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.

• L. Zheng and D. N. C. Tse, “Communication on the Grassmann manifold: A

geometric approach to the noncoherent multiple-antenna channel," IEEE Trans.

Information Theory, Feb. 2002.

• A. Lozano, R. W. Heath Jr., and J. G. Andrews, “Fundamental limits of cooperation,”

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