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

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

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

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

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

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

Layered Broadcast Coding with Successive Refinement* 1010111 ??????? Superposition Coding Refinement Layer 111 Base Layer 1010 How to allocate transmit power among the layers? *Joint with C. Ng.

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.

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.

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

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

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

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.

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.

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

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

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”

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?

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

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

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]

Decode and Forward Each source encodes using superposition coding X1 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]

Combined MAC/BC Approach X1 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.

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

Rate Comparison

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

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?

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