PETROS ELIA
(EURECOM – FRANCE)
Part 2 of
CACHING IN WIRELESS NETWORKS
Intro
• This part of the tutorial is about a novel use of caching in wireless communication networks
• Using on-board memory at the nodes:
�NOT to reduce the volume/size of the problem
�“Prefetch something today so that you don’t have to send it tomorrow”
�BUT to surgically alter the informational structure of networks
�Use on-board memory to change the network to something faster, simpler, more efficient.
2
Outline of Part 2
• Challenges of modern wireless communications
� The need of a new technology
• Basic elements of coded caching
� Basic properties
� Main gains
� Important variants
� Main bottlenecks
3
Outline of Part 2• Need to fuse coded caching with advanced PHY techniques
• Some differences between wired and wireless coded caching
• Coded caching in multi-user MIMO settings� Cache-aided BC and IC
• The fundamental interplay between coded-caching and feedback� Competing + synergistic duality between feedback and caching
� Feedback-aided coded caching
� Caching to reduce CSI load!
• Coded caching in a variety of wireless networks– Cache-aided cloud-based Wyner networks
– Femtocaching
– Caching on the edge
– Coded caching in erasure networks
– Wireless multihop D2D caching networks
• Theoretical and practical open problems
4
A Promising New Approach: Coded Caching
5
• Main difference:
�Careful caching of subfiles across caches
�Careful coding across files requested by different users
• Provides substantial performance gains, BUT :
� Algorithm needs file size to scale exponentially in the number of users � �������� > �…
� Potentially small fraction of interference removed (small DOF)
DOF ≈ ���������������������� � !"�#� (for larger �)
Unlike Typical Approach in Wireless
Networks
Feedback Unicasting opportunities Interference
• Signal-separation
– Different users’ signals separated by powerful
feedback-aided PHY algorithms
6
Dual (caching) approach: Signal mixing
Caching Multicasting opportunities Interference
7
caching Feedback-aided PHY
Disconnected?
Caching: MAC feedback: PHY layer
8
• Interesting connections/duality
• Example:
� Incomplete feedback forces incomplete signal separation
� Paradoxically boosts impact of multicasting (basis for coded caching)
� Holds in reverse. Each builds on the imperfections of the other.
• A structural link due to parallel problems (uncertain location)
� How we cache accounts for uncertainty on identity of receiver
� How we transmit accounts for uncertainty on channel of receiver
Why Should They Be Connected
Feedback
(disseminating CSI today)
Coded Caching
(preemptive data-storage
yesterday)
• Example
9
Feedback-PHY
Reducing
Interference
Caching
Synergistic Effect of Two
Complementary Approaches
10
Limitations of Current
Communications Paradigms
11
Main Challenges
Data
Feedback
• `Feedback’: channel-state information (CSI)
� The instantaneous strengths of each propagation-path between different nodes
• As � increases, the overhead consumes more and more resources
� No room for actual data
� Brings current systems and envisioned methods to a halt
12
Multi-cell Cooperation
• Even full BS cooperation cannot handle interference
• Spectral efficiency upper bound that is independent of the transmit
power
• Cooperation possible only within clusters of limited size (due to CSI)
� subject to out-of-cluster interference with power similar to in-cluster signals
source: Lozano et al. (2012)
$%� ≝ '� ("� )�*���+!,-. /01 → 0 �$%� ≝ '� ("� )�*���+!,-. /01 → 0 (as � increases)
13
Wireless Network Densification
Deployment of more base-stations/access-points per unit area
• Short-range wireless channels different from classical cellular counterparts
• Exhibit path loss subduction (reduced path loss exponent)
• Extreme fading (more severe deep-fades)
• SINR decrease after certain densification threshold
• Similar trends are observed for the throughput⇒ Disruption of densification gainssource: Andrews et al. (2015)
14
Massive MIMO and mm-Wave
Massive MIMO:
• Gains in spectral efficiency
• Gains reduced by expensive channel
estimation
� Pilot contamination*
Mm-Wave Communications:
• High frequency results in sparse and
easier to estimate channels
• Channels though can fluctuate
between sparse and denser
� think of AoD in urban settings
• Introduces FB delays/overhead
• Also directionality can create signal
“holes” for users**
**source: Rappaport et al. (2014)
*source: Marzetta (2010)15
Single Stream Coded Caching
16
• Transmission sequence:
Single stream channel: No caching (6 = 0)Library: 9 files
.
.
.: = �
Rx1
Rx2
Rx�;���<���1
>?@?>�AB1
17
Simple non-coded caching (uniform popularity – for now)
Library: 9 files
.
.
.
6
69Rx1
Rx2
Rx�• Transmission sequence:
1 − 6/9• Local cache gain: 1 −6/9 for each user
• The rate: : = � 1 −6/9 = � 1 − E , E ≝ G018
Library: 9 files
.
.
.
Rx1
Rx2
Rx�
6
66
Caches
E ≝ 69 ≝ �HI�J�K?�>?>L�<�����MN?NB<���E ≝ 69 ≝ �HI�J�K?�>?>L�<�����MN?NB<���: E : IKN?A�PHP;I���J�NB@L?<�
:(E): E : IKN?A�PHP;I���J�NB@L?<�
OBJECTIVE: reduce :(E)
Recap: Basic Parameters of Coded-Caching
Key breakthrough:
• Cache so that one transmission is useful to many
� Even if requested files are different
� Increases multicast opportunities
• Substantial increase in throughput (“worst case”)
Maddah-Ali and Niesen’s coded caching (MNS)
Library: 9 files
.
.
.
Rx1
Rx2
Rx�
6
6
6
Caches
Result: Maddah-Ali, Niesen (2012)
Library: 9 = 2Caches
Example: 9 = � = 2,6 = 1(E = RS)Rx1
Rx2
TU6 = 1
6 = 1
Source: Maddah-Ali, Niesen (2012)21
T2U1 U2T1
T2
U1
U2
T1
T2⨁U1
Library: 9 = 2
• Multicasting opportunity created from caching;
� Hard case: distinct requests
Rx1
Rx2
� Easy case: same requests
T1⨁T2
6 = 1
6 = 1
T2⨁U1
T2⨁U1
T2
U1
12
T1⨁T2T2
T1⨁T2T1
Source: Maddah-Ali, Niesen (2012)
Example: 9 = � = 2,6 = 1(E = RS)
22
• Uncoded Caching rate:
• Coded Caching:
Comparison: 9 = � = 2,6 = 1(E = G0 = RS)
::� = 2 → � 1 − E = 2 W 12 = 1::� = 2 → � 1 − E = 2 W 12 = 1
: = 12: = 12• For 9 = � = 2 case, optimal rate can be achieved for 6 ∈ 0,1
Image source: Maddah-Ali, Niesen (2012)23
Another Example: 9 = � = 3,6 = 2(E = SZ)Rx1
Library: 9 = 3 files
Rx2
Rx3
TU[6 = 2
6 = 2
6 = 2A12 A13 A23
B12 B13 B23
C12 C13 C23
13
Source: Maddah-Ali, Niesen (2012)24
Example: 9 = � = 3,6 = 2(E = G0 = SZ)Rx1
Library: 9 files
A12 A13 A23
B12 B13 B23
C12 C13 C23
A12
A12
A13
A13
A23
A23 B12
B12
B13
B13
B23
B23C12
C12
C13
C13
C23
C23
13
Rx2
Rx3
6 = 2
algorithm: Maddah-Ali, Niesen (2012)
• Transmit : A23 B13 C12⨁ ⨁ (a common message for all)
: = 1 W 13 = 13: = 1 W 13 = 1325
• 9 files in library
• Split each file into G/0 = \ subfiles
• Cache: In every G0 = �E set of users, there is one part of each
file in common
• Request: Each user asks for one file (out of 9)
• Deliver to �E + 1 users at a time
� Via XORs with �E + 1 subfiles/summands. Each user (out of
the �E + 1 now served) knows all summands except one
(its own requested subfile)
• Repeat for all possible sets of �E + 1 users
Coded Caching Pseudocode (recall E ≝ G0)
Algorithm: Maddah-Ali, Niesen (2012)26
: = �(1 − E)1 + �E : = �(1 − E)1 + �E
Maddah-Ali and Niesen’s results
• Uncoded rate (local caching gain) :
• Coded-caching required :
Optimal to within a factor 12.
: = �(1 − E): = �(1 − E)
Result and image source: Maddah-Ali, Niesen (2012)
� Coding gain:
≝ (R^\)_ = 1 + �EGain ≝ (R^\)_ = 1 + �E
:
9 = � = 30
27
Example:
� = 10, E = 0.01 (�E = 0.1):: 6 = 9.9 (only local gain - prefetching):b 6 = 9.466 (decentralised caching):) 6 = 9.0 (centralised caching):∗ 6 ≥ 9.0 (MN optimal bound)
⇒Generally small gains wghijk < m� = 1000, E = 0.01 (�E = 10): : 6 = 990 :) 6 = 90:b 6 = 99 :∗ 6 ≥ 25
Generally large gains wghijk > mResult: Maddah-Ali, Niesen (2013)
28
On the Optimality of Uncoded Cache-Placement
• Maddah-Ali and Niesen’s coded caching is optimal under
� the constraint of uncoded cache placement
� the constraint of 9 ≥ �
Library: 9 files
.
.
.
Rx1
Rx2
Rx�
6
6
6
Caches o1
o2
o�
result: Wan et al. (2015)29
Bounds to optimal
Source††: Maddah-Ali, Niesen (2013)
Source†: Ghasemi, Ramamoorthy (2015)
Source***: Maddah-Ali, Niesen (2013)
Source**: Lim, Wang and Gastpar (2016)
Source*: Q. Yan, X. Tang, Q. Chen (2016) 30
• Centralized to optimal:
1 ≤ _r G_∗ G ≤ 4s ≤ 12ss• Decentralised to centralized_t(G)_r(G) ≤ 1.5∗ ≤ 4.7∗∗ ≤ 12∗∗∗
Coded vs Traditional Multicasting
(More Users than Files)
• 9 < � means that a file may be demanded by multiple users
� Implies possible additional multicasting opportunities
� Possible scenario: server to many users, selects few (9 < �), (equally)
popular files
• Original MNS misses this additional (traditional) multicast opportunity
� because it treats each sub-file demanded by each user as a district sub-file
Library: 9 files
.
.
.
Rx1
Rx2
Rx�
6
66
31
On Caching with More Users than Files
• A novel method* allows for additional (traditional) multicasting opportunities (see also [Chen et al. 2014], and [Sahraei and Gastpar, 2015])
• Optimal under the constraint of uncoded placement and � > 9 = 2• Gains are quite limited
� Coded caching automatically `covers’ almost all multicasting opportunities!
Result and image source: Wan, Tuninetti and Piantanida (2016)
T(M) vs M(load vs. memory) - centralized
system: N = 2 and K = 10
T(M) vs M(load vs. memory) - decentralized
system: N = 4 and K = 8
32
First Conclusions
E : E
• Significant gain of coded caching
� Multicasting gain (�E + 1) among users with different demands
• Significant improvement over conventional caching schemes
� Gains seen when �E > 1� For large �,then : need not scale as �
: ≈ 1 − EE� Traditional caching works when 6 is comparable with 9, while
coded caching works when �6 is comparable with 9• Potential bottlenecks for small E: : increasing sharply as E decreases
33
Coded Caching with
Non-uniform Demands
Exploiting File Popularities
• Content popularity is not uniformly distributed
• Could be modelled by a power law / Zipf distribution
Optimal approach for � = 1: – Least Frequently Used (LFU) eviction policy
– Cache M most popular files
– Can end up with identical caches
� No coded-multicasting opportunities35
Coded Caching - Non-uniform Demands
Simply assigning a larger cache to more popular files,
can result in different subpacket sizes
Part sizes must be equal to avoid padding losses
• Biggest subpacket limits rate
36
Batch Coding for Non-Uniform
Demands
• Separate files into batches of similar popularity
• Cache size allocation is proportional to average batch
popularity
• Coded caching for each batch separately
�Only code among files with same subfile sizes
Source: Maddah-Ali, Niesen (Infocom 2014)37
Index-Coding based Scheme
for Non-Uniform Demands
• Subfile size same for all files
• Popular files get more subfiles
• Improvement by creating coding opportunities between batches
• Delivery uses index coding to combine (XOR) different subfiles– graph coloring
– clique cover
Source: Ji et al. (2015)
Ji et al.
MN
38
Example
• 3 files xT, U, [y split into 3 parts each. E.g. T = xTR, TS, TZy• Cache distribution z = xT = SZ , U = RZ , [ = 0yCache realization{
Request: user1→ T, user2→ U, user3→ [Queried parts: | = xTZ, UR, UZ, [R, [S, [Zy39
Conflict Graph ),}Vertex for each requested subpart (∈ |):
- Replicate if multiple requests of a subfile
Edge if
• Not same identity (cannot connect subfile to itself)
• Request(er) not among users caching the other vertex
- see (TZ, UR)
Requests: user1→ T, user2→ U, user3→ [Queried parts: | = xTZ, UR, UZ, [R, [S, [Zy
40
Graph Coloring ),}Connected vertices must have different colors
Transmission
Gain |}|�(�r,�) (χis chromatic number)
: E = 5/3: E = 5/3 Calculation:|�|�(�),}) = � 1 − E:= 3 1 − 135/3 = 6541
Graph Coloring for non-uniform
requests
In general
• NP hard
• exponentially complex
For this particular (coded-caching) coloring problem:
• Greedy constrained coloring used*
– polynomial complexity in number of users and subfiles
*result: Ji et al. (2015)42
Caching Distribution
• To solve previous problem, we need optimal caching distribution z∗� Use approximation:
– Binary truncated caching distribution z�:
@�� = � 1H� , ; ≤ H�0, ; ≥ H� + 1– Resembling Random LFU (RLFU)
• In limit H� = 9,we get `uniform placement‘
• Use graph contrained coloring for delivery
• Similar performance as distributed MN scheme with H� ≤ 9 files
result: Ji et al. (2015)43
Simulated Rate Comparison
(non-uniform popularity) • Uniform placement (`UP–GCC‘ : H� = 9, @ = R0 , �[[ ≈ 69$)
• Reference Scheme (`RS‘ : MN within batches, variable sub packet sizes)
• LFU naive-multicast (`LFU-NM‘ : cache M most popular files every where)(no coded-multicasting) (local caching gain with identical caches)
• Random LFU (`RLFU-GCC‘ : GCC on H� most popular files)
– : H� < 9, @ = R�� , �[[)
•– a=0.6 a=1.6
image source and result: Ji et al. (2015)
o�@;: � = 0.6 o�@;: � = 1.6
44
Subpacketization Problem
(Motivates Fusing Coded-Caching and PHY)
• Recall need to split each file into \ subfiles
• So that:– In every �E caches, there is one part of each file in common
– For each XOR, each of the �E + 1 users served knows all subfiles
except one (their requested own)
• Introduces intense `sub-packetization’ problem
– Intense file-size problem
45
Subpacketization constraints
VS
� = 6, �E = 2
Users are served �E+1 at a time No multicasting between, 1-2-6
Users 1,2,6 get
content
simultaneously
No overlaps
between 1-6 and
2-646
CC with Bounded File Sizes
• No algorithm with randomized and uncoded placement can
escape
� ≤ % log �log 1E
• Conditional bound achieved by Shanmugam et al.
• Also
Results: Shanmugam et al. (2014)47
Improved Decentralized Scheme
48
System
Servers : a library of 9popular files
� Users: �requests
Advanced Feedback-aided PHY
Cache: prefilled
information
Bottlenecks Introduce Need to Combine Memory
and PHY Resources in Wireless Networks
49
Coded-caching: Non-trivial Application of Single-
Stream Coded Caching to Wireless Networks
�-user cache-aided MISO
BC with � transmit
antennas and perfect CSIT
�1�2��
Rx1
Rx2
Rx�
Library: 9 files
. .
.66
6
. .
. . .
.
Library: 9 files
.
.
.
Rx1
Rx2
Rx�
6
66
Caches
Capacity �
�-user single-stream (tree)
network with increased
capacity
Example:
� antennas:� antennas:
50
• A equivalent measurement: per-user DoF
I E = 1 − E: ∈ [0,1]� E = G0 is normalized local caching gain: prefilled content
� 1 − E excludes local caching gain
� Captures the joint effect of coded caching and PHY resources
• For one user, the interference-free optimal to serve one file: : = 1 − E� I(E) between 0 and 1 ( I = 1: Interference-free optimal DoF)
Library: 9 files
Rx1 6
Small Parenthesis: Measure of
Performance
51
MIMO and Feedback with Coded Caching:
Trivial Example (9 = � = 2,6 = 1)�1
�2
Rx1
Rx2UT9 = 2 filesT2T1 U2U112
• T2 ⊕U1 will be delivered
• multicasting phase �1 = T2⊕U10• : = RS
� Turns out it is optimal (: = 1 − E = 1 − G0 = 1 − RS = RS) (same as interference-free)
� Optimal achieved without CSIT and with just a single antenna
66A1
A2 B2
B1
UT
INSIGHT:
Coded caching can reduce need for feedback and multiple antennas, and vice-versa52
Super server: 9 files
Server
1
Server �Server
2. .
.
Perfect Network-
topology
Knowledge
User
1
User
2. .
.
User �
Centralized Multi-Server Coded Caching (MISO BC)
Result: Shariatpanahi et al. (2015)
�-user cache-aided MISO
BC with � transmit
antennas and perfect CSIT
�1�2��
Rx1
Rx2
Rx�
Library: 9 files
. .
.66
6
. .
. . .
.
53
Example (first trivial) : 9 = � = 3, � = 2,6 = 1
• Just like MISO-BC with perfect CSIT (full connectivity)
• Combining
� FB-aided unicasting : using CSIT (�1, �2, �3)� With coded caching delivery of T2, U1 ; T3, [1 ; U3, [2
A1 A2 A3
B1 B2 B3
C1 C2 C3
A1
A2
A3
B2
B1
B3
C1
C2
C3
13 �1
�2
�3
Rx1
Rx2
Rx3
Algorithm: Shariatpanahi et al. (2015)54
• :
• The corresponding DoF:
� Equal contribution of MIMO (�), and caches (E)
� Non-trivial fusing of CC and multiplexing gains
� Gap-to-optimal less than 2 (Naderializadeh et al.)
Centralized Multi-server Coded caching
result: Shariatpanahi et al. (2015)
:(E) = � 1 − E��Hx� + �E, �(1 − E)y = 1 − E��Hx� + E, 1 − Ey .(� = ��):(E) = � 1 − E��Hx� + �E, �(1 − E)y = 1 − E��Hx� + E, 1 − Ey .(� = ��):(E): 1 − EE → 1 − E� + E:(E): 1 − EE → 1 − E� + E
I E ≝ 1 − E: → � + E < 1I E ≝ 1 − E: → � + E < 1
55
:"" E = � 1 − E1 + �E → : E = �� (1 − E)1 + �� E = �(1 − E)� + �E
� k = k + mj/� = k + �j = k + �
Intuition
6
Super sever: 9 files
Server 1 Server �Server 2 . . .
Rx1 Rx � +1. . . Rx
� Rx S�. . .
6 66Rx
�^� +1 Rx �. . . 66 . . .. . .
. . .
� ≝ ��E ≝ 6956
• As if method created � parallel sub-networks, with � users each
Cooperative Interference Channel
IC � XC � BC
Effect of different forms of CSI
on NDT for 2 W 2 Network
Image Source and result: Sengupta, Tandon, Simenone (2015)
See also Maddah-Ali and Niesen (ISIT 2015) 57
• Caching only at the Txs
One Shot Cache-aided Interference channel
Rx 1
. .
.
Rx�
6�Rx 2 6�
6�
Tx 1: 6:
.
.
.
Tx 2: 6:
Tx�: 6:
. .
.
Result: Naderializadeh et al. (2016)
• Cache-aided interference channel
• � interfering transmitter/ receiver pairs (fully connected)
• Each transmitter has cache with size 6_ < 9(E_ ≝ G�0 )• Each receiver has cache with size 61 < 9(E1 ≝ G�0 )
Note:�6_ ≥ 9
58
Example: 9 = � = 3,6: = 2,61 = 1
• 9 files: W1 = T,W2 = U,W3 = [; (E: = G_0 = SZ ,E� = G_0 = RZ)• Split each file into
\_\1 = ZS ZR = 9 partsT = (T12,1, T12,2, T12,3, T13,1, T13,2, T13,3, T23,1, T23,2, T23,3)
• Cache Tx 1: Tm2,1, Tm2,2, Tm2,3, Tm3,1, Tm3,2• Cache Rx 1: T12, m, T13, m, T23, m
Rx1
Rx3
6�Rx 2 6�
6�
Tx1:6:Tx2:6:Tx3:6:
Source: Naderializadeh et al. (2016)59
• Rx1 needs: T12,2, T12,3, T13,2, T13,3, T23,2, T23,3• Rx2 needs: U23,3, U13,1, U12,3, U23,1, U13,3, U12,1• Rx3 needs: [13,1, [23,2, [23,1, [12,2, [12,1, [13,2
Rx1
Rx3
Rx 2
Server 1
Server 2
Server 3
X1 = �(T12,2[13,1)X2 = �(T12,2U23,3)
X3 = �(U23,3[13,1)
Decoder[13,1T12,2
DecoderT12,2U23,3
DecoderU23,3[13,1
• Other triple symbols are the same: : = SZ I¢ = (G_£G�)0 = 3
Source: Naderializadeh et al. (2016)
Example: 9 = � = 3,6: = 2,61 = 1
1/960
Idea for the General Case
• With transmitter cooperation and perfect quality CSIT
� interference can be cancelled
• Combining with the caching content
� recover the missing information in cache
Rx 1
. . .
Rx�
Rx 2
6�Server 1:6:
.
.
.
Server 2:6:
Server �:6:
Decoder
algorithm: Naderializadeh et al. (2016)
CSIT
61
Conclusion – Cache Aided IC (one shot)
• The one-shot linear sum-DoF:
�Within a factor of 2 of the one-shot linear-DoF optimal
�Equal contribution of transmitter and receiver caches
� Linear scaling of DoF with network size
�Covers single-stream and multi-server cases.
I¢ = minx�6: + �619 ,�yI¢ = minx�6: + �619 ,�yI E_ , E1 = E_ + E1 ≤ 1I E_ , E1 = E_ + E1 ≤ 1
result: Naderializadeh et al. (2016)62
Interplay between Coded
Caching and Feedback
Understanding the Behavior of two Crucial
Ingredients of Wireless Communications
Coded Caching
under CSI-Feedback Considerations
�1�2��
Rx1
Rx2
Rx�. . .
6
. . .
. . .
66
Library: 9 files
• Explore interplay between feedback and coded caching
• First consider issues relating to feedback timeliness
(synergy)
• Then incorporate feedback quality (tradeoff)
64
Caching and Feedback Timeliness• We introduce two resources
• Coded caching which, by itself, yields gain
� k ≈ k (for larger �)
• �-transmit antennas and delayed CSIT, offering gain
�§¨© ≈ mª«¬ j → (as � increases)*
• Upon combining resources, should we expect
�®¯® ≈ � k + �§¨© → k + = k? ?*Result: Maddah-Ali and Tse (2012)
�1�2��
6
. . .
66
Library: 9 files
.
.
.
Delayed CSIT
65
Main Result
�1 1
log 1E
Under the logarithmic approximation (also large �): E = log 1E ≪ 1EPer-user DoF
I E = 1 − Elog 1E .
Corollary :
NOTE:- : E : R\ → log R\- log is base-e *Result: Zhang and Elia (2015)66
Comparison of Gains (large )
• : (CC+DCSIT) vs. :"" (single-stream, eq. MISO - no DCSIT)
• The main gains appear for smaller values of E67
Typical DoF gain �(k) − �∗(k = )attributed solely to coded caching (dotted line) vs. synergistic gains derived here (large �)
Synergistic DoF Gains
*Result: Zhang and Elia (2015)68
• A synergistic gain from caching and CSIT� k > �³³ k +�´µ¶(k = )• Exceeds the sum of the two individual components
• The gains imply an exponential effect of
coded caching
�A microscopic E = �^· can offer a very
satisfactory
� I = 1Only a factor � from the interference-free (cache-free) optimal I = 1
Synergistic DoF Gains
*Result: Zhang and Elia (2015)69
I(E = �^·) ≈ 1�I(E = �^·) ≈ 1�
High Impact of Coded Caching
Example
• In a MISO BC system with only delayed CSIT, � antennas
and � users:
I∗ E = 0 = R�¸ → 0 (as � increases)
• A DoF of I(E ≈ R¹º) = R» for all �• A DoF of I(E ≈ RRººº) = R¼ for all �• A DoF of I E ≈ 10^¹ > RRS for all �70
CSIT-Aided Amelioration of the
Sub-Packetization Problem
• When the CC per-user DoF gain I· ,is, we needed
• Synergistically, this same DoF gain I· needs only
�½¾/¿À�½¾/¿À Sub-packets
\ = �À\ = �À Sub-packets
71
� I· = RÁ : /Á → �½Â ≈ /»ººExample (large �): I· = RÁ : Then /Á → �½Â ≈ /»ºº
Interplay between Coded Caching and Feedback Quality
(cache-aided MISO BC)
Coded Caching and Feedback Quality
72
Coded Caching and CSIT-type Feedback�1�2��
Rx1
Rx2
Rx�
6
. . .
. . .66
Library: 9 files
. . .
Feedback: ��� ≈ � ⋅ [�ÄÅ�• CSIT is typically delayed and of imperfect-quality
• High-SNR current-CSIT quality exponent
� = − lim'→ÆlogÇ ||�È − �ÉÈ||Slog Ê , Ë ∈ x1, … , �y
� � = 0 means ≈no current feedback, and � = 1 means perfect CSIT
• Here, perfect delayed CSIT is always available
Intuitive Links: Competition
Bigger E More side information
at the receivers
Less
interference
Need
Smaller �
• A higher E implies more common information
� May diminish the utility of feedback which primarily aims to facilitate
the transmission of private information.
�E.g., E = ^R , no need for CSIT to achieve the optimal performance.
74
Intuitive Links: Competition
• Conversely, a higher � can potentially diminish the utility of E� Example. For perfect CSIT (� = 1), the global gains from coded
caching vanish (symmetric MISO BC)
higher � More pronounced
broadcasting
More separated
streams
Less
multicasting
75
• E ≝ G0 = ���������������"�#���� � !"�#�• � ≝ − lim/01→Æ ,-.G/Ì,-. /01 ∈ [0,1]• Duration (rate) :(E, �) (as before)
� High �9� setting, with ; = log �9�• Per-user DoF
I E, � = 1 − E: ∈ [0,1]
Recall Measures of Performance
76
Cache-aided Prospective-hindsight Scheme
.
.
.
desired
undesired
.
.
.
desired
undesired
oR
o
Requests
Í(�, E)phases
Í+1
destination
messages
Residual
Interference
Delayed
CSIT Í + 2destination
messages
MapCaches
Phase Í + 1 Phase Í + 2QMAT method
Adaptive
caching
and folding
Zero
Forcing
Private
messages
In the end - Combining Gains:
• Coded Caching
• QMAT
• Zero Forcing
�, E
INTUITION� ↑⇒ can have more private data ⇒Less to be cached⇒ Caching can be more redundant⇒XORS have higher order⇒ multicast to more users at a time⇒ Skip more phases of QMAT
Un-cached
Private
77
CSIT/Caching Interplay: MISO BC
�� ≈ log H�
I E, � = � + 1 − � log 1E .
Under the logarithmic approximation �� ≈ log H (Exact
for large �)
:(E, �) = 1 − E ⋅ log(1E)� ⋅ log(1/E) + (1 − �)(1 − E)Per-user DoF
I E, � = � + 1 − � 1 − Elog 1E .
Corollary :
Result: Zhang and Elia (2016)78
• Initial DoF boost due to CSIT
• and then a very substantial additional DoF gain due to coded caching**
• Observe synergistic and competing nature
� DoF effect of coded caching reduces with � (proportional to 1 − �)
Intuition: compounded DoF gains (large �)
**Note: DoF gains (for large �), not a result of extra performance
boost directly from D-CSIT (vanishing per-user DoF).79
I∗ E = 0, � → �I∗ E = 0, � → �
I E, � −I∗ E = 0, � → 1 − � 1 − Elog(1E)I E, � −I∗ E = 0, � → 1 − � 1 − Elog(1E) .
:(E, �) :(�Ï)caching E
and CSIT � CSIT quality�Ï?
Example: E = 10^», � large
• Togetthesamerate,therequiredCSITquality:�Ï E, � = � + (1 − �) 1 − E
log 1E = � + 0.11(1 − �)• For example: with E = 10^», then �Ï = 0.2 → � = 0.1
� Small cache size, halved CSIT requirement
cache-aided CSIT reduction
80
Cache-aided Feedback Reductions
kÝÞ = ß^mÝ can achieve the optimal DoF I∗(E = 0, �)associated to a system with delayed CSIT and �-quality current CSIT.
Example (large j)• Assume D-CSIT and�= 1/5. Then EàáR¹Þ =�^¹ = 0.0067 ≈ 1150
I∗ E = 0.0067, � = 0 ≥ I∗(E = 0, � = 1/5)• The optimal I∗(E = 0, � = 1/5),can be achieved by substituting all
current CSIT with DCSIT and coded caching employing E ≈ 1/150.
Using Coded Caching to `Buffer' CSI
81
Caching in More Involved Networks
82
Caching at the Edge
83
Caching at Transmitters
• So far we considered caching at users/receivers
• Deviate, and consider caching at the “Edge” (BS)
�Brings content closer to the users (reduces latency)
�Reduces backhaul load
�Increases MIMO cooperation
84
FemtoCaching
Setting: Golrezaei et al. (2012)
�1 BS delivering content to users
� Introduce helper nodes with caches
�Caches are filled with different whole files
�Content follows a popularity distribution
�Users connect to helpers if their requested file is present
85
Femtocaching
Main Goal:
Reduce the usage of the BS-
UE link
Main Question:
Which files to cache and
where?
Setting: Golrezaei et al. (2012)86
FemtoCachingResults
�If each user is attached to
a single helper, then:
Optimal Solution:
Cache the most
popular content
Setting: Golrezaei et al. (2012)87
FemtoCachingResults
Source: Golrezaei et al. (2012)
� If users could be served by multiple helpers
� Main idea: If 2 or more helper-nodes share 1 or more users, then cache more than just the most popular files� Increase the union of caches of neighboring
helpers
Optimal Caching
Solution:
NP-complete
88
FemtoCaching
�Greedy algorithm is 2 from
optimal in terms of
�Hit probability
�Using the knowledge of user
positions
Main Result (simulation):
4-5 times more users served
simultaneously
Result: Golrezaei et al. (2012)
Result contributed
substantially to the revival
of caching
89
RS-coded Caching at the Edge
• Main BS with all content
• Helper BSs with fraction
of content cached
• Users requesting files
• Users can connect to
multiple helper BSs, and
to the main BS if
necessary
Altman, Avrachenkov, Goseling (2014)
Also Bioglio, Gabry, Land (2015)(image source)90
• N files, each split in D subfiles
• RS code each file: D�D’ subfiles
• Each helper BS gets at least one
element of each codeword
– No overlaps/no content
repetition
• User needs only D (out of D’)
elements of a codeword (RS)
• Look for subfiles in neighboring BS
• The rest from main BS
• Effort – reduce (remaining) amount
of information leaving main BS
• Simulation results as a function of:
– radius of vicinity (more HBSs
per user)
– Cache size (increases D’)
• Increases chance to get file
from HBs
RS-coded Caching at the Edge
91Altman, E., Avrachenkov, K. and Goseling (2014)
Also Bioglio, Gabry, Land (2015)(image source)
• Users are positioned in a grid
• 9 files
• E: fraction of each file pre-cached at each node
• Next day, users can ask for anything
• Variable Tx Radii: with and w/o spatial reuse
• Both decentralized and deterministic cases
Fundamental Limits of Caching in
Wireless D2D Networks
Goal: Delivery of the
requested content
Setting: Ji, Caire, Molisch (2013)92
D2D - No Spatial Reuse Model
• Radius covers the whole network
• One user communicates at a time
• Performance:
Result: Ji, Caire, Molisch (2013)
: E = � 1 − E�E = 1 − EE: E = � 1 − E�E = 1 − EE(order optimal)
93
D2D - Spatial Reuse Model
• Small radius ensures simultaneous transmissions
• Radius is fixed and same for all users
• Users are clustered and exchange content inside
the same cluster
• Radius/memory is big enough to ensure all the
library is available inside a cluster
• Performance
INSIGHT: Multicasting and Spatial
Reuse are competing resources
Result: Ji, Caire, Molisch (2013)
: E = 1 − EE: E = 1 − EE(order optimal)
94
D2D - Placement Schemes
Deterministic Placement Scheme
• A variation of original MN, with �E ⋅ \ subpacketization
• In the case of Spatial Reuse the subpacketization level is reduced compared
to MN
Decentralized Placement Scheme
• Files are encoded through an MDS code
• Ensures, with high probability that all the content exists in the network
• Achieves order optimality
• Is considered more practical
95
Setting: Ji, Caire, Molisch (2013)
Initial Placement with �E = 2D2D – Deterministic Delivery Example
â = 123User 1 Serves 2 & 3
User 3 Serves 1 & 2
User 4 Serves 1 & 2â = 124User 2 Serves 1 & 3
User 2 Serves 1 & 4
User 1 Serves 2 & 4â = 134User 4 Serves 1 & 3
User 3 Serves 1 & 4User 1 Serves 3 & 4â = 234User 4 Serves 2 & 3
User 3 Serves 2 & 4
User 2 Serves 3 & 4
96
General Conclusions
97
Addressed Misconceptions
• Where to install memory
� No need of deploying too many caches due to its costly nature
� Now, much higher gains though. Change of mind?
• The differences between wireless and wired caching
� Caching is an upper layer problem
� Fusion is fascinating, and very powerful
98
Open Problems and Future Directions
• Different measures of performance (beyond rate, capacity, delay, DoF, etc)
– Infuse this approach with network-theoretic considerations!!
• Subpacketization bottleneck
– Perhaps look into coded placement
• Fusing PHY and CC to improve performance and subpacketization
– Need to boost DoF gains for small E– Under subpacketization constraints
– Need to explore new cache-endowed powerful PHY resources
• CC in different network topologies.
– Topologies affect FB, interference, and multicasting capabilities (all connected)
– Currently worst-channel user `brings down’ the rest. Can this be ameliorated?
99
Open Problems and Future Directions
• Caching with secure communications (e.g. https)
– Public key encryption changes files differently at different receivers
• Cost of cache placement
– Mainly have assumed zero-cost placement
– Updating is also an issue (see `Online coded caching’)
• What is the best way to utilize file popularity and user behavior
– Open problem and could be key in unlocking CC for commercial use
• Computational and implementation complexity (subpacketization,
clique-finding, cache-allocation)
100
101
References
Limitations of current communication paradigms::::
• Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update 2014–
2019. White Paper.
• J. Andrews, X. Zhang, G. Durgin, A. Gupta, “Are we approaching the fundamental
limits of wireless network densification?,” ArXiv e-prints, Dec. 2015.
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IEEE Trans. Information Theory, Sep. 2013.
• M. A. Maddah-Ali and D. N. C. Tse, “Completely stale transmitter channel state
information is still very useful,” IEEE Trans. Information Theory, Jul. 2012.
• A. Singh, P. Elia, J. Jaldén, “Achieving a vanishing SNR-gap to exact lattice decoding
at a subexponential complexity,” IEEE Trans. Information Theory, Jun. 2012.
• A. J. Fehske, et al., “The global footprint of mobile communications: The ecological
and economic perspective,” IEEE Communications Magazine, Aug. 2011.
• T. M. Cover and J. A. Thomas, Elements of information theory. John Wiley & Sons,
2012.102
References
Feedback communication theoretic solutions::::
• V.R. Cadambe, S.A. Jafar, “Interference alignment and degrees of freedom of the K-
User interference channel,” IEEE Trans. Information Theory, Aug. 2008.
• J. Chen and P. Elia, “Toward the performance versus feedback tradeoff for the two-
user MISO broadcast channel," IEEE Trans. Information Theory, Dec. 2013.
• J. Chen, P. Elia, and S. Jafar, “On the two-user MISO broadcast channel with alternating
CSIT: A topological perspective,” IEEE Trans. Information Theory, Aug. 2015.
• R. Tandon, S. A. Jafar, S. Shamai, and H. V. Poor, “On the synergistic benefits of
alternating CSIT for the MISO broadcast channel,” IEEE Trans. Information Theory, Jul.
2013.
• C. S. Vaze, S. Karmakar, and M. K. Varanasi, “On the generalized degrees of freedom
region of the MIMO interference channel with no CSIT,” IEEE International Symposium
on Information Theory (ISIT), Aug. 2011.
• J. Chen, S. Yang, A. Ozgur, A. Goldsmith, “Achieving Full DoF in Heterogeneous Parallel
Broadcast Channels with Outdated CSIT”, IEEE Trans. Information Theory,
Sep. 2014
• P. de Kerret, D. Gesbert, J. Zhang and P. Elia, “Optimal sum-DoF of the K-user MISO BC
with current and delayed feedback,” ArXiv e-prints, Apr. 2016103
References
Single-stream Coded caching::::
• M. Maddah-Ali and U. Niesen, “Fundamental limits of caching,” IEEE Trans.
Information Theory, May 2014.
• U. Niesen and M. Maddah-Ali, “Coded caching with non-uniform demands,” in
Computer Communications Workshops (INFOCOM WKSHPS), May 2014.
• M. Maddah-Ali and U. Niesen, “Decentralized caching attains order-optimal
memory-rate tradeoff,” Allerton Conference, Monticello, IL, Oct. 2013 – see also
ArXiv e-prints, 2013.
• K.Wan, D. Tuninetti, and P. Piantanida, “On Caching with More Users than Files”,
ArXiv e-prints, Jan. 2016.
• K. Shanmugam, M. Ji, A. M.Tulino, J. Llorca, and A. G. Dimakis, “Finite length
analysis of caching-aided coded multicasting,” ArXiv e-prints, Aug. 2015.
• Z. Chen, P. Fan, and K.B. Letaief, “Fundamental Limits of Caching: Improved
Bounds For Small Buffer Users”, ArXiv e-prints, Nov. 2015.
• M. Ji, A. M. Tulino, J. Llorca, G. Caire, “Order-Optimal Rate of Caching and Coded
Multicasting with Random Demands”, ArXiv e-prints, Feb. 2015.
• S. Sahraei, M. Gastpar, “Multi-Library Coded Caching”, ArXiv e-prints, Jan. 2016104
References
Single-stream Coded caching::::
• M. Maddah-Ali and U. Niesen, “Fundamental limits of caching,” IEEE Trans.
Information Theory, May 2014.
• M. Mohammadi Amiri, D. Gunduz, “Fundamental Limits of Caching: Improved
Delivery Rate-Cache Capacity Trade-off”, ArXiv e-prints, Apr. 2016.
• R. Pedarsani, M. Ali Maddah-Ali, U. Niesen, “Online Coded Caching”, ArXiv e-prints,
Nov. 2013.
• J. Hachem, N. Karamchandani, S. Diggavi, “Effect of Number of Users in Multi-Level
Coded Caching”, ArXiv e-prints, Apr. 2015
• J. Zhang, X. Lin, X. Wang, “Coded Caching under Arbitrary Popularity Distributions”,
Information Theory and Applications Workshop (ITA), Feb. 2015
• C. Wang, S. Lim, M. Gastpar, “Information-Theoretic Caching: Sequential Coding for
Computing”, ArXiv e-prints, Feb. 2016
• U. Niesen, M. Maddah-Ali, “Coded Caching for Delay-Sensitive Content”, ArXiv e-
prints, Jul. 2014.
• S. Bidokhti, M. Wigger, R. Timo, “Noisy Broadcast Networks with Receiver
Caching”, ArXiv e-prints, May. 2016.105
References
Extensions of Coded Caching in different settings::::
• R. Timo and M. A. Wigger, “Joint cache-channel coding over erasure broadcast
channels,” ArXiv e-prints, May 2015.
• A. Ghorbel, M. Kobayashi, S. Yang, “Cache-Enabled Broadcast Packet Erasure
Channels with State Feedback”, Allerton Conference, Monticello, IL, Oct. 2015.
• N. Karamchandani, U. Niesen, M. Maddah-Ali, S. Diggavi, “Hierarchical Coded
Caching”, ArXiv e-prints, Jun 2014.
• K. Shanmugam, N. Golrezaei, A. G. Dimakis, A. F. Molisch, G. Caire"FemtoCaching:
Wireless video content delivery through distributed caching helpers", ArXiv e-
prints, Sep 2013
• M. Ji, G. Caire, A. F. Molisch, “Fundamental limits of distributed caching in D2D
wireless networks”, ArXiv e-prints, Apr 2013
• Y. Ugur, Z. Awan, A. Sezgin, "Cloud Radio Access Networks With Coded Caching",
ArXiv e-prints Feb 2016
• S. Lim, C. Wang, M. Gastpar, “Information Theoretic Caching: The Multi-User Case”,
ArXiv e-prints Apr 2016
106
References
• V. Bioglio, F. Gabry, I. Land, "Optimizing MDS Codes for Caching at the Edge", ArXiv
e-prints Sep 2015.
• Altman, E., Avrachenkov, K. and Goseling, J. “Distributed storage in the plane”. In
Networking Conference, 2014 IFIP (pp. 1-9). IEEE.
• Avrachenkov, K., Bai, X. and Goseling, J., 2016. “Optimization of Caching Devices
with Geometric Constraints,” arXiv preprint arXiv:1602.03635.
• B. Perabathini, E. Baştuğ, M. Kountouris, M. Debbah, A. Conte, “Caching at the
Edge: a Green Perspective for 5G Networks”, ArXiv e-prints Mar 2015.
• M. Deghel, E. Bastug, M. Assaad, and M. Debbah, “On the benefits of edge caching
for MIMO interference alignment,” in Signal Processing Advances in Wireless
Communications (SPAWC), Jun. 2015.
• A. Liu, V.t K. N. Lau, “Cache-Enabled Opportunistic Cooperative MIMO for Video
Streaming in Wireless Systems”, IEEE Trans. Signal Processing, Jan. 2014.
107
References
Coded Caching with Feedback::::
• S. P. Shariatpanahi, A. S. Motahari, and B. H. Khalaj, “Multi-server coded caching,”
ArXiv e-prints, Aug. 2015.
• A. Liu, V. K. N. Lau, “Mixed-Timescale Precoding and Cache Control in Cached
MIMO Interference Network”, IEEE Trans. Signal Processing, Dec. 2013.
• Maddah-Ali and Niesen, “Cache-Aided Interference Channels”, 2015.
• J. Zhang, F. Engelmann and P. Elia, “Coded caching for reducing CSIT-feedback in
wireless communications,” Allerton Conference, Monticello, IL, Oct. 2015.
• J. Zhang and P. Elia, “Fundamental limits of cache-aided wireless BC: Interplay of
coded-caching and CSIT feedback,” ArXiv e-prints, Nov. 2015.
• J. Zhang and P. Elia, “The synergistic gains of coded caching and delayed feedback,”
ArXiv e-prints, Apr. 2016
• N. Naderializadeh, M. Maddah-Ali and A. Avestimehr, “Fundamental Limits of
Cache-Aided Interference Management”, ArXiv e-prints, Apr. 2015.
• G. Paschos, E. Baştuğ, I. Land, G. Caire, M. Debbah, “Wireless Caching: Technical
Misconceptions and Business Barriers”, ArXiv e-prints, Jan. 2016.
• M. Wigger, R. Timo, S. Shamai (Shitz), “Complete Interference Mitigation Through
Receiver-Caching in Wyner's Networks”, ArXiv e-prints, May. 2016.108
References
Outer bounds of Coded Caching
• H. Ghasemi and A. Ramamoorthy, “Improved lower bounds for coded caching,” ArXiv
e-prints, Jan. 2015.
• R. Timo and M. A. Wigger, “Joint cache-channel coding over erasure broadcast S.
Lim, C. Wang, M. Gastpar, “Information Theoretic Caching: The Multi-User Case”, ArXiv
e-prints Apr. 2016
• K. Wan, D. Tuninetti, P. Piantanida, “On the Optimality of Uncoded Cache Placement”,
ArXiv e-prints, Nov. 2015.
• A. N., N. S. Prem, V. M. Prabhakaran, R. Vaze, “Critical Database Size for Effective
Caching”, ArXiv e-prints, Jan. 2015.
• Q. Yan, X. Tang, Q. Chen, "On the Gap Between Decentralized and Centralized Coded
Caching Schemes," Arxiv May 2016.
109