Adaptive Signal Processing and Information Theory Group
Efficient Control Signaling
for Resource Allocation
Gwanmo Ku
May 21, 2014
Ph.D. Thesis Defense
Adaptive Signal Processing and Information Theory Group 2
Overview
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling
Independent CEO
Rate Region
Calculation
Independent CEO with
Resource Allocation
1
2
3
4
Adaptive Signal Processing and Information Theory Group 3
Overview
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling*
Independent CEO
Rate Region
Calculation
Independent CEO with
Resource Allocation
* G. Ku, J.M. Walsh, “Resource Allocation and Link Adaptation in LTE and LTE Advanced : A Tutorial”, IEEE Communications Surveys and Tutorial
Adaptive Signal Processing and Information Theory Group 4
Units : Resource Allocation & Scheduling 1/26
Resource Grid
Adaptive Signal Processing and Information Theory Group 5
Downlink Control Region by PCFICH 1/26
Control Region : PDCCH Region
Adaptive Signal Processing and Information Theory Group 6
Contents of Downlink Control Information 1/26
Downlink Control Information in PDCCH
Adaptive Signal Processing and Information Theory Group 7
2/26
Resource Allocation
Adaptive Signal Processing and Information Theory Group 8
2/26
Reference : 3GPP Technical Specification TS 36.213
MCS Index and CQI
Adaptive Signal Processing and Information Theory Group 9
2/26
Reference : 3GPP Technical Specification TS 36.213
CQI Reporting Modes
Adaptive Signal Processing and Information Theory Group 10
Control Channels 21% 32% 11% Reference Signals 2/26
Reference : 3GPP Technical Specification TS 36.211
Control Signaling Overhead
Adaptive Signal Processing and Information Theory Group 11
Overview
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling
Independent CEO
Rate Region
Calculation
Independent CEO with
Resource Allocation
Adaptive Signal Processing and Information Theory Group 12
Overview
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling
Independent CEO
Rate Region
Calculation**
Independent CEO with
Resource Allocation
**G. Ku, J. Ren, J.M. Walsh, “Computing the Rate Distortion Region for the CEO Problem with Independent Sources”,
IEEE Transactions on Signal Processing
Adaptive Signal Processing and Information Theory Group 13
System Diagram & Rate Region Expression 1/26
Independent CEO Model
(𝓡,𝐷)
∀𝑚 ∈ 𝓜 𝑅𝑚 ≥ 𝐼(𝑋𝑚; 𝑈𝑚)𝑈𝑚 ↔ 𝑋𝑚 ↔ 𝑿𝓜\𝑚, 𝑼𝓜\𝑚, 𝑇
𝑇 ↔ 𝑼𝓜 ↔ 𝑇,𝑿𝓜
𝔼 𝑑(𝑇, 𝑇 ) ≤ 𝐷
Adaptive Signal Processing and Information Theory Group 14
Calculating Rate Region 1/26
Rate Region Calculation
(𝓡, 𝐷)
∀𝑚 ∈ 𝓜 𝑅𝑚 ≥ 𝐼(𝑋𝑚; 𝑈𝑚)𝑈𝑚 ↔ 𝑋𝑚 ↔ 𝑿𝓜\𝑚, 𝑼𝓜\𝑚, 𝑇
𝑇 ↔ 𝑼𝓜 ↔ 𝑇,𝑿𝓜
𝔼 𝑑(𝑇, 𝑇 ) ≤ 𝐷
Algorithm
Fixed
𝑝𝑋𝑚(𝑥𝑚),𝑑
Adaptive Signal Processing and Information Theory Group 15
Calculating Rate Region 1/26
Flowchart
Grid of 𝝀 and 𝜇
min 𝜆𝑖(𝑘)
𝐼 𝑋𝑖; 𝑈𝑖
𝑖∈𝓜
+ 𝜇(𝑘)𝔼 𝑑(𝑇, 𝑇 )
Polyhedral Rep. conversion
𝑟 , 𝑑 |𝐇𝑟 + ℎ𝑑 ≥ 𝟎
(𝑟𝑖(𝑘)
, 𝑑(𝑘)) Redundancy Removal
different
slope
Adaptive Signal Processing and Information Theory Group 16
Calculating Rate Region
where
1/26
Standard BA Relaxation
𝓛𝝀𝜇 𝑸,𝒒, Λ = 𝜆𝑖𝑖∈𝓜
𝑝𝑋𝑖𝑥𝑖 𝑄𝑖 𝑢𝑖 𝑥𝑖 log
𝑄𝑖(𝑢𝑖|𝑥𝑖)
𝑞𝑖(𝑢𝑖)(𝑥𝑖,𝑢𝑖)
+𝜇 𝑑 𝑡, 𝑡 𝑝𝑇|𝑿 𝑡 𝒙 Λ 𝑡 𝒖 𝑄𝑖 𝑢𝑖 𝑥𝑖𝑖∈𝓜𝑢,𝑥,𝑡,𝑡
𝑸 ≐ 𝑄𝑖 𝑢𝑖 𝑥𝑖) | 𝑢𝑖 ∈ 𝓤𝑖 , 𝑥𝑖 ∈ 𝓧𝑖 , 𝑖 ∈ 𝓜
𝒒 ≐ 𝑞𝑖(𝑢𝑖) | 𝑢𝑖 ∈ 𝓤𝑖 , 𝑖 ∈ 𝓜
Λ ≐ Λ(𝑡 |𝑢)|𝑡 ∈ 𝓣 , 𝒖 ∈ 𝓤𝑖 ×⋯×𝓤𝑀
Adaptive Signal Processing and Information Theory Group 17
1/26
Flowchart of Calculating Rate Region
Adaptive Signal Processing and Information Theory Group 18
1/26
Flowchart
𝑄𝑖(𝑙,𝑘𝑖+1) 𝑢𝑖|𝑥𝑖 =
𝑞𝑖(𝑙,𝑘𝑖) 𝑢𝑖 2
−𝜇𝜆𝑖𝑑𝑖(𝑙,𝑖)
(𝑥𝑖,𝑢𝑖)
𝑞𝑖(𝑙,𝑘𝑖)(𝑢𝑖
′)𝑢𝑖′2−𝜇𝜆𝑖𝑑𝑖(𝑙,𝑖)
(𝑥𝑖,𝑢𝑖′)
𝑞𝑖(𝑙,𝑘𝑖) 𝑢𝑖 = 𝑝𝑋𝑖
𝑥𝑖 𝑄𝑖(𝑙,𝑘𝑖)(𝑢𝑖|𝑥𝑖)
𝑥𝑖
𝑑𝑖(𝑙,𝑖)
𝑥𝑖 , 𝑢𝑖 = 𝑑 𝑡, 𝑡 𝑝𝑇,𝑿 𝑡, 𝒙 Λ(𝑙,𝑖) 𝑡 𝑢
𝑡,𝑡 ,𝒙\𝑖,𝒖\𝑖
𝑄𝑗(𝑙,∗)
(𝑢𝑗|𝑥𝑗)
𝑗<𝑖
𝑄𝑗′(𝑙−1,∗)
(𝑢𝑗′|𝑥𝑗′)
𝑗′≥𝑖
Adaptive Signal Processing and Information Theory Group 19
1/26
Flowchart
Λ(𝑙′,𝑖′) 𝑡 𝒖 = 𝛼(𝑙′,𝑖 )′ (𝒖) 𝑡 ∈ argmin
𝑡 ∈𝓣 𝐽 𝑙,𝑖 (𝑡 , 𝑢)
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Λ 𝑙′,𝑖′ (𝑡 |𝒖)
𝑡
= 1
𝐽 𝑙,𝑖 (𝑡 , 𝑢)
= 𝑑 𝑡, 𝑡 𝑝𝑇,𝑿 𝑡, 𝒙 𝑄𝑗(𝑙,∗)
(𝑢𝑗|𝑥𝑗)
𝑗≤𝑖
𝑄𝑗′(𝑙−1,∗)
(𝑢𝑗′|𝑥𝑗′)
𝑗′>𝑖𝑡,𝑡 ,𝒙\𝑚,𝒖\𝑚
Adaptive Signal Processing and Information Theory Group 20
Convex & Non-Convex 1/26
Convergence
Global minimum Local minimum
Global minimum
Adaptive Signal Processing and Information Theory Group 21
𝓛𝝀𝜇 𝑸, 𝒒, Λ is a convex function of 𝑸, 𝒒, Λ
⇒ Ind. CEO BA will converge to a global minimum.
1/26
Theorem
𝔼 𝑑(𝑇, 𝑇 ) is Convex
𝓛𝝀𝜇 𝑸, 𝒒, Λ is Convex
Global Convergence
Adaptive Signal Processing and Information Theory Group 22
Binary Hamming, Global Convergence 1/26
Convex
Adaptive Signal Processing and Information Theory Group 23
Convex & Non-Convex 1/26
Convergence
Global minimum Local minimum
Global minimum
Adaptive Signal Processing and Information Theory Group 24
Initialization by Graph Entropy at 𝒅𝐦𝐢𝐧 1/26
Non-convex
min𝑄𝑖 ⋅ ⋅)∈Γ(𝓖𝑖)
𝐼(𝑋𝑖; 𝑈𝑖)
𝑀
𝑖=1
𝐷
𝑅𝑖
𝑖
𝑑min
𝓖𝑖 : Characteristic graph of vertices ढ𝑖
Adjacent 𝑥𝑖 and 𝑥𝑖′
∃ 𝒙\𝑖 ∈ 𝑿\𝑖 s.t. 𝑡 𝑥𝑖 , 𝒙\𝑖 ≠ 𝑡 𝑥𝑖′, 𝒙\𝑖
Γ(𝓖𝑖): Maximal independent sets of 𝓖𝑖
Convex optimization problem
* V. Doshi, D. Shah, M. Medard, and M. Effros, "Functional compression through graph coloring," IEEE
Transactions on Information Theory, vol. 56, no. 8, pp. 3901-3917, August 2010.
** V. Doshi, D. Shah, M. Medard, and S. Jaggi, “Graph coloring and conditional graph entropy," in 40th
Asilomar Conf. on Signals, Systems, and Computers, 2006, pp. 2137{2141.
Adaptive Signal Processing and Information Theory Group 25
Tracking Previous Initialization,
1/26
Non-convex (Continued)
𝐷
𝑅𝑖
𝑖
𝑑min
Start from Graph Entropy
Initialize BA for this point nearby
Lagrange multiplier
×
×
Initialize BA for this point nearby
Lagrange multiplier Same point
Adaptive Signal Processing and Information Theory Group 26
Argmax [1 2 3] & [1 2 3 4] 1/26
Non-convex Examples
Adaptive Signal Processing and Information Theory Group 27
Redundancy Removal Description 1/26
Calculating Convex Hulll
Grid of 𝝀 and 𝜇
min 𝜆𝑖𝐼 𝑋𝑖; 𝑈𝑖
𝑖∈𝓜
+ 𝜇𝔼 𝑑(𝑇, 𝑇 )
Polyhedral Rep. conversion
𝑟 , 𝑑 |𝐇𝑟 + ℎ𝑑 ≥ 𝟎
(𝑟 ∗, 𝑑∗) Redundancy Removal
different
slope
𝑟𝑖(𝑙) = 𝑝𝑋𝑖
𝑥𝑖 𝑄𝑖(𝑙,∗)
𝑢𝑖 𝑥𝑖 log𝑄𝑖(𝑙,∗)
(𝑢𝑖|𝑥𝑖)
𝑞𝑖(𝑙,∗)
(𝑢𝑖)(𝑥𝑖,𝑢𝑖)
𝑑(𝑙) = 𝑑 𝑡, 𝑡 𝑝𝑇|𝑿 𝑡 𝒙 Λ(𝑙,∗) 𝑡 𝒖 𝑄𝑖(𝑙,∗)
𝑢𝑖 𝑥𝑖𝑖∈𝓜𝑢,𝑥,𝑡,𝑡
𝐇 =0𝑀+1×1 𝕀𝑀+1
1𝐾×1 𝐕
𝐕 =𝑟1(1)
… 𝑟𝑀(1)
𝑑(1)
𝑟1(2)
… 𝑟𝑀(2)
𝑑(2)
… … … …
Adaptive Signal Processing and Information Theory Group 28
Overview
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling
Independent CEO
Rate Region
Calculation
Independent CEO with
Resource Allocation
Adaptive Signal Processing and Information Theory Group 29
Overview
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling
Independent CEO
Rate Region
Calculation
Independent CEO with
Resource Allocation
Adaptive Signal Processing and Information Theory Group 30
Performance overhead tradeoff via Rate Distortion Curve
System Performance in Spectral Efficiency
Simple Model for Physical Layer employing DL communication
Broadcast Communication
Reteless coded Communication
Adaptive Modulation and Coding (AMC) Communication
Overhead Performance Tradeoff*
UE1
(Encoder 1)
UE2
(Encoder 2)
eNB
(CEO)
Resource Allocation Function : 𝒁
Inefficiency in Resource Allocation : 𝑫
CQI 1
CQI 2
*J. Ren, G. Ku, B. D. Boyle, S. Weber, and J. M. Walsh, “Overhead Performance Tradeoffs - A Resource Allocation Perspective,“
IEEE Transactions on Information Theory, to be submitted.
Adaptive Signal Processing and Information Theory Group 31
Private messages
• Wish to select modulation and coding rate to match the channel capacity
→ Want to know a UE attaining maximum CQI
→ Want to know the maximum CQI
AMC Communication
UE1
(Encoder 1)
UE2
(Encoder 2)
eNB
(CEO) Private Message 1
Private Message 2
𝒁?
𝒁 = ( 𝐦𝐚𝐱 𝑿𝟏, … , 𝑿𝑵 , 𝐚𝐫𝐠𝐦𝐚𝐱 𝑿𝟏, … , 𝑿𝑵 )
Adaptive Signal Processing and Information Theory Group 32
AMC 𝑍 = (max 𝑋1, 𝑋2 , argmax 𝑋1, 𝑋2 )
• Estimation at Basestation
1/26
Max & Argmax for AMC
𝑑 (𝑍, 𝑖), (𝑍 , 𝑖 ) = 𝑍 − 𝑍 𝑍 ≤ 𝑋𝑖
𝑍 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Adaptive Signal Processing and Information Theory Group 33
1/26
Simulation : Max & Argmax
Adaptive Signal Processing and Information Theory Group 34
Private messages
• Employs a near-perfect rateless code (Ex. HARQ)
→ Need to know a scheduled UE attaining the maximum CQI
Rateless Coded Communication
UE1
(Encoder 1)
UE N
(Encoder N)
eNB
(CEO) Private Message N
Private Message N
𝒁 = 𝐚𝐫𝐠𝐦𝐚𝐱(𝑿𝟏, … , 𝑿𝑵)
𝒁?
Adaptive Signal Processing and Information Theory Group 35
Rateless Communication 𝑍 = argmax(𝑋1, 𝑋2)
• Estimation at Basestation
1/26
Argmax
𝑑 𝑍, 𝑍 = 𝑋𝑍 − 𝑋𝑍
Adaptive Signal Processing and Information Theory Group 36
1/26
Simulation : Argmax
Adaptive Signal Processing and Information Theory Group 37
Common message
• For each UE to successfully decode on each channel
→ Need to know the lowest CQI level between UEs
→ Want to know the maximum negative CQI
Broadcast Communication
UE1
(Encoder 1)
UE N
(Encoder N)
eNB
(CEO)
A Common Message 𝒁?
𝒁 = 𝐦𝐚𝐱(𝑿𝟏, … , 𝑿𝑵)
Adaptive Signal Processing and Information Theory Group 38
𝑍 = max(𝑋1, 𝑋2)
• Estimation at eNB
1/26
Max Function for Broadcast
𝑑 𝑍, 𝑍 = 𝑍 − 𝑍 𝑍 ≤ 𝑍𝑍 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Adaptive Signal Processing and Information Theory Group 39
1/26
Simulation : Max
Adaptive Signal Processing and Information Theory Group 40
1/26
Simulation : Overall
Adaptive Signal Processing and Information Theory Group 41
Overview
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling
Independent CEO
Rate Region
Calculation
Independent CEO with
Resource Allocation
Adaptive Signal Processing and Information Theory Group 42
Overview
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling
Independent CEO
Rate Region
Calculation
Independent CEO with
Resource Allocation
Adaptive Signal Processing and Information Theory Group 43
Flowchart 1/26
Quantizer
Find Bayes detector for fixed thresholds
argmin𝑡
𝔼 𝑑 𝑇, 𝑡 |𝑋1 ∈ 𝐈1,𝑘1 , … , 𝑋𝑀 ∈ 𝐈1,𝑘𝑀
Average distortion of Bayes detector
in terms of thresholds
min𝔼 𝑑(𝑇, 𝑇 )
Minimize distortion w.r.t. thresholds
min𝔼 𝑑(𝑇, 𝑇 )
Adaptive Signal Processing and Information Theory Group 44
1/26
Max & Argmax Quantizer
Adaptive Signal Processing and Information Theory Group 45
1/26
Max & Argmax Quantizer
Converging
𝑲 → ∞
Adaptive Signal Processing and Information Theory Group 46
1/26
Argmax Quantizer
Adaptive Signal Processing and Information Theory Group 47
1/26
Argmax Quantizer
Converging
𝑲 → ∞
Adaptive Signal Processing and Information Theory Group 48
1/26
Max Quantizer
Adaptive Signal Processing and Information Theory Group 49
1/26
Max Quantizer
Converging
𝑲 → ∞
Adaptive Signal Processing and Information Theory Group 50
Summary
Control (Collaboration) Info.
System Performance
(Spectral Efficiency)
for Data
Information Theory Bound
Practical Source Coding
LTE Control Signaling
Independent CEO
Rate Region
Calculation
Independent CEO with
Resource Allocation
Adaptive Signal Processing and Information Theory Group 51
Thank you
2/26