Coded Caching: Discussing Promises and Challenges
Eleftherios Lampiris lampiris@eurecom.fr
EURECOM
September 2017
Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 1 / 28
Outlook
Promises
Coded Caching
MIMO Coded Caching D2D Coded Caching Decentralised Approach Caching under Popularity Distributions
Challenges
Uneven Channel Strengths CSI Requirements
Subpacketization issues
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
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
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 = Kγ + 1
Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 3 / 28
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 = Kγ + 1
Optimality
Optimal within a multiplicative factor of 2.008.
[Qian, Maddah-Ali, Avestimehr ’17]
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
Kγ + 1 ≈ 1 − γ γ
Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 4 / 28
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
Kγ + 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!!
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
Kγ + 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
Example 1
3 Users - 3 Files - γ = 2 3
Server
User 1 User 2
User 3 A B
A
12B
12C
12C
13B
13A
13A
23B
23C
23A
12B
12C
12A
23B
23C
23C
13B
13A
13C
M = 2
Files are divided into 3 parts { 12, 13, 23 }
Cache i is filled-up with all
parts indexed with i
Example 1
3 Users - 3 Files - γ = 2 3
Server
User 1 User 2
User 3 A B
A
12B
12C
12C
13B
13A
13A
23B
23C
23A
12B
12C
12A
23B
23C
23C
13B
13A
13C
A
23⊕B
13⊕C
12A 23 ⊕ B 13 ⊕ C 12
Single Message serves all users at the same time
Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 5 / 28
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
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
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
12Delivery Phase
Every Message serves 3 users at the same time
x 123 = A 23 ⊕ B 13 ⊕ C 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
x
124= A
24⊕B
14⊕D
24Delivery 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
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
13Delivery 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
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
23Delivery 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
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 = Kγ + L ⋆
⋆dΣ= min{K, Kγ+L} Order Optimal Gap= 2
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 = Kγ + 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
MIMO CC Example
K = 4, N = 4, L = 2, γ = 1 4
UE1
UE
UE UE
A
B
C
A
1B
1B
2B
3B
4C
1C
2C
3C
4D
D
1D
2D
3D
4A
2A
3A
4 23 4
1
2 S E R V E R
h ij : Antenna i to User j Channel
MIMO CC Example
K = 4, N = 4, L = 2, γ = 1 4
UE1
UE
UE UE
A
B
C
A
1B
1B
2B
3B
4C
1C
2C
3C
4D
D
1D
2D
3D
4A
2A
3A
4 23 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
MIMO CC Example
K = 4, N = 4, L = 2, γ = 1 4
UE1
UE
UE UE
A
B
C
A
1B
1B
2B
3B
4C
1C
2C
3C
4D
D
1D
2D
3D
4A
2A
3A
4 23 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 )
MIMO CC Example
K = 4, N = 4, L = 2, γ = 1 4
UE1
UE
UE UE
A
B
C
A
1B
1B
2B
3B
4C
1C
2C
3C
4D
D
1D
2D
3D
4A
2A
3A
4 23 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
MIMO CC Example
K = 4, N = 4, L = 2, γ = 1 4
UE1
UE
UE UE
A
B
C
A
1B
1B
2B
3B
4C
1C
2C
3C
4D
D
1D
2D
3D
4A
2A
3A
4 23 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
]
MIMO CC Example
K = 4, N = 4, L = 2, γ = 1 4
UE1
UE
UE UE
A B
C
A
1B
1B
2B
3B
4C
1C
2C
3C
4D
D
1D
2D
3D
4A
2A
3A
4 23 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
D2D Coded Caching
N
1N
3cache
N
2N
Kcache
cache cache
cache
N
4[Ji, Caire, Molisch ’14]
K users N files
M files cache capacity
D2D Coded Caching
N
1N
3cache
N
2N
Kcache
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
D2D Coded Caching
In a nutshell
Results
Kγ users served at a time T = 1 − γ
γ
Surprising Result
D2D Gains are the same with or without spatial reuse
1
1
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
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]
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
Decentralized Coded Caching
Example
Algorithm
Start from higher order cliques and move to lower order Greedy approach
Requests
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
Decentralized Coded Caching
Example
Algorithm
Start from higher order cliques and move to lower order Greedy approach
Clique of 2
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
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]
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
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?
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
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
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
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
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
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
Implementation Challenges
Achievable Cache-Aided GDoF of Interference Channel
T (γ T ,γ R ) = Kγ 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 Kγ − 1
R
) ( K
Kγ
R+1
) − γ T
( K − 1
Kγ
R) − ( Kγ Kγ
RT+1 ) K − Kγ K
R− 1 ≈ Kγ 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
Implementation Challenges
Achievable Cache-Aided GDoF of Interference Channel
T (γ T ,γ R ) = K γ T (1 − γ R ) K(1 − τ )+
(KγR+1)(
min{2τ−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
Implementation Challenges
Achievable Cache-Aided GDoF of Interference Channel
T (γ T ,γ R ) = K γ T (1 − γ R ) K(1 − τ )+
(KγR+1)(
min{2τ−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
Implementation Challenges
Achievable Cache-Aided GDoF of Interference Channel
T (γ T ,γ R ) = K γ T (1 − γ R ) K(1 − τ )+
(KγR+1)(
min{2τ−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
Implementation Challenges
Impact of Transmitter Side Cache
τ = 0.3, K = 100
KγR= 0 KγR= 1 KγR= 2 KγR= 10 KγR= 20
0.1 0.3 0.5 0.7 0.9 150
250 350
0 γ
TT
50
τ = 0.7, K = 100
KγR= 0 KγR= 1 KγR= 2 KγR= 10 KγR= 20
0.1 0.3 0.5 0.7 0.9 100
0 140
20 60
γ
TT
T (γ T ,γ R ) = Kγ T (1 − γ R ) K(1 − τ )+(Kγ R +1)
(
min { 1 2τ − − γ
T1 , 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
Implementation Challenges
Impact of Transmitter Side Cache
τ = 0.3, K = 100
KγR= 0 KγR= 1 KγR= 2 KγR= 10 KγR= 20
0.1 0.3 0.5 0.7 0.9 150
250 350
0
1−γT=τ
γ
TT
50
τ = 0.7, K = 100
KγR= 0 KγR= 1 KγR= 2 KγR= 10 KγR= 20
0.1 0.3 0.5 0.7 0.9 100
0 140
20 60
1 − γ
T= τ
γ
TT
T (γ T ,γ R ) = Kγ T (1 − γ R ) K(1 − τ )+(Kγ R +1)
(
min { 1 2τ − − γ
T1 , τ } ) + + K(1 − γ T )(1 − γ R ) K g min
{ τ 1 − γ
T, 1
} x s
Implementation Challenges
Impact of Receiver Side Cache
τ = 0.3, K = 100
150 250 350
0
KγT= 1 KγT= 20 KγT= 80
0.04 0.08 0.12 0.16 γ
RT
50
τ = 0.7, K = 100
140
20 60 100
0
KγT= 1 KγT= 20 KγT= 80
0.04 0.08 0.12 0.16 γ
RT
T (γ T ,γ R ) = Kγ T (1 − γ R ) K(1 − τ )+(Kγ R +1)
(
min { 1 2τ − − γ
T1 , 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
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
?
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
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
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
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 ) Kγ For a gain of g under any decentralized scheme
| F | = O ( ( 1
γ ) g
)
[Shanmugam, Ji, Tulino, Llorca, Dimakis ’15]
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 ) Kγ 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
Implementation Challenges
3) Subpacketization
Original Subpacketization S M N =
( K Kγ
)
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
Implementation Challenges
3) Subpacketization
Original Subpacketization S M N =
( K Kγ
)
Reduced Subpacketization S 2 =
( 1 γ
) Kγ − 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
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]
Implementation Challenges
3) Subpacketization: Other Schemes
More Coming Soon Stay tuned!
[Lampiris, Elia ’17]
Lampiris (EURECOM) Coded Caching: Promises - Challenges September 2017 26 / 28
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?
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