## Mathematical modeling of Energy Consumption

IISc is undertaking a collaborative research to create insights into consumption pattern from energy data. The project aims at reducing the peak and aggregate energy consumption at a fraction of the cost when compared to conventional methods. The project will create a stochastic model of consumption and activity patters. It is likely to be implemented with a utility in South India over the duration of a year.

## Power Allocation in fading MAC: Polymatroidal and Game theoretic Methods

This is my independent work. This work is extension of two famous papers on fading Multiple access channel one by David Tse & Hanly and Liu and H. Elgamal. The results of both papers are extended to the case where there is security constraint in addition to reliability. Details will be added later.

## Enhancing Secrecy Rates in Wiretap Channel

Since the seminal paper of A. D Wyner [1], it is well knows that the positive secrecy rate is achieved at the cost of rate loss. We tried to address this issue in wiretap channel. First we proposed an alternative metric for security (privacy to be more precise), i.e., probability of error at the eavesdropper. We consider degraded wiretap channel, where the legitimate receiver's channel is better than eve's channel. If we transmit at rate higher that the channel capacity of Eve's channel but close to the rate of mail receiver, then strong converse guarantees that the probability of error drives to one as codeword length approaches infinity.

We also consider usual secrecy measure (i.e., equivocation based) and propose a simple and novel coding scheme where we use previous message as key for transmission in next slot, thus doubling the rate. We continue this till the secrecy rate gets saturated by main channel capacity.

This work resulted into following publications

[C1] R. Rajesh, Shahid M Shah, V. Sharma, "On secercy above the secrecy capacity", IEEE ICCS 2012, Singapore.

[C2] Shahid M Shah, Parameshwaram, V. Sharma, "Previous Messages provide key to achive Shannon capacity in wiretap channel", in proceedings of IEEE ICC workshop on Physical Layer security 2013, Hungary

[C3] Shahid M Shah, V. Sharma, "Achieving Shannon Capacity region in Multiple Access Wiretap Channel", IEEE WCNC 2015, New Orleans, USA

[J1] Shahid M Shah, V. Sharma, "Achieving Shannon Capacity in Fading Wiretap Channel" to be submitted

[J2] Shahid M Shah, V. Sharma, "Mitigating rate loss in fading multiple access wiretap channel to achieve Shannon Capacity region", to be submitted

We also consider usual secrecy measure (i.e., equivocation based) and propose a simple and novel coding scheme where we use previous message as key for transmission in next slot, thus doubling the rate. We continue this till the secrecy rate gets saturated by main channel capacity.

This work resulted into following publications

[C1] R. Rajesh, Shahid M Shah, V. Sharma, "On secercy above the secrecy capacity", IEEE ICCS 2012, Singapore.

[C2] Shahid M Shah, Parameshwaram, V. Sharma, "Previous Messages provide key to achive Shannon capacity in wiretap channel", in proceedings of IEEE ICC workshop on Physical Layer security 2013, Hungary

[C3] Shahid M Shah, V. Sharma, "Achieving Shannon Capacity region in Multiple Access Wiretap Channel", IEEE WCNC 2015, New Orleans, USA

**Journal Work**[J1] Shahid M Shah, V. Sharma, "Achieving Shannon Capacity in Fading Wiretap Channel" to be submitted

[J2] Shahid M Shah, V. Sharma, "Mitigating rate loss in fading multiple access wiretap channel to achieve Shannon Capacity region", to be submitted

## Resource Allocation using Algorithmic Game Theory

Channel state estimation introduces overhead in the transmission of packets and also increases complexity of the communication systems. Also in various cases it is not possible to estimate the channel state with high accuracy. In this paper we first study a fading multiple access channel where each user can estimate only his channel gain to the receiver, but is completely ignorant of the other users channel state. We assume that receiver can send 1-bit feedback after every transmission slot acknowledging weather the message has been correctly decoded (ACK) or not (NACK). Each user tries to pick power level (action) to transmit a message at fixed rate subject to power constraint. We pose this as stochastic game and we use multiplicative weight no-regret algorithm to obtain coarse correlated equilibrium (joint pdf on action set). Next we assume that users can also listen to ACK/NACK of each other, hence we try to maximize sum-utility of all users. We obtain policy which is Pareto optimal. Since Pareto optimal policy is unfair to individual users, hence we also obtain Nash bargaining solution. We also consider the scenario where users can choose (as part of action) any rate (from rate set) to transmit message. We extend all the results to F-MAC with eavesdropper. First we assume CSI of Eve known at each user and find CCE, PP, NB solution. Finally we assume that each user only knows the distribution of the CSI of Eve and find all the equilibria points.

[C1] Shahid M Shah, K. Chaitanya A, V. Sharma, "Resourse Allocation in Fading Multiple Access Wiretap Channel via Game Theoretic Learning", presented at 2016 IEEE Information theory and applications (ITA) workshop, San Diego, USA

Journal

[J1] Shahid M Shah, K. Chaitanya, V. Sharma, "Resource Allocation in Fading Multiple Access Channel via Game Theoretic Learning: with and without security", submitted to EURASIP Journal of Wireless communication and networking

**Publications**[C1] Shahid M Shah, K. Chaitanya A, V. Sharma, "Resourse Allocation in Fading Multiple Access Wiretap Channel via Game Theoretic Learning", presented at 2016 IEEE Information theory and applications (ITA) workshop, San Diego, USA

Journal

[J1] Shahid M Shah, K. Chaitanya, V. Sharma, "Resource Allocation in Fading Multiple Access Channel via Game Theoretic Learning: with and without security", submitted to EURASIP Journal of Wireless communication and networking