presentation

Interactive Communication for ResourceAllocation

Jie [email protected]

John MacLaren [email protected]

Adaptive Signal Processing and Information Theory GroupDepartment of Electrical and Computer Engineering

Drexel University, Philadelphia, PA 19104

This research has been supported by the Air Force Research Laboratoryunder agreement number FA9550-12-1-0086.

March 19th, 2014

Jie Ren (Drexel ASPITRG) ICFRA March 19th, 2014 1 / 20

Introduction

Outline

1 Introduction

2 Problem Model

3 Analysis

4 Results

5 Conclusions


Introduction

Motivation

M. I. Salman etc. ”IETE Technical Review”

• Which user to assign thesubcarrier to

• Which modulation and codingscheme to employ

X1

X2

X3


Introduction

Adaptive Modulation and Coding

• Overheads• Reference Signals• Channel Quality Indicators• Control Decisions

• Occupy the OFDMA resourceblocks

• Approximately 1/4 to 1/3 of alldownlink transmission in LTE


Introduction

BackgroundRateless Codes

http://www.telematica.polito.it/oldsite/sas-ipl/

• Almost achieve channel capacity

• Without requiring of channelinformation at the transmitterside

• Allow variable block length

3 dB

2 dB

2 dB

Ut(�t = 3dB)

X1

X2

X3

V 1t = 1

V 2t = 0

V 3t = 0

• BS: wishes to maximize thesystem throughput

• Only needs to learn the arg-max


Introduction

BackgroundInteractive Communication

• Interaction for Lossy SourceReproduction (Kaspi 1985)

• Interaction for functioncomputation (Ishwar & Ma2011)

• Benefit can be arbitrarily large• Infinite rounds interaction

may help

Rt ={R|∃Ut , s.t.∀i = 1, · · · , tRi ≥ I (X ;Ui |Y ,U i−1), Ui − (X ,U i−1)− Y , i odd

Ri ≥ I (Y ;Ui |Y ,U i−1), Ui − (Y ,U i−1)− X , i even

H(f (X ,Y )|Y ,Ut) = 0}

(1)


Introduction

Main Contribution

Achievable Interactive Communication Scheme for ResourceAllocation

• Determine the arg-max (use rateless codes for data transmission)

• Solve by dynamic programming

• Show huge savings


Problem Model

Outline

1 Introduction

2 Problem Model

3 Analysis

4 Results

5 Conclusions


Problem Model

Problem Model

3 dB

2 dB

2 dB

Ut(�t = 3dB)

X1

X2

X3

V 1t = 1

V 2t = 0

V 3t = 0

Notations

• Xi ∈ Xt = {at , . . . , bt}• Ut Broadcasting message at

round t

• V it Replied message from MS i

at round t

Achievable Interaction Scheme

1: BS broadcasts a threshold λt atround t

2: MS i replies a 1 if Xi ≥ λt and 0otherwise

3: Stops when BS knows arg-maxreliably


Problem Model

Problem Model

3 dB

2 dB

2 dB

Ut(�t = 3dB)

X1

X2

X3

V 1t = 1

V 2t = 0

V 3t = 0

Some Assumptions

• BS knows the initial distributionof X

• BS knows the initial number ofMSs

• MSs are not allowed tocommunicate with each other


Analysis

Outline

1 Introduction

2 Problem Model

3 Analysis

4 Results

5 Conclusions


Analysis

Analysis

Non-increasing Support set of X

If some users reply 1

at+1 = λt

bt+1 = bt

Ft+1(x) =Ft(x)− Ft(λt)

Ft(bt)− Ft(λt)

(2)

If no user replies 1

at+1 = at

bt+1 = λt

Ft+1(x) =Ft(x)− Ft(at)

Ft(λt)− Ft(at)

(3)


Analysis

Analysis

Aggregate rate

Rt(λ) = H(λ|λ1, · · · , λt−1) + Nt + (Ft(λ))NtR∗(Nt , at , λ)

+Nt∑i=1

(1− Ft(λ))iFt(λ)Nt−i Nt !

i !(Nt − i)!R∗(i , λ, bt) (4)

Policy Iteration

λ∗t = arg minλ

Rt(λ) (5)


Analysis

Analysis

• Efficiently Encode the Threshold

H(λt |λ1, . . . , λt−1) (6)

• Why H(Nt |Nt−1) works?• Xt and Nt determines λ∗t• Xt−1,Nt−1 and Nt determinesXt

• Two other strategies• Non-conditioning Encode the

Threshold: H(λt)• Encode the Number of Users:

H(Nt |Nt−1)

Xt =

{λ∗t−1, bt−1} if Nt < Nt−1

{at−1, λ∗t−1} if Nt = Nt−1 and λ∗t−1 > xi

{λ∗t−1, bt−1} if Nt = Nt−1 and λ∗t−1 ≤ xi

(7)


Results

Outline

1 Introduction

2 Problem Model

3 Analysis

4 Results

5 Conclusions


Results

Results

• X = {1, . . . , 16}

2 3 4 5 6 7 8 9 10 11 125

10

15

20

25

30

35

40

45

50

number of users

overh

eads

Non−interaction

Interaction

Sending Threshold

Sending Number of Uers

One−way Limit


Results

Some Extensions

Interaction with Distortion

E[max{X1, . . . ,XNt} − Xi ] ≤ D (8)

Bits Cost Vs. Time Cost

C = µR + (1− µ)T (9)


Conclusions

Outline

1 Introduction

2 Problem Model

3 Analysis

4 Results

5 Conclusions


Conclusions

Contribution & Future Work

Review of Contribution

• Achievable Interactive Communication Scheme for ResourceAllocation

• Solve by Dynamic Programming

Future Work

• Consider Scalar Quantization than the 1-bit Message

• Fundamental Limits (Rate-distortion Curve)

• Resource Allocation in MIMO system


Conclusions

Acknowledgments

Supported by the AFOSR under agreement number FA9550-12-1-0086


presentation

Documents

db ut t

round t v i t

threshold t

problem model problem

resource allocation

problem model outline

db x1 x2 x3

introduction outline