Multicast Scaling Laws with Hierarchical Cooperation

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Multicast Scaling Laws with Hierarchical
Cooperation

• Chenhui Hu, Xinbing Wang, Ding Nie, Jun Zhao
• Shanghai Jiao Tong University, China

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Outline

• Introduction
• Motivations
• Objectives
• Models and Definitions
• Multi-hop Hierarchical Cooperative Schemes
• Achievable Multicast Capacity
• Delay and Energy Consumption
• Conclusion and Future Works

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Motivation

• Non-cooperative wireless networks uses multi-hop
  transmission E.g. unicast 3, GuptaKumar,
  multicast 19, Li
• Capacity of wireless ad hoc networks is
  constrained by interference between concurrent
  transmissions.
• Protocol Model
• TDMA Scheduling

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Motivation

• Cooperative networks obtain capacity gain by
  turning mutually interfering signals into useful
  ones. 1,Özg?r
• Realize cooperative communication by Distributed
  MIMO.
• Two clusters each with M nodes
• 1) Source node distributes its bits
• 2) Every sender holds a different bit,
• and transmits simultaneously
• 3) Receiver nodes interchange their
• observations to decode

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Objectives

• Hierarchical Cooperative MIMO has been shown in
  2,Özg?r achieves a linear throughput scaling
  for unicast.
• In our work, we focus on multicast scaling laws
  using hierarchical MIMO.1. How to hierarchically
  schedule multicast traffic to optimize the
  throughput?2. Delay performance and
  energy-efficiency when achieving optimal
  throughput?3. Delay-throughput tradeoff in our
  hierarchical cooperative multicast strategies?

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Outline

• Introduction
• Models and Definitions
• Multi-hop Hierarchical Cooperative Scheme
• Achievable Multicast Capacity
• Delay and Energy Consumption
• Conclusion and Future Works

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Models and Definitions I/II

• Network Model and Traffic
• n nodes independently uniformly distributed in
  a unit suquare
• Randomly and independently choose a set of k
  nodes Ui ui,j 1 j k as destination
  nodes for each node vi
• Physical-layer Model
• Channel gain for the transmission from vj to vi
• Signal received by node vi at time t

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Models and Definitions II/II

• Def. of Throughput
• A throughput of bits/sec is feasible if
  there is a spatial and temporal scheme for
  scheduling, s.t. every node can send
  bits per second on average to all its destination
  nodes.
• Aggregate multicast throughput
• Def. of Energy-Per-Bit
• Average energy required to carry one bit from a
  source node to one of its destination nodes
• Def. of Delay
• Average time it takes for a bit to reach its
  destination nodes

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Outline

• Introduction
• Models and Definitions
• Multi-hop Hierarchical Cooperative Scheme
• General Multicast Structue
• MMM CMMM scheme
• Achievable Multicast Capacity
• Delay and Energy Consumption
• Conclusion and Future Works

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General Multicast Structure

• Divide the network into clusters, with M nodes in
  each cluster.
• Step 1 Source node will distribute its
  bits among the nodes, one for each.
• Step 2 Conduct MIMO transmissions along a
  spanning tree connecting the clusters where the
  source and its destinations nodes locate.
• Step 3 In a cluster having destination nodes,
  nodes deliver its observation to the destinations
  for decoding.

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MMM CMMM scheme

• Two methods to schedule transmissions in Step 3
• Multi-hop MIMO Multicast (MMM)
• Converge based Multi-hop MIMO Multicast (CMMM)
• Both schemes involve a hierarchical solution to
  the transmission problem of Step 3.
• MMM Treat the traffic in Step 3 as multicast
  problem
• CMMM Treat the traffic in Step 3 as converge
  multicast problem, with multi-hop MIMO
  transmissions

Converge Multicast Problem Randomly choose a
set of nodes as
destinations. Each node in thenetwork acts as a
source node andsends one identical bit to all
nodes in the set.
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MMM Scheme

• Step 1. Preparing for Cooperation
• Each node distributes data to other
  nodes
• Step 2. Multi-hop MIMO Transmissions
• Routing on the multicast tree
• Step 3. Cooperative Decoding To decode, all
  nodes in the destination cluster first quantify
  an observation into Q bits. Then each node
  conveys the Q bits to all destination nodes in
  the cluster.

The multicast problem in step 3 can also be
solved by the same three-step structure. Thus,
Implementing it recursively get a hierarchical
solution.
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CMMM Scheme

• Step 3-1. Multi-hop MIMO Transmissions Since all
  nodes must send one bit to destination nodes, all
  clusters act as source clusters and transmit to
  destination clusters by multi-hop MIMO.
• Step 3-2. Cooperative Decoding After a
  destination cluster receives a MIMO transmission,
  all nodes quantify the observation and converge
  them to the destination nodes in the cluster.
• The multicast problem in step 3-2 is also a
  converge multicast problem. Implementing the same
  two-step structure recursively we get a
  multi-layer solution to converge multicast
  problem.

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Notations

• Notations
• of layers,
• indicator for a particular layer
• of nodes,
• of destination nodes for each source
• denotes of clusters
• denotes of destination clusters at layer
  
• denotes of multicast sessions at layer
• We use Knuth's notation in this paper. Also we
  use
• to indicate
  and
• , for any
  .

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Outline

• Introduction
• Models and Definitions
• Multi-hop Hierarchical Cooperative Scheme
• Achievable Multicast Capacity
• Upper bound of throughput
• Achievable throughput of MMM
• Delay and Energy Consumption
• Conclusion and Future Works

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Upper bound of throughput

• The. Aggregate multicast throughput is whp
  bounded by
• where is a constant independent of
  and .
• Can we achieve this optimal bound?
• Intuition We need make use of interference
• How can we minimize the delay and energy
  consumption?

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Achievable Throughput of MMM

• Calculate time required in the three steps
• To optimize the throughput, certain network
  division is used

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Achievable Throughput of MMM

• Lem. When , the number of nodes
  at each layer to achieve optimal throughput in
  MMM strategy is given by
• The. By MMM strategy, we can achieve an
  aggregate throughput of

Note Throughput analysis of CMMM is similar to
that of MMM
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Achievable Throughput of MMM

• Results comparison

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Outline

• Introduction
• Models and Definitions
• Multi-hop Hierarchical Cooperative Scheme
• Achievable Multicast Capacity
• Delay and Energy Consumption
• Delay and Energy Consumption
• Discussion
• Conclusion and Future Works

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Delay and Energy Consumption

• Delay of MMM
• Consider the delay of MMM recursively
• Delay-Throughput Tradeoff
• Energy Consumption of MMM

Poor!
huge bulk size
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Delay and Energy Consumption

• Delay of CMMM
• Delay-Throughput Tradeoff
• Energy Consumption of CMMM

Delay reduces from exponential to linear!
Similar to energy cost of MMM
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Discussion

• The Advantage of Cooperation improve the
  aggregate throughput by compared to
  non-cooperative scheme in 19.
• The Effect of Different Network Division we
  divide the network into fewer clusters as gets
  bigger.Special case in broadcast , our
  cooperative scheme cannot render any gain on
  throughput.
• Delay-Throughput Tradeoff nearly the same as
  non-cooperative multicast .
• The Advantage of Multi-hop MIMO Transmission
  achieve a gain on throughput compared with direct
  transmission in 1,Özg?r the energy consumption
  also decreases by .

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Outline

• Introduction
• Models and Definitions
• Multi-hop Hierarchical Cooperative Scheme
• Achievable Multicast Capacity
• Delay and Energy Consumption
• Conclusion and Future Works

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Conclusion and Future Works

• We study the scaling laws for multicast and
  develop a multi-hop hierarchical cooperation
  scheme achieving throughput of , where
  .
• Our scheme achieves a capacity gain compared
  with non-cooperative scheme, and also cuts down
  the energy consumption and delay.
• Our converge-based Multi-hop MIMO Multicast
  scheme achieves the delay-throughput tradeoff
  identical to that of non-cooperative schemes when
  .

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Thank you !
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Reference
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Reference
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