Advances in Wireless Network Coding for IMT-Advanced & Beyond Afif Osseiran∗, Ming Xiao§ , Slimane Ben Slimane§, Mikael Skoglund§ and Jawad Manssour∗ ∗

Ericsson AB, Stockholm, Sweden; § Royal Institute of Technology (KTH), Stockholm, Sweden ∗ {Afif.Osseiran, Jawad.Manssour}@ericsson.com; § {mingx, slimane, [email protected]}

Abstract—In a classical network, data streams originating from a source and intended to a desired destination are routed through intermediate nodes before reaching their final destination. By contrast, Network Coding (NC) manipulates at an intermediate node those data streams by combining the data from the streams before forwarding it to the destination. This paper describes the advances of NC in wireless communication for IMT-Advanced and beyond. A short overview of NC in wireless communications is given first. Afterward, the application of NC to broadcasting is described. Thereafter, NC methods in uplink wireless communications, such as User Grouping (UG) and Relay Selection (RS) are described. Further, the advantage of non-binary over binary network NC is shown in a multi-user multi-relay scenario. Finally the performance of NC is analyzed. In particular, in the uplink Multiple Access Relay Channel (MARC) scenario, the joint UG and RS methods lift the system capacity by 70%. The non-binary NC improves the SNR up to 4 dB. Finally the efficient broadcast method yields up to 22% overhead reduction compared to ARQ.

Keywords: Broadcast, Cooperative Networks, Multiple-Access Relay Channel, Network Coding, Non-Binary Network Coding, User Grouping

I. I NTRODUCTION Modern wireless systems distinguish themselves from their predecessors via the significantly higher bit rates and the stricter quality of service (QoS) constraints in terms of e.g. coverage and delay that they can support. These advances were made possible through, the availability of wider spectrum bands, the utilization of better coding techniques, higher order modulations, multiple antennas, smarter and more efficient receivers and advanced radio resource management schemes. These trends in terms of higher data rates and stricter QoS will be even more aggressive with the international mobile telecommunications-advanced (IMT-A) compatible cellular systems. For instance, bit rates in the order of 1 Gbps for downlink and 300 Mbps for uplink are to be expected. Meanwhile, the research community is already investigating techniques for beyond IMT-A systems that are expected to support bit rate hungry applications such as high-definition TV. With the classical physical layer and radio resource management techniques nearing their theoretical limits, novel techniques and approaches are required to meet the expected performance. Some of the candidate techniques include network coding (NC), cooperative relaying, device-to-device communications, and backhaul-assisted interference management. In this article, we focus on the area of NC and its application to wireless cooperative relaying networks where we present some novel concepts and some selected results. It should be mentioned that

although the publications on NC have been extensive during the last a few years, NC has still to find the way to wireless standards such as LTE-A and IEEE 802.16m. Nonetheless, proposals have been already initiated [1]. The present-day communication networks share the same fundamental principle of operation: the information or packet sent from one source to a destination through a certain router or relay node (RN) is transported independently from other information sent from another source through that same RN. In contrast to those communication networks, NC is a new area of networking, in which data is manipulated at the intermediate RNs inside the network to improve throughput, delay, and/or robustness. In particular, NC allows instead the RN to recombine several input packets into fewer output packets leading to a more efficient utilization of the network’s resources. The concept of NC was first introduced for satellite communication networks in [2] and then fully developed in [3] where initially the term network coding was used. Thereafter the electrical and computer engineering communities took huge interest in it. In particular a plethora of work appeared on the data communication and information theory aspects of network coding for different application scenarios. In this paper, we will summarize the advances of NC in wireless communication for IMT-Advanced and Beyond. More details on the advances of NC in Wireless Communications can be found in [4, Chap. 8]. The paper is structured as follows. A short overview of NC in wireless communications is given in Section II. Afterward, the application of NC to broadcasting is described in Section III. Thereafter, NC methods in uplink wireless communications, such as User Grouping (UG) and Relay Selection (RS) are described in Section IV. Further the advantage of non-binary over binary NC is shown in Section V. Finally a summary and the future directions of NC are given in Section VI. II. N ETWORK C ODING

IN

W IRELESS C OMMUNICATIONS

The NC concept was first adopted by the multicast wireline community, but the concept’s utility quickly reached much further. In fact, due to the broadcast nature of wireless channels, NC is a very promising technique for wireless communication applications with its potential benefits including an improved energy efficiency, a more robust link performance, and an increased system throughput for several wireless topologies in general and cooperative relaying networks in particular [5],

[6]. In fact, the form of network coding is well suited for cooperative wireless networks. This cooperation can be obtained via a relay node within the cell where two or more users can cooperate when communicating with a base station (BS). For instance, consider a simple network model where two user equipments (UEs) transmit on the uplink to the base station (see Fig. 1). Using NC, the cooperative transmission progresses in two phases. In the first phase, each UE transmits its own data on orthogonal channels while the relay receives and decodes the data of both users. In the second phase the relay assists both users with network coding by transmitting the XOR-ed version of information from both UEs. If the orthogonality is achieved through temporal separation, a total of three time slots is needed. If any two of the three transmissions succeed, the BS can still recover the data of both UEs. This network coded cooperation scheme provides a diversity of 2 for each user [6]. For comparison, consider the two UEs using conventional relay-based cooperation without network coding. In this case, four time slots are needed to achieve diversity order of 2. This effectively means a gain of one time slot when network coding is employed. A more detailed performance comparison for the gains obtained from using network coding can be found e.g. in [5], [6], [7]. The above-described scheme for the case of two users and one relay can also be generalized to the case of a cellular network with N users and M relays communicating with the BS. In this scheme, each user still transmits its own data in the first phase on orthogonal channels. In the second phase, a single best relay is selected from the M candidates that maximizes the worst instantaneous channel conditions of links from users to the relay and from the relay to the base station, and broadcasts the XOR-ed version of data received from each user to the BS [8]. With time division, a total of N + 1 time slots are needed with N time slots in the first phase and one time slot in the second phase to broadcast the XOR-ed message for all N users. Intuitively, the multiplexing gain of the system can be improved by increasing N . However, the diversity is limited to 2. This limitation in diversity gain is due to the fact that, although the coded message can be potentially be helpful for any user, it can only help at most one user provided that all the other users data is decoded correctly, no matter what the number of relays is. III. NC FOR B ROADCAST C HANNELS Wireless data broadcast (DB) applications such as multimedia real-time broadcasting are becoming popular since the digital format allows for quality improvements as compared to traditional analogue broadcast. Though currently these applications are mainly used through digital TV, more applications are available in wireless cellular systems (e.g. LTE MBMS). In a typical DB scenario, a BS broadcasts common information to a set of UEs through wireless channels. In DB systems, error control strategies should be introduced to improve the reliability and QoS such as delay. Broadcast transmission from the BS to the set of UEs shown










+








RN BS 

 

Fig. 1.

Two-user one-relay network.

in Fig. 2, where pi is the block-erasure probability of the i-th UE which is designated as Ui . Coding schemes applied across a sequence of broadcast information packets are typically considered for error control. For instance, ARQ [9] is a widely used error control for packet-level transmission. In an ARQ scenario, a retransmission is initiated by any UE with an erased packet. When the number of UEs increases in a broadcast scenario, ARQ becomes increasingly inefficient, both in terms of feedback and retransmissions. To improve the system efficiency, the use of NC [10], [11], [12] during the retransmission phase has been proposed for wireless broadcasting [13], [14], [15], [16]. In most of these schemes, packets lost by different UEs are jointly encoded with a suitable network code, leading to a reduction in the total number of transmitted blocks required for retransmission. In [13], an analytical approach is proposed to determine the improvements in efficiency obtained by Network Coding, while a lower bound on the transmission overhead is developed in [14]. A specific NC scheme for two UEs is further proposed in [14]. Furthermore, in [17] and [16], NC is combined with ARQ and hybrid ARQ schemes for unicast transmission, respectively. In the following, we show how NC can be used in wireless broadcasting. In general, the application of NC leads to higher efficiency than traditional ARQ schemes. The benefits of using NC for broadcasting can be seen from the following simple example. In a broadcast session a set of N information blocks si , i = 1, 2, ..., N has to be broadcast from a BS to a set of M ≥ 2 UEs. Since they are at different locations, the M BS -to-UE block-erasure channels are assumed to be independent with block-erasure probabilities pi , i = 1, 2, ..., M , respectively. To facilitate the analysis, the transmission process is divided into two phases: the information transmission phase and the retransmission phase. In the information transmission phase, the BS broadcasts N information blocks, and during the transmission, some blocks are lost over the respective BS -to-UE block-erasure channels. Each UE feeds back a packet with indices of the erased blocks. Feedback is considered as instantaneous and error-free. A corresponding error matrix E is evaluated at the BS to indicate the block-erasure status of the UEs. The dimension of E is M × N , where ei,j = 1 if

1.5

1.45

BS ARQ 1.4

Scheme in (Xiao et al. 2008) Scheme in (Lu et al. 2010)







1.35

 η



Fig. 2.











A wireless broadcast system with M UEs.

Lower Bound

1.3

1.25

1.2

1.15

the j-th block of Ui is erased; otherwise, ei,j = 0. Assuming M = 2 and N = 6, one snapshot of E can be, for instance,   1 0 0 1 0 1 E= . (1) 0 1 1 0 0 1 Clearly, when traditional ARQ is applied, each individual erased block for any UE will be retransmitted separately. Thus, blocks s1 , s2 , s3 , s4 , and s6 are retransmitted separately, making a total of 5 retransmitted blocks. However, if NC is used, only 3 (encoded) blocks, s1 ⊕ s2 , s3 ⊕ s4 and s6 are needed. Assuming that in the information broadcast period, U1 and U2 have correctly received s2 , s3 , s5 and s1 , s4 , s5 , respectively. Then, both UEs can retrieve, after correctly receiving the retransmissions packets, the respective erased blocks through simple modulo-2 addition. Clearly, transmission efficiency is improved by using even a simple NC scheme. Recently, a more efficient coding scheme was proposed in [18]. In order to measure the system efficiency, a normalized overhead η can be defined as X . (2) N Here X denotes the number of blocks sent from the BS until termination of the broadcast session. The encoding constraint enforced by the column groupings rule simplifies the decoding process and minimizes delay with no loss of throughput performance. A UE retrieves an erased block for each received retransmitted block through a simple modulo-2 addition. ∆

η=

A. Performance The performance of different NC schemes is compared against the performance of traditional ARQ. Specifically, the impact of M on the normalized overhead η is considered. Assume that the links have unequal erasure probabilities. Let p1 , the erasure rate on link 1, is given by p1 > p; and let all other links have identical erasure rate e.g. pi = p for i = 2, 3, ..., M . In Fig. 3, the normalized overhead (given by Equation 2) is shown as a function of M . It can be observed that the proposed scheme by (Lu et al. 2010) in [18] enjoys substantially better performance compared to ARQ. Also, the performance of the proposed scheme in [18] outperforms the scheme of (Xiao et

1.1

3

4

5

6 M

7

8

9

Fig. 3. The impact of M on the normalized overhead η for divers methods. N = 100, p1 = 0.1 and pi = 0.05 for i 6= 1.

al. 2008) [13]. For instance, for M = 5 (resp. M = 9) the overhead in [18] is improved by 13% (resp. 22%). Further, the results of [18] are close to lower bound performance designated by n ˆ , namely, the maximum number of packet erasures among all UEs. IV. U SER G ROUPING

R ELAY S ELECTION FOR U PLINK N ETWORK C ODING

AND

WITH

The scenario where more than one UE try to communication with a common destination via a common relaying node is known in the literature as the multiple access relay channel (MARC). This can be likened to the uplink relay-aided transmission in a cellular system. The majority of the works in the area of NC-based MARC consider a setup of two UEs and a single relay node. However, in an actual system, several UEs are active simultaneously which can be conveniently grouped together. Hence, the first design challenge that one is faced with at a network level is which set of UEs shall be selected and how shall be grouped to perform the network coding operation and cooperation. Obviously a random selection will not achieve the optimal system capacity, and might even lead to losses in some special cases and scenarios when compared to a conventional system not utilizing NC. To illustrate how different sets of UEs can possibly be formed, consider the case where a total of 4 UEs, U1 , . . . , U4 , have data to transmit to the BS and can cooperate via one RN. For simplicity, let us assume that only 2 UEs are allowed to cooperate at a time, then three sets can be formed S1 S2

= =

{G1 ; G2 } = {(U1 , U2 ); (U3 , U4 )} , {G3 ; G4 } = {(U1 , U3 ); (U2 , U4 )} ,

S3

=

{G5 ; G6 } = {(U1 , U4 ); (U2 , U3 )} .

Each set contains 2 groups of 2 UEs each. As an illustration, the set S1 is shown in Fig. 4. One of the works that investigated the performance gains from the application of user grouping for the NC-based MARC is [19] whose contribution is described subsequently. The proposed user grouping algorithm is based on splitting a large

1



0.9

0.8



0.7

BS

 CDF

0.6

0.5

0.4

 

RN



0.3



0.2

NC User Grouping, Pool of 4 UEs

0

Fig. 4.

An example of user grouping for a set of 4 active UEs.

set of active UEs into groups, then perform an exhaustive search within every set to determine the user grouping that satisfies a certain cost function based on the users’ channel conditions towards the RN and the BS. Grouping refers to which associated users the NC operation should be performed on. In [19], the cost function was based on maximizing the sum-capacity of the whole pool of active UEs and the allocation of UEs to pools was done randomly. On the other hand, other alternatives and improvements can be thought of such as minimizing the outage probability of a pool of active UEs and allocating the UEs to pools e.g. based on their average channel conditions towards the BS and/or the RN. To illustrate the effects of user grouping on the performance of NC-based MARC system, the normalized average sumcapacity per cell has been simulated in a multi-cell system and the results are shown in Fig. 5. It is assumed that the NC operates on two UEs at a time (i.e. group size of two UEs). The results show the performance of random pairing (i.e. a group of two UEs) compared User grouping for sets of four and six UEs. One can notice that as the set/pool size increases, a better performance is achieved by user grouping as evidenced by the simulation results. A normalized mean capacity of 1.27 bps/Hz can be achieved for random network coding, as compared to 1.52 bps/Hz for a set/pool of size four, and 1.70 bps/Hz for a pool of size six. That is the equivalent of mean capacity gains of 34% and 16% for pools of size six and four, respectively. Increasing the pool size would still further increase the capacity gains but at the expense of more complexity as the number of possible pairings is proportional to the pool size. Further analysis of the gains and impacts on user grouping from an error performance perspective have been done in [20] which gives recommendations on which UEs to pair thus avoiding an exhaustive search approach. In addition to multi-user diversity, another degree of freedom can be further exploited to enhance the performance of NC-based MARC. As already mentioned, multiple RNs are deployed per cell to assist the different active users in forwarding their data to the BS. However, similar to user grouping, a random or inappropriate selection of a relay to perform the NC operation over might lead to significant performance degradation compared to a system utilizing conventional relaying

Random NC

0.1

NC User Grouping, Pool of 6 UEs

0

1

2

3 Capacity [bps/Hz]

4

5

6

Fig. 5. CDF of the cell capacity of Random NC and NC with user grouping in MARC.

without NC. When applying relay selection in conjunction with network coding, the problem gets even more challenging. This is because the data of both sources to be encoded together should be available at the network coding node. In [21] an opportunistic relay selection algorithm for MARC with network coding based scenario was proposed and studied. The opportunistic algorithm tries to maximize the sum capacity of the cooperating pair of users by selecting the appropriate relay node. The achieved results showed that a network coding based system in the presence of opportunistic relay selection can provide up to 48% gain in the median capacity as opposed to similar systems where the relay selection algorithm only takes one of the users into consideration. However, it is clear that the opportunistic relay selection algorithm can be made more general and efficient by selecting the appropriate relay node and the pair of users that should cooperate via that relay node. In fact, it was observed in [21] that applying a joint user grouping and opportunistic relay selection algorithm can achieve this purpose. V. N ON -B INARY N ETWORK C ODING This section discusses the design of NC for cooperative and relaying networks with the objective to increase the wireless diversity. In general, binary NC can not exploit networks containing inherently a diversity order higher than 2. In addition the XOR operation may not be optimal, in the sense of asymptotic performance for certain network settings. By contrast, non-binary NC, exploit such networks and further improve their performance. Mathematically speaking, in nonbinary NC scenarios, the combining operation of the data streams at the NC nodes, is based on the finite field GF(n), where n is an integer greater than 2. Non-binary network coding has been applied to user and fixed relay cooperative networks. In user cooperation networks [22], the UEs are assumed to help each other by relaying information. The assumption relies heavily on the users’ capabilities to do so. An alternative way would be to use a separate fixed RN to perform the relay and NC

  

+



RN1 BS 



+



RN2 

Fig. 6.

A two-user two-relay wireless network.

are presented. Further we compare binary-based NC and nonbinary-based NC, in terms FER versus SNR. As channel codes, regular (3, 6) Gallager low-density parity-check (LDPC) codes are used for a block length of 400 code bits. It can be seen from the figure, the diversity orders are predicted correctly. Finally as it is shown from the same figure, the non-binary NC compared to binary NC yield a gain of 3.8 dB at a FER of 10−2 . It shall be noted that in the case of cooperative networks, it was shown in [22] that the proposed non-binary method yields a gain of 2.6 dB at a FER of 10−3 . 0

10

−1

10

FER

operation. Then UEs do not have to spend computation and transmission resource to relay partner information. Higher rates and lower complexity are possible for UEs. Further, in IMT-Advanced networks, it is expected that more and more RNs shall be employed to increase the system throughput. Thus it is reasonable to model the beyond IMT-A relaying networks as multi-user multi-relay networks. A schematic of a two-user two-relay network is shown in Fig. 6 to illustrate the idea. In the network the channels among users and relays are orthogonal. In Fig. 6, if the source nodes communicate to the BS both relay nodes will also receive the corresponding codewords from the source nodes. Then, the RNs try to decode, and if the decoding is successful, they can forward the information to the BS with suitable processing, e.g. by applying network coding. In order to illustrate the impact of different network codes on the system performance, the binary and non-binary network coding schemes are compared as follows. The binary-based NC employs a binary network code [7] at both RNs, where both RNs try to decode the received codewords. If the relays can decode the source messages from both users, they XOR the corresponding messages and transmit them to the BS using the same channel code on the physical layer. At the BS the receiver performs MRC of the channel codewords from the two RNs and subsequently decodes the resulting codeword. If a RN cannot decode the message from a source, say, I1 , then it forwards the other message I2 with the same channel codeword as the source U2 . In such a scenario the BS performs MRC for the codewords directly received from the source U2 and from the relay. For non-binary-based NC, linearly independent global encoding kernels (LI-GEKs) at the two relays are used as in Fig. 6. Here, a GEK denotes the linear relation between the network codewords and source messages, i.e., C = G I, where C denotes the network codeword at the relay, G is the GEK, and I = [I1 , I2 ] represent the source messages. For example, in Fig. 6, RN1 has the GEK G1 = [α1 , β1 ] = [1, 1], and RN2 the GEK G2 = [α2 , β2 ] = [1, 2], respectively. It is easy to see that the vectors G1 and G2 are linearly independent in GF(4). Clearly, since the BS receives a codeword directly from each of the two sources, the four different codewords I1 , I2 , I1 + I2 and I1 + 2I2 are available at the BS if perfect Source Relay (SR) channels are assumed. If the RN can only successfully decode one source codeword because of an outage event in one of the SR channels, it re-encodes the corresponding message by using the same channel codeword as the source. At the BS, the two channel codewords of this message are combined via MRC and decoded. In this case GEKs are [1, 0] or [0, 1]. For the binary-based NC the diversity order is D = 2 since the outage probability for both users is proportional to Pe2 . The diversity order is unchanged regardless the one or two RNs are associated with each user. For non-binary-based NC, it can be shown that the outage probability for U1 can be approximated by 6Pe3 . Since the information of each user is transmitted through three independent paths a maximum diversity order of D = 3 is obtained. Clearly, it is higher than that of binarybased NC. In Fig. 7 simulation results of two-user two-relay scenario

−2

10

Binary−NC Non−Binary−NC

−3

10

−4

10

0

2

4

6

8

10 SNR [dB]

12

14

16

18

Fig. 7. Frame Error Rate versus SNR for two-user two-relay networks with network coding.

VI. C ONCLUSIONS Wireless Network Coding is among the most promising techniques for beyond IMT-Advanced. Herein, we gave an overview of the recent advances of NC. We focused on the broadcasting and cooperative network coding. We have shown that an efficient broadcast NC-based can yield up to 22% overhead reducing. For the case of fixed

20

NC Method UG & RS Non-Binary NC Broadcast NC Coded Bidirectional

Gain 70% 3.8 dB 22% 100%

Metric Throughput SNR Overhead Throughput

Ref. Random NC at 10−2 FER ARQ [23, Chap. 11]

TABLE I P ERFORMANCE GAINS OF N ETWORK C ODING M ETHODS RELATIVE A CONVENTIONAL RELAYING SYSTEM

relay nodes, it has been shown that user grouping in the cooperation process and the selection of the relay node are important parameters to consider when designing high data rate systems. The obtained results showed that a joint user grouping and relay node selection can provide capacity gain up to 70% as compared to the case of random user grouping. Finally, it has also been shown that non-binary network coding in a two-relay scenario can provide a diversity order of 3 and a signal-to-noise ratio (SNR) gain up to 4 dB. The relative performance gains of the most promising Network Coding schemes in Wireless Networks are summarized in Table I. These gains are mostly relative to a conventional two-hop relaying scenario. If otherwise, it is mentioned under the reference field (i.e. Ref. ) of Table I. Although the publications on Network Coding have been extensive during the last five years, NC has still to find the way to be adopted in wireless standards such as LTE-A and 802.16m. Moreover, the idea of NC has been applied to areas not mentioned herein such as MIMO [24], Coordinated MultiPoint scenario [25], and more recently, unicast retransmissions [26]. The research community continues to have high interest in the application of NC to wireless communications. The plethora of publications on that topics did not solve all the related challenges. Hence, there are many opportunities which are still unexplored. More specifically, some areas with a high potential for future research are: • To jointly optimize source coding, channel coding and Network Coding. • To optimally use Network Coding for retransmission under a unicast scenario. • To apply Network Coding to a multi-cell context for instance in a CoMP scenario. • To investigate whether the Network Coding operation shall be applied at the signal or bit or symbol level. • To design Resource allocation for Network Coding-based wireless networks. Finally NC can be applied to emerging areas such as cognitive radio and Power/energy efficiency. ACKNOWLEDGEMENT The authors would like to thank Dr. Claes Tidestav from Ericsson for his helpful comments. R EFERENCES [1] Alcatel-Lucent, “Applications of network coding in LTE-A,” in 3GPP Third Generation Partnership Project, Working Group RAN1, meeting 56, ser. R1-090774, Feb. 2009.

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