Cooperative Network Coding Cooperative Networks Chapter 12: Cooperative Network Coding Authors: H. Rashvand, C. Khirallah, V. Stanković, and L. Stanković Editors: M. S. Obaidat and S. Misra Publisher Wiley

Outline Introduction Network coding (NC) concept Cooperative relaying Cooperation strategies – Performance measure High SNR regime Low SNR regime Cooperation via Network Coding (CNC) Clusters are formed in ac hoc fashion.

Introduction Most dynamic and unstructured networks with distributed sources and destinations are wireless and due to distributed variable interference conditions they suffer from heavy outage and extensive loss of data. Diversity, which is an inherent part of the broadcasting nature of wireless channels, is often used to combat fading effects by increasing the signal-to-noise ratio (SNR) of the received signals. Diversity is achieved using several schemes such as frequency, time, polarization, space, multi-user, cooperative diversity. Diversity comes at the cost of additional complexity to the network routing process and effective node capacity as well as increasing waste of bandwidth resources due to additional overheads, and the need for multiple antennas for spatial diversity (e.g., multiple-input multiple-output MIMO).

Introduction Cooperative communications networks improve the system performance in terms of: reduced power consumption, increased system capacity and greater resilience. For example, physical layer cooperation among wireless nodes or users resemble virtual MIMO → Spatial diversity gain or Rate multiplexing gains.

Network coding (NC) NC is proposed by Ahlswede [1] as an generalised evolution of the simple network routing protocols. NC allows nodes in the network to go beyond the simple forwarding of received messages to further mix (or encode) these messages, at the intermediate nodes, before forwarding them to destination, or decode these messages at destination nodes, NC differs from simple network routing due to the fact that NC aims at whole network optimization rather than individual classes of users or applications being the objective, Unlike traditional use of error control coding in the networks where coding is performed at the edges (end-to-end) to detect and/or correct the errors on individual packets for a given link, NC seeks to combine different diversified routes in a multi-path network routing fashion at the network level for the purpose of better usage of network resources.

Network coding (NC) Figure 12.1 shows a NC example where: Two sources nodes X1 and X2 want to communicate two messages A and B with out-of-range destination nodes Y1 and Y2, via nodes J and K, Sending A and B directly (without NC) will require the use of 4 separate links, X1-Y1, X1-Y2, X2-Y1 and X2-Y2 while, Sending A and B using NC will require one shared link J-K, to transfer NC encoded A+B, and two side links X1-Y1 and X2-Y2, NC for this 2-by-2 nodes setup →1/4 = 25% save in links. Figure 12.1. NC on a 2-by-2 butterfly network[1] (IEEE copyright line ©2010).

Figure 12.3. The three-node relay channel Cooperative relaying The information-theoretic properties of classic three-node relay network, shown in Figure 12.3, with a source (S) that transmits information, a destination (D) that receives information and a relay (R) that both receives and transmits can be traced back to the seminal work of Cover and El Gamal [7]. This work analyses the relaying capacity under an additive white Gaussian noise (AWGN) relayed channel, and comes up with several optimum relaying strategies. In Figure 12.3, hSR, hRD and hSD are the channel coefficients which are modeled as zero-mean, complex Gaussian random variables with variances and , and PR and PS denote the power transmitted by the relay and the source, respectively. Figure 12.3. The three-node relay channel

Cooperative relaying Wireless cooperation involve two phases. The coordination phase - the strategy is to decide on the best source node broadcasting method to adopt for its signals being sent to both destination and relay. The cooperation phase - the decisions to make involves further processes on the overhead signals and the method of forwarding them to the destination. The terminology full-duplex is used for the relay nodes to transmit and receive simultaneously [7] compared to the half-duplex setup [10], [11] where relays cannot transmit and receive simultaneously in the same band, i.e., relays cannot use the same frequency band in Frequency division multiple access (FDMA) and orthogonal frequencies (OFDMA) or the same time-slots in Time division multiple access (TDMA) systems.

Cooperative strategies Cooperative diversity can be performed based on different relaying strategies such as: Amplify and Forward (AF) allows the relay node to amplify the received noisy signal from the source node and then forward it to the destination, simplest relaying strategies with low implementation cost, provides a better performance when the relay is located half the way between the source and destination [14]. Decode and Forward (DF) allows the relay node to decode the received noisy signal from the source node, re-encode it and forward it to the destination, DF outperforms AF when the source-relay channel ensures error-free detection of the received signal at the relay [10], [11], receiver need CSI between source and relay for optimum decoding.

High SNR regime Zheng and Tse [25] show that: the outage capacity for the system is equivalent to the diversity- multiplexing tradeoffs (DMT) in the high SNR. Therefore they propose to use DMT as a performance measure for various MIMO schemes. DMT demonstrate that although it is not possible to achieve full diversity and full multiplexing gains simultaneously but it is possible to use part of available antennas to increase the data rate and then use the remaining antennas to increase the error reliability which indicates tradeoffs between these two gains, For a transmission scheme to achieve a mutual multiplexing gain r and diversity gain d at high SNR, it should be able to send data at rate R (SNR) and an average error probability Pe (SNR), where both are functions of channel SNR and satisfy: (12.11) (12.10)

three-node relay channel [25] (IEEE copyright line ©2010). High SNR regime The optimal tradeoff curve for any scheme operating in Rayleigh fading channels, and with fading block length l exceeding the total number of transmit antennas MT and the receive antennas MR (l ≥ MT + MR-1), becomes a piecewise linear function connecting the points (r, doptimal (r)). doptimal (r) is defined as the best achievable diversity gain at data rate r, where: Figure 12.4 shows MIMO scheme with MT = MR = 6. (12.12) (12.13) Figure 12.4. The optimal diversity multiplexing tradeoffs curve doptimal(r) for the general number of m = MT, n = MR and MR (l ≥ MT + MR-1). three-node relay channel [25] (IEEE copyright line ©2010).

Low SNR regime Assumptions used during the calculation of the upper bound for high SNR channel conditions (e.g., DMT curves) are not valid for applications such as wireless sensor networks that operate within limited bandwidth and energy resources, hence, cooperation strategies that can ensure efficient energy transfer, through fading networks under low SNR channel condition, are needed, Avestimehr and Tse [19] show that in a simple point to point network, operating at low SNR and low outage probability the loss in the achieved capacity given as a ratio between the outage capacity and the AWGN capacity CAWGN, is significantly higher than that observed at high SNR with , as shown in Figure 12.8, On solution to improve the outage capacity at low SNR is to employ diversity. Figure 12.9 shows that the outage capacity (CI), of a network operating in low SNR channels, can be reduced by a factor of , where L is diversity order, and this improvement is higher at low outage probability.

[19] (IEEE copyright line ©2010). Low SNR regime Figure 12.8. The loss in the outage capacity in the fading channel to AWGN capacity under Rayleigh fading, for = 0.1 and = 0.01 [19] (IEEE copyright line ©2010). Figure 12.9. Improvement in the outage capacity (CI) as a function of the diversity order L under Rayleigh fading for different outage probability = 1, 5, 8, and 10%.

Cooperation via Network Coding Network coding protocols Packet level NC, Physical Layer NC (PNC), Analog NC (ANC) Cooperative network coding (CNC) Network spread coding (NSC) Network coding and diversity (NCD)

Packet level NC Existing packet-level NC designs offer limited features for the current classic signal processing capabilities due to: increased complexity and cost of encoding and decoding nodes, which present a major obstacle for NC applications such as wireless sensor networks, where, NC is probably needed most to reduce the number of transmissions and preserve the scarce energy supply, wireless networks are broadcast channels in nature, where, a signal transmitted by one node may reach several other nodes at the same time, and a destination node may receive signals from multiple nodes simultaneously, that can result in excessive interference and therefore reduction in overall network throughput,

Physical layer NC (PNC) and Analog NC (ANC) Physical –NC (PNC) can make use of additive nature of the wireless channels to seek higher capacity than the packet-level NC [2], however, strict synchronization conditions of the PNC limits its use in practical wireless networks, where signals suffer from variable delays. ANC from Katti et al. [3], exploits signal interference at the intermediate nodes to increase throughput, whilst relaxing the condition of synchronization between the mixed signals, however, ANC scheme outperforms packet-level NC, when a high SNR is assumed with no fading in the communication channel, and the mixed signals have similar power levels. Otherwise, severe degradation in performance can be experienced.

Physical-Layer Wireless Network Coding User 1 User 2 A B A+B Exploit broadcast nature of the wireless link to reduce the required bandwidth Information from each user are combined on the signal level Problem: low noise and no fading assumed and power levels of the two signals must be the same

Cooperative Network coding (CNC) Xiao et al. study the complex case of combining cooperative strategies with NC and error control codes [6] introducing the concept of cooperative network coding (CNC) as a way to address inefficient resource usage of a network. In their proposed scheme the transmitting nodes perform some algebraic superposition of locally generated information prior to that of the partners encoded using a convolutional code generator matrix. This system outperforms classic cooperative strategies for its time sharing and simple message superposition, e.g., using simple XOR operation for locally generated and relayed bits. With the channel coding involved, however, this scheme comes at the expense of increased complexity.

Cooperative Network coding Yu, et al. combine NC with cooperative communication to reduce overall inter-user interference [5]. This improvement is achieved by increasing the diversity gain in multiuser fading channels compared to the traditional time-sharing relaying strategies. For this they consider a scheme that each relay transmits codewords that contain three parts: Its own message Parts of its partner’s previously transmitted codeword (parity bits) or codewords Parity bits generated from joint encoding of the two parts.

Network Spread coding (NSC) In [4], authors proposed the use of the network spread coding (NSC) scheme as a novel PNC based on spread spectrum using the mutually orthogonal complete complementary (CC) sequences [47]. NSC allows transmitted signals from different nodes to: mix in the shared channel→ virtual network coding, combats the effects of interference and noise → spread spectrum NSC uses the linearly independent CC sequences to generate local and global encoding vectors [38] that maintain their orthogonality over asynchronous communications, high interference, and adverse channel conditions, Similar to ANC [3], signal-mixing occurs within a channel at the physical layer. However, in contrast to ANC and PNC [2], the proposed NSC scheme can operate at different SNR levels and under high level of interference caused by the de-synchronization mixing of signals in mobile fading channels.

Spread Spectrum User 1 User 2 A B Expand the bandwidth to enable multiple access and reduce interference, fading and noise effects

NSC- F and NSC-DSF The proposed NSC scheme can use two operation modes, at intermediate nodes to facilitate various complexity/cost/performance trade-offs: the low-complexity ‘forward’ mode (NSC-F) where each intermediate node simply forwards the received mixed signal to its destination without further processing, the more error-robust ‘despread-spread-forward’ mode (NSC-DSF) where each intermediate node despreads the incoming mixed signals to recover the transmitted signals and then re-spreads and forwards them to their destination nodes. The proposed NSC system brings together NC and spread spectrum techniques, exploiting the advantages of both, i.e., bandwidth efficiency of NC and interference and noise robustness of spread spectrum.

Network Spread coding (NSC) Figure 12.11(a)-(c) shows a single-session multicast wireless network with 2-source nodes sending signals to 2-destination nodes through one intermediate node (relay) using the: the general NC scheme [1], which can be either packet-level NC or PNC, shown in Figure 12.11(a), the traditional spreading scheme using CC sequences but without NC, shown in Figure 12.11(b) and, the proposed NSC scheme in Figure 12.11(c). Figure 12.11. The example of the standard Butterfly-like wireless network: (a) a general NC [1]; (b) a traditional spreading scheme without NC; (c) the single-session multicast NSC (NC + CC).

Network coding and diversity (NCD) Ding et al. [49] studied the extension of the PNC to the multipath fading channels, in which pass-loss and phase-shift hinders the PNC usage, and proposed combining network coding and diversity (NCD), shown in Figure 12.13. The NCD scheme is performed in two steps: In the 1st step, the nodes broadcast their messages, with no relaying at this stage, then the NCD requests the help of the upper medium access layer (MAC) to sort the available relays according to their local channels qualities. This ensures better PNC performance. In the 2nd step, then chosen best relay employs AF strategy and broadcasts the mixture. [49] provides detailed simulation results comparing the outage capacity and ergodic capacity of the proposed NCD, conventional PNC scheme, and the direct transmission. Figure 12.13. A diagram of the proposed NCD transmission strategy [49] (IEEE copyright line ©2010).

Network coding and diversity (NCD) Figure 12.14 (a) and (b) shows the outage capacity of the three transmission schemes at different SNR (10 and 20dB), where the proposed NCD achieves larger outage and ergodic capacities than those of the conventional PNC in the high SNR channel condition. (a) SNR = 10dB (b) SNR = 20dB Figure 12.11. Mutual information complementary cumulative distribution functions for (a) SNR=10dB, and (b) SNR = 20dB. The distance of the two sources is 2m. Solid line represents the results obtained by using the Monte-Carlo simulations, and the dotted line represents the results calculated by using the proposed analytical formulations [49] (IEEE copyright line©2008).