is an unintended node that tries to know what the wireless transmitter sends. The eavesdropper can cause security hazards to the intended receiver by causing leakage of the message and causing intentional manipulations. These manipulations can in turn, lead to wrong message being delivered. The wireless physical layer is the lowermost level of the 7 layer OSI (Open System Interconnection) model. In many existing systems the security aspects are dealt mostly at the link layer and the network layer. These schemes have their drawbacks like, complex cryptographic cyphering, power consumption, hardware cost to name a few. Physical  layer security is destined to be the future, where systems can be implemented in low battery power devices using improved simplicity. 

The physical layer security is dealt with the help of the CSI information available at the transmitter and receiver[1]. The CSI information is independent at the eavesdropper and receiver. This helps us to manipulate the order of the interleaving bits. The scheme of the interleaver requires that the channel state observed by the receiver and the eavesdropper are both independent. This prompts us to look for methods that are statistically independent with the users, but at the same time observable. In this context we try to provide a scheme that is a combination of the CSI and the proposed scheme of Energy Harvesting Information.

Courtesy : https://arxiv.org/pdf/1505.07929.pdf
Fig 1: Communication and Security Model

Harvested Energy Model 

We consider the case of a device that is capable of harvesting/collecting renewable energy from sources such as solar, wind, piezo, etc. In general as energy impinges on the photo sensors(in the case of a solar panel) some part is lost in the conversion process to electrical energy. Thus, the harvested energy at any given time is high or low, ie a Bernouli random process. Depending on the position of the device the amount of energy harvested (say in a block interval) is an independent sequence. So the interleaving pattern can be made a function of the random energy harvested.

Fig 2 : The Block diagram of the OFDM scheme using the Energy Harvesting Information (EHI)

The schematic for the physical layer security using the OFDM scheme is described. The channel is estimated and used as an input to the interleaver along with the energy harvesting input. The combined inputs fed to the interleaver will allow for an improvement in the security and decoding performance. The system has been tested under the USRP test condition with the the eavesdropper being placed in a separation. Initially channel measurements are performed using perfect channel knowledge. Later it is modified to the case where in the absence of the perfect channel state information, an estimation is performed at both the transmitter and receiver.

Reference

[1] H. Li, X. Wang and Y. Zou, "Dynamic Subcarrier Coordinate Interleaving for Eavesdropping Prevention in OFDM Systems," in IEEE Communications Letters, vol. 18, no. 6, pp. 1059-1062, June 2014

[2] Universally near-optimal online power control for energy harvesting nodes
D Shaviv, A Özgür - arXiv preprint arXiv:1511.00353, 2015

This is joint work with a M.Tech student at the Wireless Communication Lab, SSET