Network-Coded Relaying in Multiuser Multicast D2D Network

D2D communication trades short-range communication for achieving high communication rate and short communication latency. Relay aided D2D communication can further tackle the problem of intermediate obstacles blocking the communication. In this work, multidevice multicast communication via a layer of parallel relay nodes is considered. Two relaying strategies, respectively, called the conventional relaying (CR) and network-coded relaying (NCR), are proposed. The throughput of these two schemes is analytically derived and evaluated through numerical study.Theoretically, NCR shows advantage over CR in twofold: one is higher throughput and the other is requiring less relay nodes and, hence, consuming less aggregate power. Numerical studies verify the analysis and show that the throughput performance gap between the two schemes increases significantly, actually exponentially with the number of devices.


Introduction
The main idea of D2D communication is to use short-range communication to trade for high rate communication, short delivery latency, and low aggregate consumption power [1][2][3].Sometimes, due to the mobility of devices (devices move out of the communication coverage) or due to the fact that intermediate obstacles are blocking the communication, the communication link may be down intermittently [4].These facts render relay-aided D2D communication necessary.
The full-duplex relay assumption in the above investigations is not practical [26].In practice, if "cheap" relay is adopted, namely, half-duplex relay [27], which cannot transmit and receive simultaneously, the advantage of NC shown in the above investigations may be lost due to the orthogonal transmission nature of the multiple transmitters.
In this paper, we investigate a more general and practical model by considering the scenario where multiple devices exchange information via a layer of intermediate relays, namely, relay-aided D2D multicasting communication.For this model, we propose two relaying protocols based on the physical-layer and NC technique, respectively.Details of each technique are illustrated below.
Physical-Layer Technique.Firstly, for the special case where there is a single relay, the communication stage when all the devices transmit simultaneously can be viewed as multiple access channel (MAC) [28].After this MAC stage, the International Journal of Antennas and Propagation relay broadcasts superimposed signals originating from the devices, and the corresponding channel can be viewed as broadcast channel (BC).In the BC stage, power allocation among all the information streams originating from different devices may degrade the system performance.In addition, due to heavy burden on the single relay, multiple cheap relays cooperately share the burden become a preference.One natural solution is that a lot of parallel relays are deployed between the devices, with each relay serving a single device, respectively, a device, a relay that serves it, and the other destination devices form a multicast single relay network.We call this strategy conventional multicast relaying (CMCR).The most desirable feature of this scheme is the simple operation at each relay.However, since each relay only decodes one device's information while treating the other devices' signals as interference, the performance of CMCR is interference-limited [29].
NC Technique.After the MAC stage, each relay firstly applies NC operation on some information flows originating from different devices and then multicasts the resultant information flow to all the devices.Each device can employ the idea of side information-aided decoding [30].More specifically, each device performs decoding utilizing the message originating from itself.We call this strategy network-coded multicast relaying (NCMCR).The most desirable feature of NCMCR is that the interference can be reduced to some extent, since more devices' signals are decoded at each relay and hence less devices' signals are treated as interference.Besides, this does not involve power allocation among the information streams at each relay node, which also embodies NC's advantage over the physical relaying technique.

System Model
Refer to Figure 1.Consider  devices, denoted as   for  = {1, 2, . . ., } ≜ M, exchanging information over a layer of  parallel relays, denoted as   for  = {1, 2, . . ., } ≜ N. Define device terminal set U ≜ { 1 ,  2 , . . .,   } and relay node set R ≜ { 1 ,  2 , . . .,   }.Device   multicasts information   to the other devices U/{  },  ∈ M. The devices are assumed to be so far away that the wireless link between them can be neglected.We assume that the communication between any pair of devices experiences two hops, that is, through certain relay nodes.Each node in the network is assumed to have one single antenna and operates in half-duplex mode.Node  ∈ U ∪ R is subject to power constraint   .For simplicity, we consider additive white Gaussian noise (AWGN) at the receiver.
The communication between any pair of devices is performed in two time slots.During the first time slot, the devices simultaneously distribute their data while the relays listen.During the second time slot, the relays forward the messages to the devices.
Let   [],   [], and   [] be, respectively, the transmitted symbol from node , the received symbol, and the thermal noise at node , at time , respectively,  ∈ U ∪ R. The first hop's input-output relationship is represented by the following formula: which is subject to For simplicity, we assume that   =  and   [] ∼ CN(0,  2 ) for all  ∈ U∪R.Define signal-to-noise ratio (SNR) Γ ≜ / 2 .The second hop's input-output relationship depends on the selected transmission scheme and is hence detailed in the following sections.Define    and    ,  as the data rate of information flow originating from source   and the data rate of information flows originating from sources   and   , respectively, ,  ∈ U,  ̸ = .
Remark 1.Throughout this paper, we assume that matchedfilter receiver is used; hence, the achievable rate in each hop can be denoted by its capacity, and we let () ≜ log 2 (1 + ).

Proposed Transmission Protocols
For easy understanding, we first consider the special case where there are three devices in Section 3.1.We then generalize the above results to an arbitrary number of devices together with mathematical analysis, that is, to  > 3, in Section 3.2.

Proposed Schemes for Three Devices.
We describe the conventional method, the proposed method, and the refined proposed method, respectively.

Conventional Multicast Relaying (CMCR).
Refer to Figure 2. Relay   adopts decode-and-forward (DF) strategy to relay device   's signal to the other devices,  ∈ {1, 2, 3} ≜ U 3 .In the following, we derive the achievable rate of each device.Note that there are totally two stages of transmission and the achievable rate is the minimum of these two stages.
In the first stage, since relay   only decodes the message originating from device   , the signals originating from other devices' are treated as interference,  ∈ U 3 .In this case, the achievable rate region is which is simplified to In the second stage, device   intends to decode the messages from relays   's for  ∈ U 3 /{}.This stage can be viewed as a two-user MAC by treating the signal from relay   as interference.In this case, the achievable rate region is From ( 5), we obtain that the achievable rate region of the message rate originating from device  in the second stage is Combining ( 4) and ( 6), we obtain that the achievable rate region of each device by CMCR is

Network-Coded Multicast Relaying (NCMCR).
Refer to Figure 3. Device   selects relays   for all  ∈ U 3 \ {} as the intermediate relays to forward its message to the other devices.Relay   performs the following procedures.Firstly, it decodes the messages from devices   for  ∈ U 3 \ {}.Afterwards, it performs exclusive OR (XOR) operation on the decoded information bits.Finally, it encodes the resultant information bits into new codeword and sends the resultant codeword out.We derive the achieved rate region in the following.
In the first stage, relay   needs to decode the signals from devices   's for  ∈ U 3 \{}.This stage can be viewed as a twouser MAC.The achievable rate region is From ( 9), we obtain the achievable rate region of device   in the first stage as ) .
In the second stage, since device   intends to decode the messages from relays   's for  ∈ U 3 \{}, the channel can also International Journal of Antennas and Propagation be viewed as a two-user MAC.The achievable rate region at decoder   is Note that From ( 11) and ( 12), we obtain that the achievable rate region of device   in the second stage is ) .
Combining ( 10) and ( 13), we obtain that the achievable rate region of device   by NCMCR is ) .
3.1.3.Refined NCMCR.Combining ( 8) and ( 14), we can obtain which shows the advantage of NCMCR over CMCR.However, for more than 3 devices, the number of relays needed by intuitively applying NCMCR should be  2  , while CMCR requires only  relays.
In the following, we propose a method based on NCMCR to reduce the number of relays required to be even less than the number of devices.Without loss of generality, we first illustrate the case for  = 3.We remove relay  1 and keep the operations performed on the other relay nodes the same as those described in Section 3.1.2(refer to Figure 4).Obviously, the decoding at device  1 can be made the same as before.Now, let us consider the decoding operation at devices  2 and  3 .Without loss of generality, we consider node  2 only.It intends to decode  1 and  3 .Since  2 is available to  2 and hence can be viewed as side information [31], node  2 first performs XOR operation on  2 with  1 ⊕  2 which is forwarded by relay  2 , obtaining  1 .Afterwards,  2 performs XOR operation again on  1 and  1 ⊕  3 which is forwarded by relay  3 , obtaining  3 .We name this protocol as refined network-coded multicast relaying (RNCMCR).In the following, we derive the achievable rate region of RNCMCR.
In the first stage, consider relay  2 .It needs to decode the message from devices  1 and  2 , respectively.The channel can be viewed as a two-user MAC.The achievable rate region is, therefore, Similarly, for relay  3 in the first stage, we have We then obtain that the achievable rate region of device   in the first stage is ) .
In the second stage, for device  2 , we have We then obtain that the achievable rate region of device   in the second stage is Combining (18) with (20), we obtain that the achievable rate region of device   by RNCMCR is which is the same as (14).It naturally indicates a conjecture that, for  devices,  − 1 relays are enough for RNCMCR without performance penalty with respect to that composed of  2  relays.In the next subsection, we analytically verify this conjecture and compare RNCMCR with CMCR.

Analysis for General Number of Devices.
We first derive the achievable rate region obtained by CMCR and RNCMCR, respectively.We then compare these two schemes.

CMCR.
Following the above derivation steps, we can obtain that the achievable rate region by CMCR for  devices and  relays in each stage is as follows.
By jointly considering these two stages, we obtain where the proof of ( 25) is given in The Appendix.

RNCMCR.
Following the above derivation steps, we can obtain that the achievable rate region by RNCMCR for  devices and  − 1 relays in each stage as follows.
By jointly considering these two stages, we obtain  25) with ( 29), we obtain

Comparison. Comparing (
It reveals the fact that RNCMCR outperforms CMCR twofold.On one hand, it uses less relays and hence needs less aggregate power budget.On the other hand, according to (30), RNCMCR outperforms CMCR in terms of achievable rate.

Numerical Study
In this section, we compare the achievable throughput of different schemes, where throughput is defined as the sum rate of all devices in the network.We set  = 1.
For  = 3, the achievable throughput of NCMCR and CMCR is plotted in Figure 5.We can see that the performance improvement in the high SNR region is around 33%.
In Figure 6, we consider the case where  = 100.We can see that the performance improvement is much more significant than the  = 3 case.
To show the advantage under different number of devices, we plot Figure 7 with the horizontal axis representing the number of devices.We can see that the performance advantage increases linearly with respect to the logarithm of .This indicates that our proposed scheme scales well with the network size (in terms of the number of devices).

Conclusion
The throughput of a D2D communication aided by a multidevice multicast two-hop Gaussian parallel relay network is analyzed.Both conventional relaying (CR) strategy and network-coded relaying (NCR) strategy together with refined version are proposed.Their achievable rates are evaluated theoretically and numerically.Comparison results show that International Journal of Antennas and Propagation  outperforms CR; advantage increases linearly with to the logarithm the number of devices, which that the proposed scheme scales well with the size.