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