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A comparative taxonomy of wireless networks in thewideband regime – Fawaz, Thakur, Médard
MAIN ACHIEVEMENT:
HOW IT WORKS:• Hypergraph models
• Model the broadcast nature of wireless transmission• Clarify correlation between messages• Correspondance with transmission schemes for
wideband AWGN and fading models• MAC and BC: equivalent hypergraph model• Relay channel: comparison of min-cuts of achievable
hypergraphs[Peaky binning hypergraph] vs. [Concatenation of BC and MAC
equivalent hypergraph: superposition coding and FD] vs. [AFhypergraph]
ASSUMPTIONS AND LIMITATIONS:• Wideband regime assumption• Single source systems
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•Capacity of wideband BC and MAC known•Capacity of wideband relay channelunknown, but achievable rates + cut-setupper-bound•Capacities linear in received SNR inwideband regime
Low SNR regime:P/W -> 0 on all links
Wideband point-to-point, BC, MAC andrelay channels:• Equivalent or achievable hypergraph models• Transmission schemes achieving hypergraph min-cut for the AWGN and non-coherent multipath fadingchannels•How does the optimal scheme for wideband BC andMAC perform in the relay channel?
1. Hypergraph = wired-likeerror-free models for error-pronewireless systems => apply networkoptimization tools
2. Achievable hypegraphs of largerwideband networks built fromhypergraphs of small blocks (Point-to-Point, BC, MAC,Relay)
3. Wideband relay channel >concatenation of wideband BC andMAC- Highest rate achieved by block markovDF in AGWN/peaky binning DF in fading-Superposition coding is suboptimal inAWGN, yet close to optimal and easy toscale- AF equivalent to direct transmission
- Converse for relay channel
- Extension to optimizationproblem in larger networks inlow SNR thanks to hypergaphmodel
- Optimal relay placement andgeometry of wireless networks inwideband regime
Equivalent and achievable hyperpgrah models for building blocks of MANETs
vs.
Optimal relay positioning showsgains compared to seeminglyinteresting positions
Achievable hypergraphapproach (superposition codingand frequency division) forlow-SNR networks offers asimple and easily scalablenetwork model andtransmission scheme
(
Optimal relay location and power allocation for low SNRbroadcast relay channels - Thakur, Fawaz, Médard
Exploring geometricproperties of multicastin wireless networksto significantly reducecomplexity.
Extension to multiplerelay scenario
A comprehensive approach based on network optimization, computational geometry andinformation theory for optimal relay positioning is presented for low-SNR networks
MAIN RESULT:
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Optimal relay positioning shows strong gains overseemingly interesting relay positions (e.g. centroid)
ASSUMPTIONS AND LIMITATIONS:Single source-multiple destination networks with asingle relay as the only intermediate node.Multicast rate maximization is considered.Non-convex network optimization.
HOW IT WORKS:Using superposition coding and frequency division – awireline like model is created – Achievable hypergraph.2-D plane is divided into disjoint regions for different relaypositions with invariant network hypergraph (k-nearestneighbour problem).Using switch functions, a combined network optimizationproblem is formulated.
Problem: relay position and powerallocation to maximize multicastrate in wideband broadcast relaychannel
Hypergraph model =function ofpower allocation and relay location
Continuous switch functions tomodel varying hypergraph as relayposition changes
Wireless relay networks•optimization of relay locationaddressed in high SNR regime only•optimization of power allocation aloneaddressed in low SNR regime
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A converse for the wideband relay channel – Fawaz, Médard
MAIN ACHIEVEMENT:
HOW IT WORKS:Assuming that the relay cannot decode:• Split total mutual information into two parts
• contribution from relay• remaining contribution from source after deducting
contribution from relay• Bound contributions using equivalence theory and rate
distortion theory, in particular to justify• Gaussian input at source• Estimation with distortion at relay• Error-free R-D link with finite capacity
• Analyze the limit of these contributions in the low SNRregime and show that the total converges to the direct linkcapacity
Conclusion: the relay should decode in the low SNR
ASSUMPTIONS AND LIMITATIONS:• Low SNR assumption
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Capacity of general relay channelunknown•Bounds on general relay channel• In wideband regime, cut-set upper-bound and lower bounds onAWGN/Fading relay channel
Relay channel in low SNR /widebandregime:- At low SNR, cut-set upper-bound= virtual MIMO with perfect channel R-D,is not achievable- Block Markov DF/ peaky binninghypergraph lower-bound is tight =capacity
1. Capacity of multipath fading/AGWN relay channel in lowSNR regime
- Hypergraph min-cut
- Achieved by block Markov DF inAWG relay channel and simplenon-coherent peaky binning DFinthe fading channel
2. Network Coding in the digitaldomain at low SNR
3. New upper-boundingtechnique for capacity basedon network equivalencetheory
-Scalability of optimal relayingscheme-Comparison with simpler and easyto scale linear schemes
Characterizing the capacity of the relay channel in the wideband regime
<
Resolution of a long-standingproblem: fully distributed,efficient MAC that is positiverecurrent (can deal withdynamic demand)
New theory for learning rates oftime varying Poisson processusing noisy observations
Positive Recurrent Medium AccessPI: Shah
Resolution of a long standing challenge for network & information theory ---efficient, distributed wireless medium access
MAIN ACHIEVEMENT:Efficient, distributed MAC that can deal with
dynamics in demand• Formally, it is positive recurrent• Random access probability :
• function of queue-size, learnt info.• Totally distributed, no message-passing
HOW IT WORKS:• Learning rates of time varying Poisson process
• Appropriate filter design• Using a clever choice of function
ASSUMPTIONS AND LIMITATIONS:• Collision based model of physical layer
Medium Access Control (MAC) isfundamental protocol of modernwireless communication•Random backoff with CSMAprovably works when demand isstatic (prior work of PI)•In practice, demand could bedynamic
Beyond Inference=Noise
• Dealing with hidden terminals• Improving delay throughutilization of geometry
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Learning Parameters ofTime Varying Poisson
Process based on VeryNoisy Observations
New detection framework:compressive detection allowsfor lower complexity front-endfor all types of MUD detectors:linear detector, decorrelator,iterative detector, maximumlikelihood detector.
Other applications:Compressive ARQ protocol,wideband white spacedetection, multi-sensordetection
Complexity-performancetradeoff
Reduced-Dimension Multiuser DetectionY. Xie, Y. C. Eldar and A. Goldsmith
•The number of active users K can bemuch smaller than N users – usersparsity
•Correlate with much fewer correlatingwaveforms can achieve similardetection BER to MF bank
Low-complexity multiuser detection employs sparsity in the number of active users withanalog processing
MAIN RESULTS:Compressive detection is done by first correlating with M sensing
signals, then postprocessing to detect active users andtheir symbols. Sensing signals are constructed by linearlycombining bi-orthogonal waveforms.
Performance guarantee of linear detector using worst coherence ofcombination partial DFT coefficient matrix
• Without noise, achieve correct detection:• K = 1, M = 2, BER = 0• K > 1, µ < 1/(D×(2K-1)), µ = max ai’aj
• With noise• µ < 1/(D×(2K-1)) f(SNR, N)
Intuition: project the original space consisting of N-dimensionalwaveforms onto an M-dimensional subspace.
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. • Conventional multiuser detectoremploys a matched filter bank• MF bank requires correlation with allpossible signature waveforms• High complexity with many users
M
Prob
abili
ty o
f err
or
N
Performance lowerbound
• Noise in RD-MUD is colored. Howto optimally detect in colored noise• Develop tighter performanceguarantee based on restrictedisometry constants (RIC)• Performance guarantee based forother detectors: decorrelator,iterative detector based on OMP,maximum likelihood detector.
The Conventional MUD (A. Duel-HallenEt.al., Multiuser detection for CDMA systems, 1995)
Base Station Users
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Dynamic auctions with learninghave been widely studiedacross economics andengineering, but with littlestructural insight.
Our work provides a simple,intuitive description of how weexpect bidders to play.
Mean Field Equilibria of Dynamic Auctions withLearning
K. Iyer, R. Johari, and M. Sundararajan
We study a dynamic auction withlearning.
Example: Multiple devices bid toshare a channel; devices mustlearn their own channel quality.
We apply mean field equilibriumto obtain structural insights.
A sentence why it is important/useful
MAIN ACHIEVEMENT:We show there exists a structurally simple MFE
of a dynamic auction with learning, where at eachtime step a bidder participates in a Vickrey auction.
At each time step a bidder bids:
HOW IT WORKS:Consider a limiting regime where # of bidders
(N) and # of auctions (k) grows large, whileholding # of bidders per auction (α) fixed.
An individual bidder’s problem simplifies in this limit.
ASSUMPTIONS AND LIMITATIONS:Our work provides existence of a simple equilibrium,
but does not show how to converge to it.We are applying a form of model predictive control
to show that such equilibria can be easily found bybidders.
Provide a mechanism toconverge to MFE.•Leverage methodologydeveloped in earlier work onstochastic games withcomplementarities•Also study how equilibria vary asparameters of the system arechanged (i.e., # of bidders perauction)
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Many cognitive radio models do notaccount for reaction of other devicesto a single device’s action.In prior work, we developed a generalstochastic game model to tractablycapture interactions of many devicesvia mean field equilibrium.
Devices
Cha
nnel
qua
lity
Conditional expectedvalue of channel quality
(given posterior)+ Expected marginal value of
one additional observationof channel quality
α α α α. . .k
Instantaneous Efficiency of Communication
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•Informationmeasured in rate anderror exponent, lackof measure of softinformation exchange• Optimality in termsof long time averageperformance, notnecessarily efficient atevery time instance
Information transmissionwith a single observationcan be described assplitting of posteriordistribution over messages,The measure of efficiencyis however not unique,depends on how theinformation is combinedwith other observations
MAIN RESULT:• Capacity and Error exponent optimal
random coding schemes can beviewed as instantaneous optimizationof certain metrics;
• Family of Renyi divergences measureinformation according to the urgencyof decision making;
• Instantaneous efficiency particularlyapplicable for lossy processing.
• Two elements in designing ofinstantaneously efficient signaling
• Choice of metrics• Progress balancing
•Demonstrate thepower of instantaneousdesigns in codedtransmissions• Apply to classicalproblems such asdistributed hypothesistesting
General design based oninstantaneous efficiencyshould have broaderapplications in networkedproblems, utilizing all thetemporal information
Different coding metrics at different time of a block
L. Zheng
Separation of Source-Network Coding and ChannelCoding in Wireline Networks: Effros and Jalali
Source-network coding and channel coding separate in a wireline network.
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ASSUMPTIONS AND LIMITATIONS:-Channels are single-input single-output-Channels are memoryless
HOW IT WORKS:-Given a code that achieves small distortion forsome source-sink pair, by treating thereconstruction block generated by the code asside information, the extra rate required forlossless reconstruction of the source at the sink isnegligible.
Separation of source-network coding and channelcoding in wireline networkswith correlated sources andlossless reconstructions isnot known.
Equivalence of zero-distortion reconstructionand lossless reconstructionin general memoryless(wireless or wireline)networks is shown.
Source-network codingand channel coding canbe separated in wirelinenetworks with correlatedsources, and lossless orlossy reconstructions.
- Channels with memory:Does separation still holdfor acyclic networks wherechannels have memory?
- Multi-user channels: Canwe use the techniquesused for deriving theseresults to general wirelessnetworks and derivebounds?
- This asymptotically negligible rate can beconveyed using the channel induced by thecode between the source and sink nodes.
- For using this channel, we need to fix the otherinputs to appropriate blocks.
This result shows that inwireline networks, with lossyor lossless reconstructions,even when the sources arecorrelated, source-networkcodes and channel codescan be designed separatelywithout any loss in theperformance.For computing thedistortion region of such anetwork, this result showsthat it suffices to study thedistortion region of anequivalent network of bit-pipes.
Optimal Control of ARQ Interference Networks Levorato, Firouzabadi, Goldsmith
Optimal Control of ARQ Interference NetworksIM
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Binary idle/busy model of thestate of the network Specifically designed to avoidinterference (collision assumption)
Channel sensing can beextended to manage advancedcommunication techniques Nodes can sense the Channel,and possibly use informationcollected by decoding controlmessages, headers, etc
Cognitive network Problem primary source: dumb ARQ protocolwith random arrivals secondary source: optimizes its ownthroughput with constraints on primarysource’s throughput
Collision-based approach :
Compact representation of the state space :
Reinforcement learning based on the aggregated state space(coarse empty/non empty primary users’ queuerepresentation and retransmission state):
No a priori knowledge of Statistics Iteratively learns from experience Automatically adapts to variations
Having a single constrainton degradation of the primaryuser’s performance, the globaloptimum solution can be found.
We proposed an on line learningalgorithm for optimizing the channelaccess strategy of the cognitivenetwork under some constraints onthe performance degradation ofprimary users’ performance andshowed that the performance of thelearning algorithm is close to thecase where we have full-knowledgeof the network statistics
Tx 1
Tx 2
Rx 1
Rx 2
How can we generalize it to anetwork of primary/secondary users
What is theeffect of noise inobserving the stateof the system?
(Noisy packet decoding/loss of theheader/ Channel sensing error, etc.)
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Metrics and Control Algorithms for Media Streaming inHeterogeneous Environments: Medard and Ozdaglar
The availability of the helper server significantly improves the user experience, not itsusage!
MAIN ACHIEVEMENT:• Designed several access control policies for a system
with two classes of servers (costly and free)1. Off-‐line policy: Queue-‐length not observable2. On-‐line Safe policy: Use the costly server unDl the
safety threshold is crossed3. On-‐line Risky policy: Use the costly server only when
the queue crosses the low-‐buffer threshold• Explicit performance characterizaDon of these
policies• CharacterizaDon of the opDmal policy via HJB
equaDon
HOW IT WORKS:• Using random linear network coding allows us to
model the receiver’s buffer as an M/D/1 queue• Problem formulated as an MDP with a probabilis1c
constraint: opDmal policy not necessarily Markov• Dynamic programming equaDon for the problem is
achieved by state-‐space expansionASSUMPTIONS AND LIMITATIONS: Packet arrivals are assumed to be a Poisson process.
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• Quality of user Experience (QoE) forstreaming applicaDons is captured byiniDal waiDng Dme and interrupDons inmedia playback.
• Use random linear network coding tocombine streams and avoid duplicatepacket recepDon at the receiver
• Some resources are more costly or limitedcompared to the others
• Consider the ini1al buffer size and theinterrup1on probability as Quality of userExperience metrics
• Goal: Design resource allocaDon policiesthat minimize the access cost given QoErequirements
• We take into account morerealisDc user experience metricsfor media streaming applicaDonsto capture their transientbehavior
• Using proper dynamic controlalgorithms, we may decrease theusage cost of expensiveequipments
• Less usage of costly back-‐upservers also results in largercapacity of such servers, hencefewer servers need to installed toachieve a reasonable quality ofservice
• Design opDmal resourceallocaDon policies for mulDpleusers with heterogeneousinterrupDon probability and iniDalwaiDng Dme targets
• Design resource allocaDonalgorithms when broadcasDngdelay-‐sensiDve content tomulDple cooperaDve users
Access Cost
Zero-cost
Infeasible
Non-degenerate
3G/LTE
A poly-time schedulingalgorithm for the multi-user,multi-channel system with aprovably good worst-case delayperformance. Brings the new intuition ofiterative resource allocation,that may be applicable to awider class of problems.
Scheduling for Small Delay in WirelessDownlink Networks: Shreeshankar Bodas
Throughput and delay are notconflicting requirements.Iterative resource allocationalgorithms yield good throughputand small per-user delay.
Iterative resource allocation schemes Low per-user delay, in addition to network stability
MAIN ACHIEVEMENT:Polynomial-time resource allocation algorithm (K-
MTLB) that is throughput-optimal, and yieldsprovably good per-user delay performance.
MTLB: Max Throughput, Load-Balancing
HOW IT WORKS: OFDM-based system: one freq. band can serve
only one mobile user. Channels are “ON-OFF” type (the only
interesting case). In each timeslot, allocate freq. bands to users
with preference to longer backlogs (user-queuesat the base-station).
ASSUMPTIONS AND LIMITATIONS:• Equal priority for all users• Poly-time complexity, but somewhat higher
exponent: O(n3) computations per time-slot
Multi-channel (OFDM-based)networks: 4G Standard•Many users, large bandwidth•Need: resource allocation schemeswith good (low) per-user delay
Extensions to multi-sourcenetworks•Femto/Pico-cell networks•Minimal coordination
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Resource 1
Resource 2
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Start with a candidate resource(freq. band) allocation, modifywith preference to longer queues.Result: Balanced queues (in amin-max sense)
Channel 1
Channel 2
Channel 3
Channel 4
Channel 5
Channel 6
Channel Realizations Allocation Decisions
Network Equivalence in the Presence ofAdversary - Effros
-When the sum of rates of allmessages is less than the capacityof a noisy link, the noisy link isequivalent to noiseless link
-Noise is emulated on the noisy linkby source coding and randomlychoosing a codebook from a set ofpossibilities
Network Equivalence extends to networks with Adversaries
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ASSUMPTIONS AND LIMITATIONS:-Memoryless, point-to-point channels, acyclic network-Sum of rates of messages is less than capacity of thenoisy link under consideration-Adversary can see links in a causal order
HOW IT WORKS:- First prove equivalence between the original networkand a “stacked network” consisting of N copies of theoriginal network. Unlike in the non-adversarial case,errors for different layers are dependent. Upper boundthe error probability by considering the worst caseadversarial strategy and using an error correcting codewith a hamming distance based decoding- A code Cnoiseless for the noiseless networks can be usedon the noisy network by adding a channel code at eachlink- A code Cnoisy for noisy network can be modified to acode Cnoiseless for noiseless network: - Randomly design a source code for the noiseless link - Remove those outputs from the source code forwhich the error probability for any message exceeds athreshold.
- Equivalence between noisy andnoiseless known in networks ofindependent point-to-point channels –relies on the random nature of errors
- Adversary can introduce errors thatare not independent of each other
- Simplifies capacity calculations –noiseless networks with adversariesare better understood than noisynetworks with adveraries-Simplifies code design for the classof adversarial networks where thisapplies by enabling a two stepdesign – network code followed bychannel code- By removing the assumption ofindependence of noise on links, thisresult opens the door to extendingequivalence to more general cases
Network Code
Channel Code
=
- Remove the sum rateConstraint on messages
- Extend beyond the point-to-point case – MAC, Broadcastetc
- Other transmission models?
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Theorem 2: The sampled capacitywith multi-channel sampling is:
MIMO Interpretation:
Shannon meets Nyquist --- Capacity Limits of Sampled Analog Channels
Yuxin Chen, Andrea J. Goldsmith and Yonina C. Eldar
• Info Theory meets Sampling Theory
• What is the capacity limit of the sampled analogchannel
• What is the tradeoff between capacity andsampling rate
• How to jointly optimize input and samplingmethods
A first attempt to study the tradeoff between data rate and hardware complexity
Single-channel Prefiltered Uniform Sampling
Theorem 1: The sampled channel capacity is
MISO Interpretations: -- Filtered channel, colored noise -- Combining (due to uniform sampling) -- Maximum Ratio Combining
Optimal Prefilter:
-- Selection Combining + Noise Suppression -- Suppress Aliasing -- Minimize MMSE reconstruction error
Non-monotonicity: -- due to UNIFORM sampling grid
-- Need NON-UNIFORM sampling
Multi-channel Prefiltered Uniform Sampling
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.• Information Theory -- Traditional Shannon framework deals withcontinuous domain. -- Optimize input for a given channel
•Sampling Theory -- analog signals digital sequences (Nyquist rate sampling) -- Optimize sampling mechanisms for giveninput
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A Network Equivalence-Based Analysis of the MultipleAccess and Broadcast Channels: Calmon and Médard
Bounding multiterminal channels by point-to-point models can be an effective approach!
MAIN ACHIEVEMENT:• An effecDve approach for finding capacity region
bounds for discrete and memoryless mulDterminalchannels as components of larger networks.
• This method also provides valuable insights whenapplied to channels in isolaDon.
• Precise bounds for the mulDple access AWGN channelwithin a larger network.
• AlternaDve look at the MAC with correlated sourcesand at the broadcast channel.
HOW IT WORKS:• If a network can reproduce the same input-‐output
relaDon of a given channel, it represents an upperbound model for the capacity region of the channel.
• Furthermore, if this upper bound consists ofindependent, point-‐to-‐point links, we can determinethe upper bounding capacity region.
• By taking the intersecDon of different bounds we canfind be^er results.
ASSUMPTIONS AND LIMITATIONS:• Only useful for discrete memoryless channels.• Difficult to determine Dghtness of bounds.
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• Analyzing the capacity region of anintricate network is intractable withcurrent techniques.
• Recent Network Equivalence resultshave provided a new approach for theproblem.
• If one network can “emulate” on itsborder nodes any coding scheme ofthe mulDterminal channel, it alsobounds the capacity region of thechannel (and vice-‐versa).
• Goal: try to find simple yet effecDvepoint-‐to-‐point upper boundingnetworks for mulDterminal channelsthat can provide relevant results.
• A new approach for difficult andopen problems in networkinformaDon theory.
• MoDvates the idea of analyzing acomplicated network withheterogeneous links byappropriately modeling it asanother equivalent networkcomposed by point-‐to-‐point bitpipes.
• Provides relevant results withoutthe need of intricatemathemaDcal formulaDons, aswell as key insights forunderstanding complicatednetworks
• Extend this method for findingbounds for more generalmulDterminal channels.
• Compare results with exisDngbounds in literature and invesDgateif new upper bounds can be provedusing this technique.
Upper bound:at most ½ bit from
lower bound.
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