Interplay between caching, feedback and topology in the wireless broadcast channel

Current PHY-based communication solutions do not successfully scale in large

networks, because as the number of users increases, these solutions cannot

fully separate all users' signals. This problem in turn can gradually leave each

user (i.e., each receiver) with small communication rates, and it comes at a

time when wireless data trac is expected to increase dramatically. Recently

a new type of technology was proposed, in the form of an upper-layer solution,

that relied on caching network-coded data at the receiving devices. The

proposed solution  termed as 'coded caching'  was motivated by the fact

that wireless trac is heavily predictable, and it was based on pre-caching content

from an existing library of many popular les. This promising approach

naturally came with its own limitations though, and the corresponding performance

would still remain limited. These two approaches (advanced PHY-based

techniques, and coded-caching which used caching at the receivers) had been

treated independently; after all, one uses feedback on the PHY layer, the other

uses receiver-side memory on MAC.

With this as a starting point, part of what we show here is that there are

interesting interplays between the two, which can potentially allow for a combination

that bypasses each approach's limitations. More generally, the main

work of this thesis on advanced wireless caching, is about exploring the deep

connections between caching and fundamental primitives of wireless networks,

such as feedback and topology.

The rst part of the work explores the synergistic gains between coded

caching and delayed CSIT feedback (i.e., Channel State Information at the

Transmitters). Here we consider the K-user cache-aided wireless MISO broadcast

channel (BC) with random fading and delayed CSIT, and identify the

optimal cache-aided degrees-of-freedom (DoF) performance within a factor of

4. To achieve this, we propose a new scheme that combines basic codedcaching

with MAT-type schemes, and which eciently exploits the prospectivehindsight

similarities between these two methods. This delivers a powerful

synergy between coded caching and delayed feedback, in the sense that the

total synergistic DoF-gain can be much larger than the sum of the individual

gains from delayed CSIT and from coded caching. The derived performance

interestingly reveals  for the rst time  substantial DoF gains from coded

caching when the (normalized) cache size 

 (fraction of the library stored at each receiving device) is very small. Specically, a microscopic 

  e􀀀G can

come within a factor of G from the interference-free optimal. For example,

storing at each device only a thousandth of what is deemed as 'popular' content

(

  10􀀀3), we approach the interference-free optimal within a factor of

ln(103)  7 (per user DoF of 1=7), for any number of users. This result carries

an additional practical ramication as it reveals how to use coded caching to

essentially buer CSI, thus partially ameliorating the burden of having to acquire

real-time CSIT (considered by many as the main bottleneck in wireless

networks).

The second part of the work explores an interesting interplay (and tradeo

) between caching and current CSIT feedback quality. For the same setting

as before, but now with an additional ability to incorporate imperfect-quality

current CSIT, this part explores the link between feedback-quality and the

size of the caches. This is guided by the intuition that the bigger the caches,

the more side information the receivers have in their caches, the less interference

one needs to handle (because of the side information), and the lesser

the feedback that is potentially needed to steer interference. Conversely, more

feedback may diminish the utility of memory because the better the feedback

is, the more pronounced the broadcast element should be, leading to more

separated streams of information, and thus fewer commonly-heard (not separated)

streams which are the basis of cache-aided multi-casting. This work

provides another new scheme that utilizes current and delayed feedback, to

again come within a factor of at most 4 from optimal. Furthermore we describe

the savings in current CSIT that we can have due to coded caching,

while we also show how much caching can allow us to entirely remove current

CSIT without degrading performance, basically describing the memory cost

for buering CSI.

The third part of the thesis explores feedback-aided coded caching for the

same MISO BC, but with emphasis on very small caches, focusing on the case

where the cumulative cache size is smaller than the library size. Here the work

proposes new schemes that boost the impact of small caches, dealing with the

additional challenge of having some of the library content entirely uncached,

which in turn forces us to dynamically change the caching redundancy to

compensate for this. Our proposed scheme is near-optimal, and this part of

the thesis identies the optimal (small) cache-aided DoF performance within

a factor of 4.

The fourth part of the thesis explores  for the same K-user BC setting

 the connection between coded caching and current-quality CSIT, but now

without delayed CSIT. Here we show how caching, when combined with a ratesplitting

broadcast approach, can improve performance and reduce the need for

CSIT feedback, in the sense that the cache-aided interference-free optimal DoF

performance (directly associated to perfect-CSIT and local-caching gains), can

in fact be achieved with reduced-quality CSIT. These CSIT savings can be

traced back to an inherent relationship between caching, performance, and CSIT; caching improves performance by leveraging multi-casting of common

information, which automatically reduces the need for CSIT, by virtue of the

fact that common information is not a cause of interference. At the same time

though, too much multicasting of common information can be detrimental,

as it does not utilize existing CSIT. For this, we designed simple schemes

that build on the Maddah-Ali and Niesen coded caching scheme, by properly

balancing multicast and broadcast opportunities, and by combing caching with

rate-splitting communication schemes that are specically designed to operate

under imperfect-quality CSIT. The observed achievable CSIT savings here are

more pronounced for smaller libraries and for smaller numbers of users. In

the end, this part allows us to quantify the intuition that, in the presence of

coded-caching, there is no reason to improve CSIT beyond a certain threshold

quality.

The fth part of the thesis explores wireless coded caching from a topological

perspective. The fact that coded caching employs multicasting (i.e.,

communicating a common message to many receiving users at the same time),

causes performance to deteriorate when the links have unequal capacities. Such

uneven topologies, where some users have weaker channels than others, introduce

the problem that any multicast transmission that is meant for at least

one weak user, could conceivably have to be sent at a lower rate, thus 'slowing

down' the rest of the strong users as well. With this as motivation, we explore

coded caching in a SISO BC setting where some users have higher link capacities

than others (all users have the same cache size). Focusing on a binary

and xed topological model where strong links have a xed normalized capacity

1, and where weak links have reduced normalized capacity, we identify

 as a function of the cache size and the topology  the optimal throughput

performance, within a factor of at most 8. The transmission scheme that

achieves this performance, employs a simple form of interference enhancement,

and exploits the property that weak links attenuate interference, thus allowing

for multicasting rates to remain high even when involving weak users. This

approach ameliorates the negative eects of uneven topology in multicasting,

now allowing all users to achieve the optimal performance associated to maximal

capacity, even if the capacity of the weaker users decreases down to a

certain threshold capacity. This leads to the interesting conclusion that for

coded multicasting, the weak users need not bring down the performance of

all users, but on the contrary to a certain extent, the strong users can lift the

performance of the weak users without any penalties on their own performance.

At the end of the thesis we also present a result that does not involve

caching. This part explores the DoF limits of the (two user) SISO X channel

with imperfect-quality CSIT, and it shows that the same DoF-optimal performance

 previously associated to perfect-quality current CSIT  can in

fact be achieved with current CSIT that is of imperfect quality. The work also

shows that the DoF performance previously associated to perfect-quality delayed

CSIT, can in fact be achieved in the presence of imperfect-quality delayed CSIT. These follow from the presented sum-DoF lower bound that bridges the

gap  as a function of the quality of delayed CSIT  between the cases of

having no feedback and having delayed feedback, and then another bound that

bridges the DoF gap  as a function of the quality of current CSIT  between

delayed and perfect current CSIT. The bounds are based on novel precoding

schemes that are presented here and which employ imperfect-quality current

and/or delayed feedback to align interference in space and in time.