Optimal Grouping and Matching for Network
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Optimal Grouping and Matching for Network Coded Cooperative Communications. Yi Shi Intelligent Automation Inc. with Sushant Sharma (Brookhaven National Laboratory), Thomas Hou , Scott Midkiff (Virginia Tech), Sastry Kompella (Naval Research Laboratory). Synopsis.

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Optimal Grouping and Matching for Network Coded Cooperative Communications

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Optimal grouping and matching for network coded cooperative communications

Optimal Grouping and Matching for Network Coded Cooperative Communications

Yi Shi

Intelligent Automation Inc.

with

Sushant Sharma (Brookhaven National Laboratory), Thomas Hou, Scott Midkiff (Virginia Tech),

SastryKompella (Naval Research Laboratory)


Synopsis

Synopsis

  • Focus: Network-Coded Cooperative Communications (NC-CC) with multiple relay nodes

  • Session/relay grouping and matching

    • NP-hard

  • An efficient heuristic solution

  • Results

    • High gains in data rate

    • Near-optimality of proposed heuristic solution


Cc a review

CC: A Review

  • A traditional wireless link

Sender

Receiver

  • Cooperative Communications (CC): Exploit antennas on neighbors to create diversity

Amplify-and-Forward

or

Decode-and-Forward

Relay Node

2ndtime slot

1sttime slot

1sttime slot

Sender

Receiver


Cc for multiple sessions

CC for Multiple Sessions

time slots

s1

d1

3

5

4

1

2

6

1

1

2

Relay

2n time-slots

Too much waste

NC can improve efficiency

4

3

6

3

s2

d2

5

5

s3

d3


Single relay nc cc

Single Relay NC-CC

d1

s1

1

time slots

1

4

1

4

2

3

Relay

NC can reduce time-slots from 2n to n+1

What about multiple relays?

2

4

s2

d2

4

3

s3

d3


Multi relay nc cc

Multi Relay NC-CC

d1

s1

Simultaneous transmissions

from multiple

relay nodes

s2

d2


Mutual information comparison

Mutual Information Comparison

Single-relay case is a special case of multi-relay NC-CC

Single-Relay NC-CC

Multi-Relay NC-CC


Overview

Overview

  • Background

  • Types of NC-CC

    • Single relay NC-CC

    • Multi relay NC-CC

  • Grouping and matching problem

  • G2M algorithm

    • Initialization phase

    • Main Program

  • Results


Grouping and matching problem

Grouping and Matching Problem

Objective:Maximize the weighted sum of data rates of all sessions.

Problem:How to break session and relays into groups and match them up optimally?


Np hardness sketch of proof

NP-Hardness: Sketch of Proof

  • Related Work: Grouping and Relay node Selection (GRS) problem [Sharma et al. INFOCOM 2011]

    • Restricts the size of each relay group to one

    • Shown to be NP-hard

  • Our problem

    • General form of GRS with unrestricted size of relay groups

    • Also NP-hard


Overview1

Overview

  • Background

  • Types of NC-CC

    • Single relay NC-CC

    • Multi relay NC-CC

  • Grouping and matching problem

  • G2M algorithm

    • Initialization phase

    • Main Program

  • Results


G 2 m algorithm basic idea

G2M Algorithm: Basic Idea

  • Start with matching each session with a group of relay nodes

  • Try to merge some pairs of session groups to improve objective.

  • Repeat Step 2 until objective stops improving.


Overview2

Overview

  • Background

  • Types of NC-CC

    • Single relay NC-CC

    • Multi relay NC-CC

  • Grouping and matching problem

  • G2M algorithm

    • Initialization phase

    • Main Program

  • Results


G 2 m algorithm initialization phase

G2M Algorithm: Initialization Phase

  • For each session (s, d): Initially assign all relays to its group

  • Iteration:

    • Check each relay (r) from the minimum SNRsr to the maximum SNRsr

    • If removing r increases objective, then r is removed

  • If any relay is removed during an iteration, then repeat Step 2 in the next iteration

  • Check if rate is greater than direct transmission

    • If not, then use direct transmission

Find a relay group for each session (NP-hard).


Overview3

Overview

  • Background

  • Types of NC-CC

    • Single relay NC-CC

    • Multi relay NC-CC

  • Grouping and matching problem

  • G2M algorithm

    • Initialization phase

    • Main Program

  • Results


G 2 m algorithm main program merging session groups

G2M Algorithm: Main Program (Merging Session Groups)

Runs in iterations

  • Start with a list of matchings obtained during initialization

  • Consider merger of every pair of current session groups

    • Intelligently merge the corresponding relay groups

    • If merger of session groups is favorable to objective

      • Then store the merged group (and relay group) in a temp-list

      • Otherwise, store each group separately with zero gain in the temp-list if not already there

  • We now have a temp-list with beneficial matchings and some matchings with zero gain


G 2 m algorithm operate on temp list

G2M Algorithm: Operate on Temp-list

  • If all the matchings in the temp-list have zero gain, then we stop

  • Otherwise, build an empty new-list and then check each matching in the temp-list in decreasing order of gains

    • If none of the sessions in current matching appears in new-list, then add this matching in the new-list

    • Otherwise, recover the matching for non-appearing sessions and add it back in the temp-list

  • We now have a new-list with every session appearing exactly once in some group

  • Repeat the iteration with this new-list


G 2 m algorithm merging relay groups

G2M Algorithm: Merging Relay Groups

  • When we merge two session groups, we need to merge their relay groups

  • Start with a group that includes relay nodes from both relay groups

  • Consider each relay that is not in both groups

    • Remove the considered relay from the relay group

    • If the sum rate of the merged sessions decrease, then add the relay back to the group


Overview4

Overview

  • Background

  • Types of NC-CC

    • Single relay NC-CC

    • Multi relay NC-CC

  • Grouping and matching problem

  • G2M algorithm

    • Initialization phase

    • Main Program

  • Results


Simulation settings

Simulation Settings

  • Preceived = Ptransmitted* ChannelGain

  • Channel path loss index: 4

  • SNR = Preceived/σ2

  • σ2: White Gaussian noise with variance 10-10 W

  • Ptransmitted = 1 W

  • 100 randomly generated networks

  • Area of 1200m x 1200m

  • 7 sessions, 16 relay nodes


G 2 m vs direct transmission

G2M vs. Direct Transmission

Equal weight for all sessions

Average Ratio: 2.53

Ratio of Objectives

Network Instance


G 2 m vs direct transmission1

G2M vs. Direct Transmission

Random session weights

Average Ratio: 2.67

Ratio of Objectives

Network Instance


Near optimality of g 2 m

Near Optimality of G2M

  • Formulated the problem as an optimization problem

    • An integer linear program

  • Solved optimization problem using CPLEX

    • Exponential time to obtain optimal solution

  • Compared the objective from G2M with optimal objective


Near optimality of g 2 m1

Near Optimality of G2M

Equal weight for all sessions

Ratio of Objectives

Average Ratio: 0.98

Network Instance


Near optimality of g 2 m2

Near Optimality of G2M

Random session weights

Ratio of Objectives

Average Ratio: 0.97

Network Instance


Conclusion

Conclusion

  • Considered multi-relay NC-CC in a network setting

  • Identified a session/relay grouping and matching problem

    • NP-hard

  • Designed an efficient heuristic algorithm: G2M

  • Validated the performance of G2M

    • Near-optimal


Thank you

Thank You


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