2327-4697 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSE.2019.2894033, IEEE
Transactions on Network Science and Engineering
3
channel cases. [25] considered the multi-tier wireless net-
works, which is effective to meet the dramatic traffic growth.
Different from the one tier network, two operators are for
two tiers. The two operators formulate the competitive
caching designs to maximize their own successful transmis-
sion probability. The problem was transformed as a game
which has a unique Nash equilibrium (NE) and was solved
by an iterative algorithm. The results showed converge to a
stationary point.
1.3 Contributions
With the above literature survey, we observe that although
the random caching strategy optimization has been well
studied, there still exist some challenging problems remain-
ing unsolved. The key problem is that all the existing works
simply assumed that only one file or content is requested by
a user. This assumption greatly limits the application area
of existing caching design results. To address this issue, in
this work we consider a more general scenario where the
user can request more than one file. With taking the video
transmission as an example in the IoT network, we consider
using scalable video coding to generate the video files such
that varying levels of user QoS can be satisfied. The main
contributions of this work are summarized as follows:
• Firstly, we propose a content-oriented video applica-
tions with random caching in a multicasting system.
By considering SVC coding, we formulate a random
caching strategy with an aim to satisfying various
levels of user QoS requirements. To this end, we
analyze the possibility of different video file com-
binations at BSs and the corresponding interference
observation at the user ends.
• By using the stochastic geometry theory, we derive
analytical expressions for different levels of user
QoS requirements at high signal-to-noise (SNR). The
asymptotic closed-form STP expressions is also ob-
tained.
• Based on the closed-form STP expressions, the ran-
dom caching strategy is further optimized by find-
ing suitable caching probability of different video
contents to enhance STP performance. We develop a
gradient based iterative algorithm to search the local
optimal solution for the general random caching
strategy optimization problem. The asymptotically
optimal caching strategy based on the asymptotic
closed-form STP expression is obtained with a lower
complexity. Furthermore, the random caching strat-
egy design with unified cache size is investigated
and the analytically optimal solutions is obtained
with KarushKuhnTucker (KKT) conditions.
The rest of the paper is organized as follows. In Section
II, we present the system model. The closed-from STP
expressions are derived in Section III. The random caching
strategy is optimized in Section IV. Numerical simulation
results are provided in Section V. Finally, we conclude the
paper in Section VI.
Notations: E(·) denotes the expectation operator. 0 and I
denote the zero and identity matrices, respectively. The dis-
tribution of a circular symmetric complex Gaussian vector
with mean vector x and covariance matrix Σ is denoted by
CN (x, Σ). R
x×y
denotes the space of real x×y matrices. ||·||
l
denotes l-norm. abs(·) denotes the absolute value.
N
K
!
denotes the combination of K elements from N elements.
min(·) denotes the minimal number in the vector. max(·) de-
notes the maximal number in the vector. N \M denotes the
sets N without the element M. P r[·] denotes the probability.
P r[A|B] denotes the probability of B under the condition
of A.
2 SYSTEM MODEL AND PROBLEM FORMULATION
In this section, we formulate the problem of random cache
strategy in video multicasting scenario with the SVC, which
encodes one video as one base layer and one or more
enhancement layers. For convenience of illustration, we
consider one base layer and one enhancement layer.
2.1 System model
For a video, SVC encodes it as two separate layer files. The
base layer file and the enhancement layer file can be stored
in one BS or two different BSs. When a user requests a video
with high resolution, the files could be transmitted from one
BS which caches both files. Otherwise, the files should be
transmitted from two BSs, each BS caches one layer of the
video. Contrast to the high resolution request, the user with
low resolution request demands only a base layer file. A
BS which has the base layer file could serve the user. We
adopt content-centric serving mechanism in this network.
When a user requests a file, this mechanism finds out all
BSs containing the file firstly and compares the distance
among the BSs and the user. Then the BSs with the shortest
distance to the user are chosen. We discuss the performance
bottleneck of video transmission and optimize the random
cache strategy in a general scenario.
We give an example here to illustrate different response
schemes of BSs when a user requests a video. Figure 1 to
Figure 3 show the same distributions of BSs and users. We
consider only one video in this example. The areas that BSs
serve are divided by voronoi diagram. Figure 1 and Figure
2 indicate that a user requests a high resolution video. In
figure 1, two serving BSs which cache base layer file and
enhancement layer file response the request respectively. In
figure 2, the serving BS which contains both base layer file
and enhancement layer file is chosen. Once the user in the
BS’s serving area requests a high resolution video, the BS
transmits two layer files to the user all together. Figure 3
shows a scenario that the user requests base layer only. The
nearest BS which contains the base layer file response the
request and serve the user.
We consider a large-scale cache-enabled network with
N videos requested by users in our model. The N ,
{1, 2, ..., N} stands for the set of N videos, and n is the index
of videos, n ∈ N . We represent the popularity a
n
in our
model to indicate the possibility that a user requests video
n, 0 ≤ a
n
≤ 1,
P
n∈N
a
n
= 1. Without loss of generality, we
assume that a
1
≥ a
2
≥ ... ≥ a
N
and the a
n
is known in ad-
vance. Since each video is encoded into two different layer
files with SVC scheme, the actual number of total files for