1. Joint Source, Channel, and Network Coding in MANETs
Andrea Goldsmith
Stanford University
Joint with Y. Liang, I. Maric, and C. Ng
DAWN ARO MURI Program Review
U.C. Santa Cruz
September 5, 2007

2. Wireless Multimedia Networks In Military Operations
Command/Control
Data, Images, Video
How to optimize QoS and end-to-end performance?

3. Challenges to meeting network performance requirements
Wireless channels are a difficult and capacity-limited broadcast communications medium
Fundamental capacity limits of wireless networks are unknown and, worse yet, poorly defined.
Wireless network protocols are generally ad-hoc and based on layering, which can be highly suboptimal
No single layer in the protocol stack can guarantee QoS: cross-layer design needed

4. Source, Channel, and Network Coding in MANETs
Separate
Design
Optimal?
Separate
Design
Optimal?
Source
Coding
Channel
Coding
Generalized
Relaying

5. Source/Channel Coding (pt2pt)
1010..
1010..
Source coding creates compressed bits from original data
Channel coding creates coded bits to send over the channel
Separation optimality implies separate source and channel coding results in no performance loss
Typically only true for ergodic point-to-point channels with full CSI

6. Source Coding under Channel Uncertainty
101
???
If the channel capacity is unknown, what strategy should be used in the source coding?
Encode source at lowest possible channel rate?
No errors; no advantage when channel is better than worst-case
Encode at higher rate
Some data will be lost
Want progressive fidelity based on channel conditions

7. Layered Broadcast Coding with Successive Refinement*
???????
Superposition Coding
Refinement Layer
111
Base Layer
1010
How to allocate transmit power among the layers?
*Joint with C. Ng.

8. Source-Channel Coding without CSI at the Transmitter
Transmission of Gaussian source without CSIT.
Quasi-static block fading. Decoding is delay-limited.
Channel is non-ergodic: separation is suboptimal.
Transmitter knows the fading distribution.
Want to minimize expected distortion EH [D]
Subject to power constraint P.
Bandwidth ratio: b channel uses per source symbol.

9. Layered Broadcast Coding Model
Superposition coding: one layer for each fading state.
Receiver decodes the layers supported by the channel realization.
Undecodable layers are treated as noise.
Successive decoding is capacity-achieving for single-antenna Gaussian broadcast channel.
Gaussian source is successively refinable:
Each layer successively refines description in the lower layer.

10. Two-Layer Power Optimization
Superposition coding:
Karush-Kuhn-Tucker (KKT) optimality condition:
Allocate power to the higher layer:
Up to a fixed power ceiling that depends only on fading distribution.
Power
Base
Layer
Refinement
Layer

11. Multilayer Optimization
Recursively apply the two-layer optimization step between an aggregate layer and the next lower layer
Aggregation based on effective channel gain and probability
Power
Base
Layer
Refinement Layers 1 2 3 4

12. Optimal Power Allocation for Continuous Fading Distributions
Limiting process as spacing between two layers tends to 0.
Solution given by a set of first-order linear differential equations:
Optimal power allocation: cumulative power at g
: pdf of the fading distribution

13. Power Allocation and Distortion
Distortion exponent:
At high SNR performance benefit from diversity exceeds that from CSIT, especially when b is large.
Optimal power distribution for different diversity order L.
Power distribution converges to that maximizes expected capacity as b 0.

14. Rethinking source and channel coding*
Rethinking capacity
- Shannon’s definition was right for information stable channels
- New definitions needed for more general channels
- When outage acceptable or not all bits need be received, outage or expected capacity are valuable metrics
Rethinking end-to-end distortion
- Typically defined as a single guaranteed maximum distortion
- New ideas: outage distortion and expected distortion
- Match source codes with new capacity definitions
* Multi-resolution/multiple description source code and degraded BC channel code or unprioritized expected-rate code
Rethinking separation
--Traditionally exchange a single value between source and channel
-- What is right source/channel interface under generalized metrics
-- How is separation and its optimality defined
*Joint with Y. Liang and M. Effros.

15. Example: Gaussian source over a Gaussian channel
Uncoded transmission optimal
Expected capacity a better “interface” than outage capacity for this example
Separation highly suboptimal

16. Next Steps Hybrid Analog/Digital Coding
Joint Source/Channel Coding for Multiple Sources

17. Channel and Network Coding*
*Joint with I. Maric and M. Medard
source1
dest1 X1
relay
X3[n] = fn(Y3[n-1] …, Y3[1])
Y3=X1+X2 X3
source2
dest2 X2
Relays in practice do store-and-forward
Independent of link transmission
Information theory indicates a more general strategy of decode/compress/amplify and forward
Has not been examined in a network setting
We investigate generalized relaying strategies that combine link and network “coding”

18. Problem Formulation Questions: Setting: Multicast in wireless networks
Goal: compare time-sharing to general relaying which allows combining of data streams at the relays
Approach:
Develop an outer bound to any time-sharing relay strategy
Evaluate schemes in which the relay simultaneously sends information about multiple streams
Questions:
Can such schemes outperform the outer bound and thus the best possible time-sharing strategy?
Which of the general encoding schemes has the best performance?

19. Channel Model
Compound Multiaccess Channel with Dedicated Relay (MAC-DR)
source 1
source 2
relay
node 5
node 4 X1 X2 Y3 Y4 Y5 X3
message W1
message W2
Y3=h13X1+h23X2+Z3
Y4=h14X1+h24X2+h34X3+Z4
Y5=h15X1+h25X2+h35X3+Z5
Smallest relevant multicast network
Power constraints on the nodes
Includes broadcasting and interference

20. Transmission Strategies
Amplify and Forward
Decode and Forward
Combined Multiple Access and Broadcast

21. Amplify and Forward X3[n]=αY3[n-1] X3[n]=αY3[n] Analog network coding:
relay X3
Analog network coding:
This combines two data streams since:
X3[n] =α(h13X1[n-1]+h23X2[n-1]+Z3[n-1])
Achievable rates from capacity of MAC w/ ISI [CheV93]
Amplify-and-forward with no delay at the relay:
Y3=X1+X2
X3[n]=αY3[n-1] X2
X3[n]=αY3[n]

22. Decode and Forward Each source encodes using superposition codingX1 W1
relay X3 X2 W2
Each source encodes using superposition coding
Xt = √Pt ( √αt Vt+ √(1- αt) Qt), t=1,2
Relay decodes (W1,W2) and encodes with two codebooks
X3 = √P3 ( √β V1+ √(1-β) V2)
0≤ α1,α2,β ≤1
Achievable rates follow from MAC capacity with DR [KraW00]

23. Combined MAC/BC ApproachX1 W1
relay X3 X2 W2
Sources transmit to the relay only.
Relay decodes and broadcasts (W1,W2) to destinations using a single codebook.
Rates constrained by the worse relay-destination channel.

24. Outer Bound: Genie-aided Timesharing
For 1 ≤ n ≤ k relay forwards for source 1: X3=f3,n(W1)
‘Genie’ gives W2 to node 5 and relay: no X2 interference
Outer bounds for the relay channel p(y5,y3| x1,x3) apply:
For k < n ≤ N relay forwards for source 2: X3=f3,n(W2)
Direct transmission of message W2
“Genie” gives W1 to node 4
 no interference from X1, X3
Y5=X1+X3+Z5 s2
Y4=X2+Z4 s1
relay
node 4 W2
node 5 W1 X1 X3 X2
Symmetric scenario except
relay decodesW2

25. Rate Comparison

26. Next Steps Small networks Extensions to larger networks
Tighten outer bounds
Propose new coopertive schemes incorporating iteration, cognitive techniques, etc.
Channel/network code separation optimality
Extensions to larger networks
Scaling laws
Simple schemes, such as amplify/forward

27. Key Research Questions
Source
Coding
Channel
Coding
Generalized
Relaying
Where are the key synergies in joint source, channel, and network coding?
When is separation optimal?
How to design scalable techniques?

28. Conclusions
End-to-end performance depends on the source, channel, and network code, and how they interaction.
Channel uncertainty requires new metrics for source, channel, and network codes
The optimal interface between a source and channel code depends on the channel and the end-to-end metric
Generalized relaying taking into account both link and network characteristics leads to large performance gains
Much work remains to be done on optimizing source, channel, and network codes, as well as the interface between these codes, for time-varying networks