Wireless Network Coding with partial Overhearing information

Wireless network coding

with partial overhearing information

Georgios S. Paschos

Massachusetts Institute of Technology (MIT)

Joint work with:

C. Fragkiadakis – University of Thessaly, Greece

L. Georgiadis – Aristotle University of Thessaloniki, Greece L. Tassiulas – University of Thessaly, Greece

Wireless network coding

•

…

use

intersession network coding

to exploit the wireless

broadcast

[Katti et al. – Sigcomm ’06 (COPE)]

•

Benefits:

•

reduces the required transmissions more

throughput

, less

power

consumption

•

The benefits apply to more scenarios using overhearing

(side information)

•

Issue:

Reporting overhearing might not be desirable

•

In this talk:

•

How to control the system without these reports

•

Transmitting XORs blindly and using feedback is very efficient

)

Overhearing example

relay

source

source

Overhearing example

overhearing

relay

source

source

Overhearing example

relay

source

source

Overhearing example

overhearing

relay

source

source

Overhearing example

relay

source

source

Overhearing example

+

+

Observations

1.

Both receivers can

decode

2.

3 txs instead of 4

(4/3 gain)

3.

Overhearing

erasures:

How does

the relay know if

packets were

overheard?

relay

source

source

Learning Side information: Two cases

ACK

•

Nodes report each overhearing

(send ACK)

•

Relay learns which packets were

overheard

ACK

•

No ACKs

•

Relay XORs blindly

•

If there is

a decoding failure

the receiver sends NACK

NACK!

NACK

+

The model

•

Focus on downlink

• 

Study relay transmissions

•

Downlink channel model

• 

Destination 1 receives

perfectly if at most

packets

are transmitted (similar for dest. 2)

• 

…

for both receivers to receive use

•

Random arrival of packets

• 

Packets arrive at the relay and with a probability

at the pairing receiver (

overhearing

)

•

Stability at the relay: the backlogs don’t grow unbounded

•

The problem:

• 

Find the stability regions of ACK and NACK systems

• 

Provide efficient transmission policies that use XOR

• 

Compare the number of feedback reports in the two approaches

p

1

p

2

r

2

r

1

r

1

min

{

r

, r

}

1

2

relay

2-user Throughput regions

1

ACK: outer bound (using arbitrary coding)

ACK: region of a XOR policy

NACK: outer bound (using XORs)

NACK: region of a XOR policy

without knowledge about the channel

ACK: = , capacity region and

simple policy

NACK: = , code-constrained

region and simple policy

We will show:

- Determine the loss

- Show cases where all

four are the same!

ACK

•

Separate packets into

good

(overheard),

bad

•

Assume we are given packets- (study

policies that evacuate these)

•

Transmissions can be: {

g

,

g

,

b

,

b

,

g

+

g

,

…

}

•

Proposed Policy

:

•

Transmit

g

+

g

until one type is not available (empty queue)

•

Then use {

g

,

g

,

b

,

b

}

•

Lower Bound on evacuation time:

•

We establish a matching bound (assuming general coding func.)

•

Use “stability via evacuation” tool [Georgiadis et al. – ITW 12’]

•

Capacity region of ACK (achieved with XORs)

ACK

g

b

buffers

input queues

k

1

, k

2

r

+

r

min

{

p

, p

}

max

{

r

, r

}



1

NACK - scheme

•

Each packet is initially

unknown

.

•

Add

u

queue

•

All packets arrive in this queue

•

Stationary decision:

to XOR or not to XOR?

•

After a XOR decoding failure a packet can

either be

bad

or

good

•

good

if one packet is NACKed

•

bad

if both packets are NACKed

•

The policies choose actions from the set:

{u

,u

,

b

,

b

,

g

,

g

, u

+u

, u

+

g

,

g

+u

,

g

+

g

, ...}

•

We establish a lower bound (on evacuation

time) assuming XORs

buffers

input queues

NACK – policy

Proposed policy:

•

If

• 

Then send u

, u

(no coding)

•

else

1. 

u

+

g

or

g

+u

2. 

u

+u

3. 

b

or

b

or other singletons

•

Result:

• 

This policy matches in evacuation performance the XOR bound

• 

Code-constrained stability region

erasure prob. of (fast) flow

buffers

input queues

Stat. condition

f

2

arg max

r

plugin

or

r

=

r

p

= 1

1.

u

+

g

or

g

+u

2.

u

+u

3.

b

or

b

or other singletons

Rules

Time:

7

6

5

4

3

2

1

The ACK policy needs 7 slots, too!

1.

u

+u

2.

u

+u

3.

u

+u

4.

u

+

g

5.

u

+u

6.

u

+u

7.

b

Transmissions

`

•

Consider packets of equal length

•

Different rates:

red

is fast,

blue

is slow

•

Plain forwarding of 2 packet takes:

•

NACK: Blind XORs – 4 cases

1.

Both packets overheard –

performance gain

2.

The

red

/fast packet overheard –

no harm

3.

The

blue

/slow packet overheard –

harming

4.

Both packets not overheard –

harming

+

+

+

+

NACK – policy operation – different rates

reception time

Throughput: ACK beats NACK

1

=

r

= 3

p

= 0

.

9

Parameters:

Throughput ratio NACK/ACK

Overhead: NACK beats ACK

W: rate of feedback messages

W

Take home messages

•

We give a characterization of the tradeoff of ACK/NACK

schemes

•

ACK Capacity region and NACK code-constrained region

•

Simple stabilizing policies that use XORs

•

Loss of throughput as function of (

p

,

r

,

λ

)

•

XORing blindly and NACKing is a good alternative to

ACKs (when probabilities are high)

•

Much less control messages

Previous results

•

For the ACK (deterministic) case

•

Same rates:

index coding

•

Same rates:

linear coding

[C.-C. Wang]

•

Different rates:

Backpressure-type policy,

XOR

constraint region

[1]

•

For the NACK (stochastic) case

•

Undecoded packets are dropped: [1]

•

2-users?

•

In practice, many user coding opportunity rarely arise

(geometrical bounds, physical model bounds,

experiments)

•

Choosing combinations from larger sets is complex

ACK

NACK!

+

Learning side-information

•

Explicit ACKs [COPE]

•

Each node announces each overhearing

•

A great number of control messages

•

Piggybacking not possible if no reverse flow (

added delay

,

lost

throughput

)

•

Feedback via NACKs [COPE, NCRAWL-Broustis et al.]

•

Router XORs blindly, and feedback messages are used only for

retransmissions

•

How efficient can this be?

•

Optimal control the system under this scheme?

•

Use intrasession network coding [I

2

NC-Seferoglou et al.,

CORE-Krigslund et al.]

•

Immediate decodability

ACK & NACK capacity region

r

1

=

r

2

p

1

= 0

.

7

p

2

= 0

.

8

ACK & NACK capacity

[1]

•

System B:

•

At time 0, packets at the input – no further arrivals

•

: is the

minimum evacuation time

•

Consider the quantity for large

•

System A is stable iff

≤

1

•

An (asymptotically) minimum evacuation policy in B can be mapped

to a throughput optimal policy in A

Methodology – evacuation times

k

T

⇤

(

k

)

T

(

t

)

t

k

t

•

Strategy for both ACK, NACK:

•

Study system B

•

Find lower bounds on the evacuation time of any policy

•

Propose an evacuation policy: compare the asymptotic performance

•

If they match, we have:

•

The proposed policy is an asymptotically minimum evacuation policy on B

•

System A stability region

•

A throughput optimal policy on A (that is based on the decisions of evacuation

policy on B)

Methodology – evacuation times (cntd)

k

T

⇤

(

k

)

k

•

Example with deterministic service rate

A simple example

40

10

k

T

(k) =

⇠

k

4

⇡

)

T

ˆ

( ) = lim

t

!1

⌃

t

4

⌥

t

=

4

Thm

:

4pkt/slot

) 

4