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Coded Caching: Discussing Promises and Challenges

Eleftherios Lampiris lampiris@eurecom.fr

EURECOM

September 2017

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 1 / 28

(2)

Outlook

Promises

Coded Caching

MIMO Coded Caching D2D Coded Caching Decentralised Approach Caching under Popularity Distributions

Challenges

Uneven Channel Strengths CSI Requirements

Subpacketization issues

(3)

Outlook

Promises

Coded Caching

MIMO Coded Caching D2D Coded Caching Decentralised Approach Caching under Popularity Distributions

Challenges

Uneven Channel Strengths CSI Requirements

Subpacketization issues

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 2 / 28

(4)

Coded Caching

1 2 · · · N

Server

User 1 User 2

User K

Cache

Cache

Cache

[Maddah-Ali, Niesen ’12]

N Files F bits per File K Users

M · F User Memory γ = M

N Normalized Cache

(5)

Coded Caching

1 2 · · · N

Server

User 1 User 2

User K

Cache

Cache

Cache

[Maddah-Ali, Niesen ’12]

N Files F bits per File K Users

M · F User Memory γ = M

N Normalized Cache Users Served Simultaneously

d Σ = + 1

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 3 / 28

(6)

Coded Caching

1 2 · · · N

Server

User 1 User 2

User K

Cache

Cache

Cache

[Maddah-Ali, Niesen ’12]

N Files F bits per File K Users

M · F User Memory γ = M

N Normalized Cache Users Served Simultaneously

d Σ = + 1

Optimality

Optimal within a multiplicative factor of 2.008.

[Qian, Maddah-Ali, Avestimehr ’17]

(7)

Effect of Coded Caching

1 2 · · · N

Server

User 1 User 2

User K

Cache

Cache

Cache

[Maddah-Ali, Niesen ’12]

Time under Uniform Demand T = K(1 γ) 1

+ 1 1 γ γ

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 4 / 28

(8)

Effect of Coded Caching

1 2 · · · N

Server

User 1 User 2

User K

Cache

Cache

Cache

[Maddah-Ali, Niesen ’12]

Time under Uniform Demand T = K(1 γ) 1

+ 1 1 γ γ

Per User Rate R u =

( γ + 1

K )

· R tot γ · R tot

Each gets a γ piece of the pie!!

(9)

Effect of Coded Caching

1 2 · · · N

Server

User 1 User 2

User K

Cache

Cache

Cache

[Maddah-Ali, Niesen ’12]

Time under Uniform Demand T = K(1 γ) 1

+ 1 1 γ γ

Per User Rate R u =

( γ + 1

K )

· R tot γ · R tot Each gets a γ piece of the pie!!

Intuition

Even unwanted packets can help reduce interference

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 4 / 28

(10)

Example 1

3 Users - 3 Files - γ = 2 3

Server

User 1 User 2

User 3 A B

A

12

B

12

C

12

C

13

B

13

A

13

A

23

B

23

C

23

A

12

B

12

C

12

A

23

B

23

C

23

C

13

B

13

A

13

C

M = 2

Files are divided into 3 parts { 12, 13, 23 }

Cache i is filled-up with all

parts indexed with i

(11)

Example 1

3 Users - 3 Files - γ = 2 3

Server

User 1 User 2

User 3 A B

A

12

B

12

C

12

C

13

B

13

A

13

A

23

B

23

C

23

A

12

B

12

C

12

A

23

B

23

C

23

C

13

B

13

A

13

C

A

23

B

13

C

12

A 23 B 13 C 12

Single Message serves all users at the same time

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 5 / 28

(12)

Example 2

4 Users - 4 Files - γ = 2 4

Server

User 1

User 2 User 3 A B C

User 4

A14 B14 C14 D14

D24 C24 B24

A24A34

B34 C34

D34 D34

A14 B24 D24 C14 D14 C24 B14

C34 B34 A34 A24

D

A12 B12 C12C13

B13 A13

A23 B23 C23 C23

B23 A23 A13 B13 C13 C12 B12 A12

D12D13

D13 D12D23 D23

Placement Phase

Files are divided into 6 parts {12, 13, 14, 23, 24, 34}

Cache i is filled-up with all

parts indexed with i

(13)

Example 2

4 Users - 4 Files - γ = 2 4

Server

User 1

User 2 User 3 A B C

User 4

A14 B14 C14 D14

D24 C24 B24

A24A34

B34 C34

D34 D34

A14 B24 D24 C14 D14 C24 B14

C34 B34 A34 A24

D

A12 B12 C12C13

B13 A13

A23 B23 C23 C23

B23 A23 A13 B13 C13 C12

B12 A12

D12D13

D13 D12D23 D23

Delivery Phase

Every Message serves 3 users at the same time

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 6 / 28

(14)

Example 2

4 Users - 4 Files - γ = 2 4

Server

User 1

User 2 User 3 A B C

User 4

A14 B14 C14 D14

D24 C24 B24

A24A34

B34 C34

D34 D34

A14 B24 D24 C14 D14 C24 B14

C34 B34 A34 A24

D

A12 B12 C12C13

B13 A13

A23 B23 C23 C23

B23 A23 A13 B13 C13 C12 B12 A12

D12D13

D13 D12D23 D23

x

123

= A

23

B

13

C

12

Delivery Phase

Every Message serves 3 users at the same time

x 123 = A 23 B 13 C 12

(15)

Example 2

4 Users - 4 Files - γ = 2 4

Server

User 1

User 2 User 3 A B C

User 4

A14 B14 C14 D14

D24 C24 B24

A24A34

B34 C34

D34 D34

A14 B24 D24 C14 D14 C24 B14

C34 B34 A34 A24

D

A12 B12 C12C13

B13 A13

A23 B23 C23 C23

B23 A23 A13 B13 C13 C12 B12 A12

D12D13

D13 D12D23 D23

x

124

= A

24

B

14

D

24

Delivery Phase

Every Message serves 3 users at the same time

x 123 = A 23 B 13 C 12

x 124 = A 24 B 14 D 24

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 6 / 28

(16)

Example 2

4 Users - 4 Files - γ = 2 4

Server

User 1

User 2 User 3 A B C

User 4

A14 B14 C14 D14

D24 C24 B24

A24A34

B34 C34

D34 D34

A14 B24 D24 C14 D14 C24 B14

C34 B34 A34 A24

D

A12 B12 C12C13

B13 A13

A23 B23 C23 C23

B23 A23 A13 B13 C13 C12 B12 A12

D12D13

D13 D12D23 D23

x

134

= A

34

C

14

D

13

Delivery Phase

Every Message serves 3 users at the same time

x 123 = A 23 B 13 C 12

x 124 = A 24 B 14 D 24

x 134 = A 34 C 14 D 13

(17)

Example 2

4 Users - 4 Files - γ = 2 4

Server

User 1

User 2 User 3 A B C

User 4

A14 B14 C14 D14

D24 C24 B24

A24A34

B34 C34

D34 D34

A14 B24 D24 C14 D14 C24 B14

C34 B34 A34 A24

D

A12 B12 C12C13

B13 A13

A23 B23 C23 C23

B23 A23 A13 B13 C13 C12

B12 A12

D12D13

D13 D12D23 D23

x

234

= B

34

C

24

D

23

Delivery Phase

Every Message serves 3 users at the same time

x 123 = A 23 B 13 C 12

x 124 = A 24 B 14 D 24

x 134 = A 34 C 14 D 13 x 234 = B 34 C 24 D 23

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 6 / 28

(18)

MIMO Coded Caching

.. .

Cache

BS

UE

Cache

UE

Cache

UE

Cache

UE

L I B R A R Y

1

L H

[Shariatpanahi, Motahari, Khalaj ’15 &

Naderializadeh, Maddah-Ali, Avestimehr ’16]

N files K users L antennas γ fractional cache Users Served

d Σ = + L

⋆dΣ= min{K, Kγ+L} Order Optimal Gap= 2

(19)

MIMO Coded Caching

.. .

Cache

BS

UE

Cache

UE

Cache

UE

Cache

UE

L I B R A R Y

1

L H

[Shariatpanahi, Motahari, Khalaj ’15 &

Naderializadeh, Maddah-Ali, Avestimehr ’16]

N files K users L antennas γ fractional cache Users Served

d Σ = + L

Intuition

Send a vector of linear Combinations such that some packets are cached-out and some packets are nulled-out.

⋆dΣ= min{K, Kγ+L} Order Optimal Gap= 2

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 7 / 28

(20)

MIMO CC Example

K = 4, N = 4, L = 2, γ = 1 4

UE1

UE

UE UE

A

B

C

A

1

B

1

B

2

B

3

B

4

C

1

C

2

C

3

C

4

D

D

1

D

2

D

3

D

4

A

2

A

3

A

4 2

3 4

1

2 S E R V E R

h ij : Antenna i to User j Channel

(21)

MIMO CC Example

K = 4, N = 4, L = 2, γ = 1 4

UE1

UE

UE UE

A

B

C

A

1

B

1

B

2

B

3

B

4

C

1

C

2

C

3

C

4

D

D

1

D

2

D

3

D

4

A

2

A

3

A

4 2

3 4

1

2 S E R V E R

h ij : Antenna i to User j Channel

x 123 =

[ h 13 1 A 2 + h 11 1 B 3 + h 12 1 C 1

h 23 1 A 2 h 21 1 B 3 h 22 1 C 1

]

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 8 / 28

(22)

MIMO CC Example

K = 4, N = 4, L = 2, γ = 1 4

UE1

UE

UE UE

A

B

C

A

1

B

1

B

2

B

3

B

4

C

1

C

2

C

3

C

4

D

D

1

D

2

D

3

D

4

A

2

A

3

A

4 2

3 4

1

2 S E R V E R

h ij : Antenna i to User j Channel

x 123 = [

h 13 1 A 2 + h 11 1 B 3 + h 12 1 C 1

h −1 23 A 2 h −1 21 B 3 h −1 22 C 1 ]

y 1 = A 2 + C 1 (h 11 h 12 1 h 21 h 22 1 )

y 2 = B 3 + A 2 (h 12 h 13 1 h 22 h 23 1 )

y 3 = C 1 + B 3 (h 13 h 11 1 h 23 h 21 1 )

(23)

MIMO CC Example

K = 4, N = 4, L = 2, γ = 1 4

UE1

UE

UE UE

A

B

C

A

1

B

1

B

2

B

3

B

4

C

1

C

2

C

3

C

4

D

D

1

D

2

D

3

D

4

A

2

A

3

A

4 2

3 4

1

2 S E R V E R

h ij : Antenna i to User j Channel

x 123 =

[ h 13 1 A 2 + h 11 1 B 3 + h 12 1 C 1

h 23 1 A 2 h 21 1 B 3 h 22 1 C 1

]

x 124 =

[ h −1 12 A 4 + h −1 14 B 1 + h −1 11 D 2

h 22 1 A 4 h 24 1 B 1 h 21 1 D 2 ]

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 8 / 28

(24)

MIMO CC Example

K = 4, N = 4, L = 2, γ = 1 4

UE1

UE

UE UE

A

B

C

A

1

B

1

B

2

B

3

B

4

C

1

C

2

C

3

C

4

D

D

1

D

2

D

3

D

4

A

2

A

3

A

4 2

3 4

1

2 S E R V E R

h ij : Antenna i to User j Channel

x 123 = [

h 13 1 A 2 + h 11 1 B 3 + h 12 1 C 1

−h 23 1 A 2 h 21 1 B 3 h 22 1 C 1

]

x 124 =

[ h 12 1 A 4 + h 14 1 B 1 + h 11 1 D 2

h 22 1 A 4 h 24 1 B 1 h 21 1 D 2

]

x 134 =

[ h 14 1 A 3 + h 11 1 C 4 + h 13 1 D 1

h 24 1 A 3 h 21 1 C 4 h 23 1 D 1

]

(25)

MIMO CC Example

K = 4, N = 4, L = 2, γ = 1 4

UE1

UE

UE UE

A B

C

A

1

B

1

B

2

B

3

B

4

C

1

C

2

C

3

C

4

D

D

1

D

2

D

3

D

4

A

2

A

3

A

4 2

3 4

1

2 S E R V E R

h ij : Antenna i to User j Channel

x 123 = [

h 13 1 A 2 + h 11 1 B 3 + h 12 1 C 1

h 23 1 A 2 h 21 1 B 3 h 22 1 C 1 ]

x 124 = [

h 12 1 A 4 + h 14 1 B 1 + h 11 1 D 2

h 22 1 A 4 h 24 1 B 1 h 21 1 D 2 ]

x 134 = [

h 14 1 A 3 + h 11 1 C 4 + h 13 1 D 1

h 24 1 A 3 h 21 1 C 4 h 23 1 D 1

]

x 234 =

[ h 13 1 B 4 + h 14 1 C 2 + h 12 1 D 3

h 23 1 B 4 h 24 1 C 2 h 22 1 D 3

]

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 8 / 28

(26)

D2D Coded Caching

N

1

N

3

cache

N

2

N

K

cache

cache cache

cache

N

4

[Ji, Caire, Molisch ’14]

K users N files

M files cache capacity

(27)

D2D Coded Caching

N

1

N

3

cache

N

2

N

K

cache

cache cache

cache

N

4

[Ji, Caire, Molisch ’14]

K users N files

M files cache capacity Intuition

Each user assumes the role of the transmitter as in original MN

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 9 / 28

(28)

D2D Coded Caching

In a nutshell

Results

users served at a time T = 1 γ

γ

Surprising Result

D2D Gains are the same with or without spatial reuse

1

1

(29)

Decentralized Coded Caching

Number of users showing up is unknown

Cache uniformly at random Result

T = (1 γ )

γ (1 (1 γ) K )

Order Optimal

[Maddah-Ali, Niesen ’13]

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 11 / 28

(30)

Decentralized Coded Caching

Number of users showing up is unknown

Cache uniformly at random Result

T = (1 γ )

γ (1 (1 γ) K )

Order Optimal

[Maddah-Ali, Niesen ’13]

[source: Maddah-Ali, Niesen ’13]

(31)

Decentralized Coded Caching

Example

Algorithm

Start from higher order cliques and move to lower order Greedy approach

Placement

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 12 / 28

(32)

Decentralized Coded Caching

Example

Algorithm

Start from higher order cliques and move to lower order Greedy approach

Requests

(33)

Decentralized Coded Caching

Example

Algorithm

Start from higher order cliques and move to lower order Greedy approach

Clique of 3

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 12 / 28

(34)

Decentralized Coded Caching

Example

Algorithm

Start from higher order cliques and move to lower order Greedy approach

Clique of 2

(35)

Decentralized Coded Caching

Example

Algorithm

Start from higher order cliques and move to lower order Greedy approach

Clique of 2

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 12 / 28

(36)

Requests under Popularity Distributions

Algorithm 1

Proved Sub-optimality of HPF Group files according to popularity

[Maddah-Ali, Niesen ’13]

[source: Maddah-Ali, Niesen ’13]

(37)

Requests under Popularity Distributions

Algorithm 1

Proved Sub-optimality of HPF Group files according to popularity

[Maddah-Ali, Niesen ’13]

Algorithm 2

Cache file if popularity 1 KM Increases γ by reducing N Order optimal with Gap = 87

[Zhang, Lin, Wang ’15]

[source: Maddah-Ali, Niesen ’13]

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 13 / 28

(38)

Requests under Popularity Distributions

Key Questions

Algorithms to achieve near optimal solutions?

How better can these algorithms perform?

Does knowledge of the popularity significantly improve original MN?

(39)

Implementation Challenges

1) Uneven Channel Strengths

1 2 · · · N

Server

User 1 User 2

User K

Cache

Cache

Cache

1

τ τ

τ 1

Worst-user effect

Common reality in Wireless

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 15 / 28

(40)

Implementation Challenges

1) Uneven Channel Strengths: SISO with Topology

[Zhang, Elia ’16 source: Zhang, Elia ’16]

W users have link capacity τ 1

K W users have link capacity 1

(41)

Implementation Challenges

1) Uneven Channel Strengths: SISO with Topology

[Zhang, Elia ’16 source: Zhang, Elia ’16]

W users have link capacity τ 1 K W users have link capacity 1

K = 500

[source: Zhang, Elia ’16]

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 16 / 28

(42)

Implementation Challenges

1) Uneven Channel Strengths: Cooperation without CSIT

Cache

Cache

Cache

Cache

Cache

Cache

1

γ T γ R

2

K

1

K 2

link capacity 1 link capacity τ ≤ 1

[Lampiris, Zhang, Elia ’17]

Assumptions No CSIT

Different Link Capacities

Allows Cooperative Transmissions Caches at both ends

Achievable Cache-Aided GDoF of MISO BC (γ T = 1)

d Σ = K(1 τ ) + (Kγ R + 1)τ

Topology and Caching complement

each other

(43)

Implementation Challenges

1) Uneven Channel Strengths: Cooperation without CSIT

Cache

Cache

Cache

Cache

Cache

Cache

1

γ T γ R

2

K

1

K 2

link capacity 1 link capacity τ ≤ 1

[Lampiris, Zhang, Elia ’17]

Assumptions No CSIT

Different Link Capacities

Allows Cooperative Transmissions Caches at both ends

Achievable Cache-Aided GDoF of MISO BC (γ T = 1)

d Σ = K(1 τ ) + (Kγ R + 1)τ Topology and Caching complement each other

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 17 / 28

(44)

Implementation Challenges

1) Uneven Channel Strengths: Cooperation without CSIT

Cache

Cache

Cache

Cache

Cache

Cache

1

γ T γ R

2

K

1

K 2

link capacity 1 link capacity τ ≤ 1

Assumptions No CSIT

Different Link Capacities

Allows Cooperative Transmissions Caches at both ends

Achievable Cache-Aided GDoF of MISO BC (γ T = 1)

d Σ = K(1 τ ) + (Kγ R + 1)τ

Topology and Caching complement

each other

(45)

Implementation Challenges

Achievable Cache-Aided GDoF of Interference Channel

TT R ) = T (1 γ R ) K(1 τ )+(Kγ R +1)

(

min { 1 2τ−1 γ

T

, τ } ) + + K(1 γ T )(1 γ R ) K g min { 1 τ γ

T

, 1 } x s

K g = K(1 γ T ) ( K 1

R

) ( K

R

+1

) γ T

( K 1

R

) (

RT

+1 ) K K

R

1 R + 1

x s = K (1 τ ) K(1 τ ) +

(

(Kγ R + 1) min { 2τ 1

1 γ

T

, τ }) +

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 18 / 28

(46)

Implementation Challenges

Achievable Cache-Aided GDoF of Interference Channel

TT R ) = K γ T (1 γ R ) K(1 τ )+

(KγR+1)

(

min{1 1−γT, τ}

)

+

+ K (1 γ T )(1 γ R ) K g

min

{

τ 1−γT,1

} x s

Transmitter Side Caching

Interference Enhancement

Coded Caching

(47)

Implementation Challenges

Achievable Cache-Aided GDoF of Interference Channel

TT R ) = K γ T (1 γ R ) K(1 τ )+

(KγR+1)

(

min{1 1−γT, τ}

)

+

+ K (1 γ T )(1 γ R ) K g

min

{

τ 1−γT,1

} x s

Transmitter Side Caching Interference Enhancement

Coded Caching

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 19 / 28

(48)

Implementation Challenges

Achievable Cache-Aided GDoF of Interference Channel

TT R ) = K γ T (1 γ R ) K(1 τ )+

(KγR+1)

(

min{1 1−γT, τ}

)

+

+ K (1 γ T )(1 γ R ) K g

min

{

τ 1−γT,1

} x s

Transmitter Side Caching

Interference Enhancement

Coded Caching

(49)

Implementation Challenges

Impact of Transmitter Side Cache

τ = 0.3, K = 100

R= 0 R= 1 R= 2 R= 10 R= 20

0.1 0.3 0.5 0.7 0.9 150

250 350

0 γ

T

T

50

τ = 0.7, K = 100

R= 0 R= 1 R= 2 R= 10 R= 20

0.1 0.3 0.5 0.7 0.9 100

0 140

20 60

γ

T

T

TT R ) = T (1 γ R ) K(1 τ )+(Kγ R +1)

(

min { 1 γ

T

1 , τ } ) + + K(1 γ T )(1 γ R ) K g min

{ τ 1 γ

T

, 1

} x s

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 20 / 28

(50)

Implementation Challenges

Impact of Transmitter Side Cache

τ = 0.3, K = 100

R= 0 R= 1 R= 2 R= 10 R= 20

0.1 0.3 0.5 0.7 0.9 150

250 350

0

1−γT=τ

γ

T

T

50

τ = 0.7, K = 100

R= 0 R= 1 R= 2 R= 10 R= 20

0.1 0.3 0.5 0.7 0.9 100

0 140

20 60

1 γ

T

= τ

γ

T

T

TT R ) = T (1 γ R ) K(1 τ )+(Kγ R +1)

(

min { 1 γ

T

1 , τ } ) + + K(1 γ T )(1 γ R ) K g min

{ τ 1 γ

T

, 1

} x s

(51)

Implementation Challenges

Impact of Receiver Side Cache

τ = 0.3, K = 100

150 250 350

0

T= 1 T= 20 T= 80

0.04 0.08 0.12 0.16 γ

R

T

50

τ = 0.7, K = 100

140

20 60 100

0

T= 1 T= 20 T= 80

0.04 0.08 0.12 0.16 γ

R

T

TT R ) = T (1 γ R ) K(1 τ )+(Kγ R +1)

(

min { 1 γ

T

1 , τ } ) + + K(1 γ T )(1 γ R ) K g min

{ τ 1 γ

T

, 1

} x s

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 21 / 28

(52)

Implementation Challenges

2) Too much CSI needed for MIMO Coded Caching

.. .

Cache

BS

UE

Cache

UE

Cache

UE

Cache

UE

L I B R A R Y

1

L

?

(53)

Implementation Challenges

2) Too much CSI needed for MIMO Coded Caching

.. .

Cache

BS

UE

Cache

UE

Cache

UE

Cache

UE

L I B R A R Y

1

L

?

RECALL

y 1 = A 2 + C 1 (h 11 h 12 1 h 21 h 22 1 ) Requires CSIR

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 22 / 28

(54)

Implementation Challenges

2) Too much CSI needed for MIMO Coded Caching

.. .

Cache

BS

UE

Cache

UE

Cache

UE

Cache

UE

L I B R A R Y

1

L

?

CSIT/CSIR required :

(Kγ + L) · L variables

MIMO CC requires a lot of

training for high gains

(55)

Implementation Challenges

2) Too much CSI needed for MIMO Coded Caching

.. .

Cache

BS

UE

Cache

UE

Cache

UE

Cache

UE

L I B R A R Y

1

L

?

CSIT/CSIR required : (Kγ + L) · L variables MIMO CC requires a lot of training for high gains More Coming Soon Stay tuned!

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 22 / 28

(56)

Implementation Challenges

3) Subpacketization: Finite Length Analysis

First result discussing the

astronomical file size requirement Results

Gain 2 for Decentralized MN if |F| ≤ ( e

γ ) For a gain of g under any decentralized scheme

| F | = O ( ( 1

γ ) g

)

[Shanmugam, Ji, Tulino, Llorca, Dimakis ’15]

(57)

Implementation Challenges

3) Subpacketization: Finite Length Analysis

First result discussing the

astronomical file size requirement Results

Gain 2 for Decentralized MN if |F| ≤ ( e

γ ) For a gain of g under any decentralized scheme

| F | = O ( ( 1

γ ) g

)

[Shanmugam, Ji, Tulino, Llorca, Dimakis ’15]

Take home message

Decentralized CC is limited by a gain of at most 7

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 23 / 28

(58)

Implementation Challenges

3) Subpacketization

Original Subpacketization S M N =

( K

)

S= 103 S= 106 S= 109

M N

0.1

0.04 0.08 γ

Gain

0.01

1 0

2

3

4

5

6

(59)

Implementation Challenges

3) Subpacketization

Original Subpacketization S M N =

( K

)

Reduced Subpacketization S 2 =

( 1 γ

) 1

[Yan, Cheng, Tang, Chen ’15 &

Tang, Ramamoorthy ’16]

1 0 2 3 4 5 6 7

0.1

0.04 0.08 γ

Gain

0.01

S= 103 S= 106 S= 109 M N Yan et al.

Yan et al.

Yan et al.

M NM N S= 103 S= 106 S= 109

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 24 / 28

(60)

Implementation Challenges

3) Subpacketization: Other Schemes

Linear Subpacketization is Possible

There exists a caching scheme with linear subpacketization and polynomial delivery time, |F | = O(K).

In reality, K → ∞ ⇒ F → ∞

[Shanmugam, Tulino, Dimakis ’17]

Centralized CC: A hypergraph approach

There exist no constant rate caching schemes with | F | = O (K) Tradeoff between performance and subpacketization

Schemes require K > 4

γ 2 for g 2

[Shangguan, Yiwei Zhang, Gennian Ge ’16]

(61)

Implementation Challenges

3) Subpacketization: Other Schemes

More Coming Soon Stay tuned!

[Lampiris, Elia ’17]

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 26 / 28

(62)

General Conclusions

Promises

Coded Caching in theory can severely reduce traffic

Merging CC with PHY leads to rich and powerful solutions

MIMO CC can pave the way to supplement MIMO gains with caching.

Hot Questions

How can subpacketization be reduced?

NO Current Algorithm can go beyond a gain of 7 for reasonable γ and subpacketization

Can feedback in MIMO CC be detangled from Caching Gains?

(63)

General Conclusions

Promises

Coded Caching in theory can severely reduce traffic

Merging CC with PHY leads to rich and powerful solutions

MIMO CC can pave the way to supplement MIMO gains with caching.

Hot Questions

How can subpacketization be reduced?

NO Current Algorithm can go beyond a gain of 7 for reasonable γ and subpacketization

Can feedback in MIMO CC be detangled from Caching Gains?

Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 27 / 28

(64)

Thanks!

Références

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