general theory of wireless networks with side information ahmad khoshnevis, debashis dash rice...

General Theory of Wireless Networks with Side Information

Ahmad Khoshnevis, Debashis DashRice University

Nokia SeminarFebruary 10, 2006

Wireless Networks

• High data rate– WiMax, Mesh– 802.11x– 4G

• Irony– Current protocols such as 802.11 cause 30-50% non-data

communication (overhead)

First question: Is existence of protocols necessary?

Why Protocols?

• Queues have time-varying state– Might be empty sometimes

• In effect, # of active nodes is time varying

• Design for Max # of user is conservative– Underutilized network for many traffic

“Active” management of queue states = Medium Access Protocols

q2

q1 S1

S2

q3

S3

How Much Overhead?

Second Question: What is the minimum amount of overhead? How can it be reduced?

Observation

• If S1 knows q2 and S2 knows q1

– No need for handshaking

– TDMA scheduling– No collision

• As load increases– Probability of queue empty reduces– Network utility increases

Having the “side information” aboutQueue states, increases the utilization

1

2q2

q1 S1

S2

D

Implementation of the idea

• Perfect carrier sense no collision

• While q1 and q2 non empty– TDMA guarantees no collision

• When – q1 and q2 are empty – |t1-t2| < – Collision happens

• Collision resolution takes resources– Modeled as wasted time, c

• Probability of Collision is determined by probability of q1=q2=

q1 S11

2q2

S2

D

t

S2

S1

t1t2

c

Performance

Generalization

• In general “side information”– Queue state– Number of nodes– Battery life, …

• Catch• The “side information” is not of interest, data is• Gathering “side information” requires resources

– Perfect information causes a lot of overhead– Partial information gives more room for data, but more uncertainty

Fundamental Tradeoff

There is a tradeoff between amount of side information and total throughput of a network.

What is the maximum data rate for a given amount of side information?

New Source Model

• There are two information need to be transmitted– The actual data, M– The source state, S

• The message– Conveys useful information– Need to be sent error free

• The source state– Can’t be sent perfectly (takes all the capacity)– The rate of source information is controlled by distortion between S

and S’

M

S S’X

S.Enc

C.E

nc

New Source Model

Channel Model

• Discrete memoryless channel

• The channel is described by P{Y|X1,X2}

Formulating the Problem

Additional Insights

• Particularly in our approach– Generalization of side information & being independent of

interpretation– Addressing penalty associated with knowing side information

• Considered in earlier models– Is extendable to a network with arbitrary number of users– Simultaneously can answer both question

• Total network throughput• Per user throughput

Road Map

• Improving the Model– More interesting case is conferencing

• Find I(M1,M2;Y|S’1,S’2)• Properties of solution space and possible solution for special

cases