This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
Network Coding for Bit Error Recovery in IEEE 802.11 Mesh Networks Mathias Kurth , Ulf Hermann† , Anatolij Zubow and Jens-Peter Redlich
Humboldt University, Berlin, Germany {kurth, zubow, jpr}@informatik.hu-berlin.de, †
[email protected]
Abstract—Opportunistic routing (OR) relies on links of intermediate quality, i.e. packet losses are common. However, the reasons for packet losses are manifold, e.g. a received packet may contain corrupted bits. According to traditional approaches, the receiver discards the whole frame in such a case. In this paper, we present measurements from an indoor IEEE 802.11 wireless mesh network (WMN), which indicate that corrupted frames still contain a significant amount of correct data, which can be utilized. In particular, corrupted frames are common for intermediate quality links. Bit errors tend to occur in proximity, i.e. they are bursty. Furthermore, bit errors are uncorrelated across different receivers in most cases. Based on our observations, we propose a HARQ scheme for OR called Hybrid ARQ with Limited Fragmentation (HALF). It operates on a hop-by-hop manner and requires only local knowledge. Due to the bursty nature of bit errors, we are dividing frames into fragments with additional error detection. Using random linear network codes, the sender transmits incremental redundancy until one of its receivers is able to decode all fragments and therefore sends an acknowledgement packet. However, the partial information at all other receivers is not lost. Instead, to increase the throughput further, it is also used in subsequent forwarding rounds along the multi-hop route. We implemented a prototype of our protocol to evaluate its performance. With the help of detailed simulations, we analyzed the reasons why HALF significantly outperforms traditional approaches like DSR.
I. I NTRODUCTION In contrast to fixed networks, fading and undesired interference are well-known problems in WMNs. They cause higher error rates and make efficient communication difficult. Thus, error control is crucial in such networks. In today’s communication systems like IEEE 802.11 [1], error control resides on the physical and data link layer, respectively. The physical layer employs Forward Error Correction (FEC), i.e. the sender adds redundancy to the data packet to allow the receiver to correct errors. In particular, a convolutional code is used in IEEE 802.11g. However, to guarantee an almost errorfree transmission using FEC alone would result in large underprovisioning and a poor utilization of the wireless channel, when taking aspects like fading and interference into account. Different from FEC, Automatic Repeat-Request (ARQ) protocols apply redundancy for error detection, which is evaluated at the receiver to request repeated transmissions. IEEE 802.11 specifies a stop-and-wait ARQ protocol. On the other hand, OR [2] introduces a link layer primitive called anycast. A transmission is considered successful if at least one candidate successfully receives the packet. OR improves the efficiency of wireless transmissions. However,
it still requires that the whole frame is correctly received. In OR, we have lots of receivers, and extracting correctly received information from corrupted frames across those receivers may allow recovering from errors. Based on these observations, we propose a hybrid ARQ (HARQ) scheme, which combines incremental redundancy and multi-user diversity in OR. Our main contributions are as follows. At first, we characterize the bit error process using measurements in an IEEE 802.11 indoor WMN, indicating that a) corrupt frames are common on intermediate quality links, b) the bit error process tends to be bursty, and c) in most cases, bit errors are uncorrelated across receivers. Thereafter, we propose an error recovery scheme called Hybrid ARQ with Limited Fragmentation (HALF), which couples HARQ and OR. We present our prototype based on the Click Modular Router framework as well as simulation results. The results demonstrate the effectiveness of our approach in terms of throughput. II. B IT-E RROR M EASUREMENTS FROM AN IEEE 802.11 I NDOOR T ESTBED We performed measurements in our indoor testbed of the Berlin RoofNet [3]. The mesh nodes were Netgear WGT634u routers with an Atheros AR5213a-based 802.11b/g WiFi card. We used 18 nodes, which we placed on four different floors of our institute’s building. There have been many other IEEE 802.11b/g access points present, which were not under our control. Note that the density of wireless networks grows especially in urban areas, and it is common that different networks operate simultaneously in overlapping regions. Hence, our setup captures the increasingly important effects resulting from the dense and unplanned deployment. A sender broadcasts 1492-byte link probe packets in slightly jittered intervals of 42ms on all available bit rates. All remaining testbed nodes passively receive all incoming frames. Each individual broadcast experiment took about 5 hours. We repeated the experiment about 10 times using different sender nodes. We will not present any OFDM results due to the activated Ambient Noise Immunity (ANI) feature [4], which we were not aware of at that time. In order to track corrupted frames, we used a modified version of the MadWiFi driver [5]. We classify arrived packets into three categories - erroneous, corrupted and correct packets. With erroneous packets, a physical error occurred during the reception of the frame including PLCP preamble and header errors. Since we have to cope with lots of competing
978-1-4244-3435-0/09/$25.00 ©2009 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
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traffic from foreign WiFi nodes, we have to identify incoming frames, which is not possible for frames with missing PSDU. Thus, erroneous packets only include frames, which we can doubtlessly identify as our measurement packets. Corrupted packets were correctly received by the PHY layer, however, with a bogus checksum (CRC). Correct packets were received with a correct CRC. Due to space limitations, we focus on one particular measurement run. However, we validated that our conclusions also apply to the other measurements. A. Erroneous and Corrupted Packets Are Common Fig. 1 depicts the results of the broadcast experiment. It is obvious that bit errors do not affect the class of high quality links. On the other hand, we encounter a considerable amount of erroneous and corrupted packets on links of intermediate quality, whereas corrupted packets are more frequent. For example, 42% of the packets received by node 34 at 1 Mbps are correct. However, it has actually received additional 34% of all packets, but they contain errors of some kind. When increasing the bit rate to 2 Mbps, the number of correctly received packets decreases. However, the number of corrupted packets increases, indicating that previously correct packets turn into corrupt ones. In sum, the number of arrived packets decreases with increasing bit rate. Using IEEE 802.11b, corrupted packets are common for all bit rates on intermediate quality links, even for the lowest bit rate of 1 Mbps. In contrast, erroneous packets are more frequent on lower bit rates. This is an indication that interference with other packets causes physical errors. Erroneous packets are often truncated. In particular, we observed that the truncation positions show a good match to a uniform distribution, especially on lower bit rates. Interestingly, the links to node 44 and 31 exhibit only a small amount of corrupt packets, but they suffer from erroneous packets. We believe that interference from hidden nodes is a key factor in the operation of these links. However, frame truncation is another source of burstiness.
Fig. 2. Empirical bit-error probability at node 34 conditional on an error having occurred k bits earlier.
In order to assess the value of correct data in corrupted frames, we are interested in the amount of data that would be usable if we were able to extract correct sections up to a minimal length. The normalized cumulated run-length fre quency product is defined as ri >=r n−1 ri P (R = ri ), i.e. the product of run-length ri and empirical occurrence probability P , summed over all run-lengths larger than the minimum threshold r. The factor n = rmax P (R = rmax ) normalizes the product to 1 for correct frames with rmax = 12280. The runlength frequency product can be interpreted as the expected amount of correct data when extracting correct sections up to a minimal section length. Fig. 3(a) depicts the run-length frequency product for node 34. For minimal run-length of 6140 (3070, 1535, 767) bits, which correspond to 1/2 (1/4, 1/8, 1/16) of a frame, the usable data increases to 134% (149%, 156%, 160%) of the arrived data in completely correct frames at 1 Mbps. The same observation holds for other links of intermediate quality (see Fig. 3(b)). Even the higher quality links to node 32 and 44 provide the potential to increase the amount of usable data by up to 10%. On the other hand, the amount of extractable and therefore usable data remains small for node 41 at all available bit rates. We suggest that this link is rather noise-limited than interference-limited. C. Bit Errors Are Only Weakly Correlated across Intermediate Quality Links The bit errors correlation across several receiver pairs is depicted in Fig. 4. We left out the results for nodes 24, 71 and 70, because they are comparable to node 72. On links of intermediate quality, the correlation is below 0.1 in almost all cases, which indicates that bit errors are almost uncorrelated. One exception is the correlation between receiver nodes 23 and 34 with a correlation coefficient of about 0.4. However,
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
possibility to evaluate the protocol under realistic conditions. However, this comes at the expense of moving the algorithms to higher layers. In particular, we are targeting the Berlin RoofNet [3] as platform for our prototype. It offers an IEEE 802.11g [1] physical layer, for which most of the physical layer parameters and routines are fixed and cannot be changed. In the design process, we have identified four key questions which we will answer the following paragraphs.
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both nodes reside in the same room with a separation of only about 10 cm. The same holds for node pairs 31-44 and 29-72. Hence, we suppose that close physical proximity causes higher bit error correlations, as it is as we already showed the case with frame reception [7]. On the other hand, a comparably tight spacing will be unlikely in real WMN deployments.
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We partition frames into smaller fixed-sized fragments and append a CRC sequence at the end of each fragment for error detection. If some fragments arrive corrupted, the source simply provides incremental redundancy. Note that the efficiency of the fragmentation scheme strongly depends on bit error distribution within a frame. Fortunately, we know from our measurements that bit errors are bursty, which justifies the design decision. Ideally, we would like to implement a new link layer primitive for the proposed scheme, which is, however, not possible with today’s hardware. Hence, as a compromise, we group several source frames into batches. A batch in the proposed protocol corresponds to a frame in a traditional unicast transmission. Note that the efficiency of OR strongly depends on the correlation of bit errors across receivers. Referring back to the previous section, we have observed low correlations in typical WMN settings. Hence, the prospective opportunistic gain is high. The fragments of a batch are linearly combined using random linear network codes. Thus, there is no need to identify individual fragments for retransmission due to the innovation property of network codes. Note that batch processing is a technical constraint and far from being optimal. However, it should be an acceptable tradeoff for realizing this scheme with real hardware.
Correlation coefficient for bit errors across all node pairs (1 Mbps).
Nodes on the third floor (31, 44, 29, 72 and also the not shown 71, 70, 24) exhibit higher bit error correlation with each other. In addition, the sender node 60 is also on the third floor. On the one hand, the propagation conditions within a single and across multiple floors may be different. On the other hand, all links on that floor are of high quality; hence, problems on the transmitter side will cause a higher bias. III. H YBRID ARQ WITH L IMITED F RAGMENTATION In the first place, HALF is proof of concept to highlight the benefits of HARQ and OR in combination. It aims at increasing the network throughput for elastic and long-lived traffic, e.g. the transfer of files via FTP. OR protocols often require modifications in the MAC layer, and even worse, HARQ has to be realized hand-in-hand with the channel coding on the physical layer. Today’s hardware like IEEE 802.11 permits only marginal modifications to both layers, if at all. We constrain our design in a way that it should be realizable with today’s hardware. In this way, we preserve the
B. How to control the exchange of incremental redundancy along a link? The batch processing has further implications: Feedback from candidates is less frequent, since a batch generally consists of several frames. Only when a candidate received sufficient fragments to decode the batch, it sends an acknowledgement (STOP) for the batch back to the sender. A sender keeps transmitting in a bursty fashion until the final STOP arrives (see Fig. 5). Now the benefits of network codes are evident. There is no need to feedback which portions of a batch are corrupted, since it is sufficient to receive a fixed amount of innovative fragments in order to decode the batch. The batch processing has another disadvantage. The frequency of STOP feedback is low, but it is important that the STOP packet is transmitted as soon as possible, because it prevents the source from transmitting non-innovative information. Furthermore, it should be reliable for the same reason. We use the IEEE 802.11 unicast mode to achieve this goal. Furthermore, a receiver may use IEEE 802.11e to prioritize STOP frames; however, this is left out for future work.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
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The extension of this scheme to the anycast transmission and OR is straightforward. The sender transmits the batch to multiple destinations using layer-2 broadcast transmissions. If a candidate has received sufficient innovative fragments to decode the batch, it acknowledges the whole batch using a STOP-packet. Now, the complete batch is available at one candidate, and in parts at the remaining candidates. However, the partial information at the remaining receivers is not lost. Instead, it is reused in multi-hop forwarding, as we will cover in the next section. C. How to coordinate forwarding along a route? With HALF, a batch propagates in the same way as a single packet in traditional single-path routing. However, a batch may consist of several frames at the MAC layer, which may take different routes through the network. For the initial prototype, we limit our scope to the case where the whole batch uses a single path, i.e. the splitting of batches along multi-path routes is left for future work. Hence, the route of a batch defines an ordering: for a node on the route, all previous nodes on the route are upstream nodes, and all following nodes are downstream. A route in HALF differs from traditional single-path routes, because a packet may opportunistically skip some hops towards the destination. We only demand that neighboring nodes on the route must be able to communicate directly with each other, because we have to exchange control packets along the reversed route. The construction of routes is out of scope; however, several efficient protocols exist [8]. For the sake of simplicity, HALF uses source routes in a way similar to DSR [9]. Although a single route seems to be a severe limitation, related approaches formulate similar constraints [8], [10]. In addition, note that the batch size is typically much smaller with HALF, and routes may change across batches. A single packet is no further divisible in traditional routing; thus, there is no doubt which node forwards next. With batch processing, several fragments of a batch may reside on different nodes; hence, there may be multiple innovative transmitters. On a route, every node falls within one of three categories. Either the node has not received any fragment of a
batch (i.e. it has no knowledge of the batch), or it has received some fragments without being able to decode the batch (partial knowledge), or, eventually, it is able to decode the batch (full knowledge). A node with partial knowledge is able to produce innovative fragments as long as it possesses fragments, which are unknown to its downstream nodes. However, the innovation property of network codes does not apply in general, and communication is necessary to prevent the creation of noninnovative fragments. Note that this problem also occurs with Multipath Code Casting [10], in the case the forwarders with partial knowledge drain their transmission credits too fast. On the other hand, the innovation property holds for nodes with full knowledge, if there are nodes without full knowledge in the downstream. For the initial prototype, only the full knowledge node closest to the destination (according to the route) transmits. The operation is illustrated in Fig. 5. Packets arrive exogenously at node 1. Hence, only node 1 has full knowledge, and it transmits the batch in Fig. 5(a). Eventually node 2 has received enough innovative fragments, and it sends the STOP packet to node 1 in Fig. 5(b). In particular, nodes with partial knowledge forward the STOP message upstream until it reaches the first node with full knowledge. In addition, node 2 starts to forward the batch. At that time, nodes 3 and 4 have already partial knowledge, since they have received some fragments of the batch. Thus, node 2 transmits fewer fragments on expectation until node 3 gets full knowledge. On receiving the STOP in Fig. 5(c), node 2 sends a START to its upstream node to indicate that the former batch is completed, and it is able to process the next batch. In this way, only a single batch can be active per node, and nodes process batches in order. The START packet is a basic means of congestion control, since it limits the amount of packets, which a traffic source may inject into the network. IV. E VALUATION We evaluated the performance of HALF in a refined JiST/SWANS packet simulator [11]. Most importantly, we used a more realistic, SINR based physical layer comparable to ns 3, and we added support for the Click Modular Router. Furthermore, it allocates bit errors according to one of three models. With the none model, corrupted frames are discarded as usual. In contrast, the uniform model uses a uniform distribution of bit errors depending on the physical layers’ bit error rate. The bursty and uniform models are similar, except that all bursty errors are concentrated at a single position in a frame chosen with equal probability. In particular, the packet error rate remains unaffected from bit error allocation. For the operation of HALF, uniform and bursty are pessimistic and optimistic bounds, respectively, and the real world is expected to fall in-between. The simulation scenario consists of 25 stationary nodes arranged in a grid of 5 by 5, 37.5 m apart. At the border of the grid, either one or three traffic sources generate saturating UDP traffic for 10 seconds, which is forwarded to sink(s) at the opposite side of the grid. From the results, we present the
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
Value Log-distance (α = 2.8) Additive noise BER Rician (Punnoose, K = 6, v = 16) none, uniform, bursty IEEE 802.11g Mode 3 (−77 dBm) Message-in-message (10 dB) −92.965 dBm 6/54 Mbps 19/15 dBm 5.4/20.6 dB (10% PER, 1000 octets) 12224/144 bits
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forwarding. As indicated by the lighter shaded bars in Fig. 6, the gain of the opportunistic effect with scheduling is about 13%. In combination with scheduling and coding on uniformly distributed errors, the gain is slightly higher with about 14%. However, with bursty bit errors, the combination of OR with coding and scheduling achieves the best result with an average throughput of about 5700 packets. Although each isolated effect improves the performance in terms of multihop throughput, the combination of them together with bursty errors delivers additional gains. 8000 7000
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HALF outperforms DSR due to three complementary effects, which we will discuss in the following. To start with, the leftmost bar in Fig. 6 corresponds to the throughput of the vanilla Berlin RoofNet DSR [3] with ETX link metric. The scheduling effect denotes the fact that the queue sizes are coordinated between nodes via the START and STOP packets, which prevents wasteful queue overflows at intermediate nodes. Operating HALF with both 1 fragment per batch and packet without opportunistic reception effectively eliminates all effects except scheduling. In Fig. 6, scheduling slightly increases the throughput compared to DSR. However, this estimate is conservative in this configuration for the following reasons. Every data packet causes an additional unicast STOP and START packet. The 802.11 MAC penalizes unicast in favor of broadcast frames. To increase the probability that a receiver gets medium access to send a STOP, the sender introduces small delays at the estimated end of a batch. Consequently, smaller batches result in more delays; hence, this HALF configuration is far from being optimal. Interestingly, when using HALF the standard deviation of the number of received packets decreases due to more persistence in route selection and fewer route errors. In Fig. 6, increasing the batch size to 16 almost doubles the throughput with HALF. In this configuration, the larger batch size reduces overhead due to delays, START and STOP packets. Furthermore, delayed and lost STOP packets cause less non-innovative transmissions. The coding (or incremental redundancy) effect is present in the two rightmost configurations in Fig. 6. Now, each of the 16 packets in a batch is coarsely split into 2 fragments. With uniform bit error distribution, there is a small increase in throughput by about 150 packets. On the other hand, with bursty errors the throughput increases visibly by 19% compared to scheduling only. In the presented results so far, the packets are forwarded along a single-path route. Finally, we investigate the opportunistic effect by allowing opportunistic reception and
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Fig. 7 depicts the influence of batch size and packet fragmentation on the multi-hop throughput. For both parameters, there is a tradeoff between coding opportunities and the above mentioned overhead. Note that there is no coding with only one fragment per batch. The batch size determines the size of the coefficient matrix, which further contributes to the overall overhead. In addition, the tradeoff is affected by the distribution of bit errors, e.g. making the 32/2 and the 128/8 configurations superior for uniform and bursty errors, respectively. Note that the number of packets per batch is 16 in both cases. V. R ELATED W ORK Several link and bit-level measurements in wireless networks were carried out. For instance, Aguayo et al. [12] observed that the majority of links in an urban outdoor IEEE 802.11b network have intermediate quality, i.e. packet errors of wireless links are common. In addition, Willig et
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
al. [13] present measurements of IEEE 802.11b in an industrial environment. In particular, they target an environment with lots of mobility, and they eliminated all external interference. Their results indicate that both packet losses and bit errors occur in bursts. Dubois-Ferriere et al. [6] observed bursty error patterns in combination with high BER during their indoor measurements with a narrowband sensor network. Furthermore, Miu et al. [14] experienced bursts of bit errors in IEEE 802.11a at the scale of up to 100 bits. Additionally, they observe that packet losses at different receivers are independent. We showed that the latter does not hold for spatially close receivers [7]. HARQ combines channel coding with ARQ. It employs the principle of incremental redundancy: Only in bad channel conditions, a lot of redundancy is necessary. The receiver provides feedback, which determines whether the transmitter has to provide additional redundancy. For example, Subramanian et al. [15] applied HARQ to point-to-point links at different layers and reported promising results. There are recent approaches, which adapt HARQ for distributed operation. For example, Dubois-Ferriere et al. [6] proposed Simple Packet Combining for sensor networks. Receivers buffer corrupted frames and employ a form of repetition coding to reconstruct the original frame. In the same way, Multi-Radio Diversity as proposed by Miu et al. [14] extracts correct information out of corrupted frames received by cooperating Access Points in the uplink of an infrastructure IEEE 802.11 network. Network codes are used in wireless networks to increase the throughput. For example, Chachulski et al. [16] presented MORE, which combines OR and the rate-less coding property of network coding to eliminate almost all feedback in routing. In addition, Radunovic et al. [8] refined the rate selection heuristics of MORE using an optimization framework, which jointly optimizes scheduling, rate selection, and bit rate adaptation under fairness constraints. In particular, the framework targets central, perfect MAC scheduling, which is not feasible on today’s hardware. However, a heuristic for IEEE 802.11 DCF medium access is given. Furthermore, Gkantsidis et al. [10] proposed the Multipath Code Casting protocol, which is based on the optimization framework. In particular, they observed that E2E-feedback as applied to MORE [16] might cause severe throughput degradation and refine the protocol’s operation with link level retransmissions, based on passive acknowledgements. However, they all favor the E2E approach. VI. C ONCLUSION AND F UTURE W ORK In this paper, we presented measurement results obtained from an indoor IEEE 802.11 WMN. They indicate that by ignoring corrupted frames a significant amount of resources is wasted, especially on links of intermediate quality. Based on these observations, we propose HALF, a HARQ scheme for OR. It uses incremental redundancy in a distributed fashion to improve the throughput in multi-hop WMNs. In the design of HALF, the emphasis lies on the hopby-hop perspective. The receivers provide STOP messages as immediate feedback in order to reduce the number of non-innovative fragments. In addition, due to the hop-by-hop
operation, the state per node for each flow is reduced, and only local knowledge is necessary for packet forwarding. In particular, we do not have to cope with the estimation of the E2E rates of flows, which was necessary in [16] and [8], [10]. In the first place, our prototype is a proof of concept, and from our simulation results, we conclude that benefits arise from the combination of HARQ and OR. As the next step, we are interested in the evaluation of HALF on real hardware within the Berlin RoofNet. Encouraged by the positive outcomes so far, we concentrate our future work on the interaction of HARQ and OR in the general setting. In particular, the tradeoff between efficiency and overhead, which arises with varying batch sizes, needs further characterization. In addition, we are interested whether and how the hop-byhop perspective of the protocol, which results in greediness, affects the overall performance, and whether the complexity reduction can outweigh a potential loss in efficiency. R EFERENCES [1] IEEE 802 LAN/MAN Standards Committee, “Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: Further Higher-Speed Physical Layer Extension in the 2.4 GHz Band. IEEE Standard 802.11g,” 2003. [2] S. Biswas and R. Morris, “Opportunistic routing in multi-hop wireless networks,” SIGCOMM Comput. Commun. Rev., vol. 34, no. 1, 2004. [3] Humboldt University Berlin, Systems Architecture Group, “Berlin RoofNet project,” www.berlinroofnet.de, 2008. [4] L. Scalia, I. Tinnirello, and D. Giustiniano, “Adverse side effects of ambient noise immunity techniques on IEEE 802.11 outdoor performance,” in IEEE GlobeCom, 2008. [5] G. Bianchi, F. Formisano, and D. Giustiniano, “802.11b/g link level measurements for an outdoor wireless campus network,” in World of Wireless, Mobile and Multimedia Networks (WOWMOM), 2006. [6] H. Dubois-Ferriere, D. Estrin, and M. Vetterli, “Packet combining in sensor networks,” in International Conference on Embedded Networked Sensor Systems (SenSys), 2005. [7] A. Zubow, M. Kurth, and J.-P. Redlich, “Considerations on forwarder selection for opportunistic protocols in wireless networks,” in European Wireless Conference, 2008. [8] B. Radunovic, C. Gkantsidis, P. Key, P. Rodriguez, and W. Hu, “An optimization framework for practical multipath routing in wireless mesh networks,” Microsoft Research, Tech. Rep., July 2007. [9] D. B. Johnson and D. A. Maltz, “Dynamic source routing in ad hoc wireless networks,” in Mobile Computing, Imielinski and Korth, Eds. Kluwer Academic Publishers, 1996, vol. 353. [10] C. Gkantsidis, W. Hu, P. Key, B. Radunovic, P. Rodriguez, and S. Gheorghiu, “Multipath code casting for wireless mesh networks,” in ACM CoNEXT, 2007. [11] U. Hermann, “Network Coding zum Ausgleich von Bitfehlern in drahtlosen Netzwerken,” Master’s thesis, Humboldt University Berlin, Germany, 2008, in German. [12] D. Aguayo, J. Bicket, S. Biswas, G. Judd, and R. Morris, “Link-level measurements from an 802.11b mesh network,” SIGCOMM Comput. Commun. Rev., vol. 34, no. 4, 2004. [13] A. Willig, M. Kubisch, C. Hoene, and A. Wolisz, “Measurements of a wireless link in an industrial environment using an ieee 802.11compliant physical layer,” IEEE Transactions on Industrial Electronics, vol. 49, no. 6, 2002. [14] A. Miu, H. Balakrishnan, and C. E. Koksal, “Improving loss resilience with multi-radio diversity in wireless networks,” in International Conference on Mobile Computing and Networking (MobiCom), 2005. [15] V. Subramanian, S. Kalyanaraman, and K. K. Ramakrishnan, “Hybrid packet FEC and retransmission-based erasure recovery mechanisms (HARQ) for lossy networks: Analysis and design,” in Wireless Systems: Advanced Research and Development (WISARD), 2007. [16] S. Chachulski, M. Jennings, S. Katti, and D. Katabi, “Trading structure for randomness in wireless opportunistic routing,” SIGCOMM Comput. Commun. Rev., vol. 37, no. 4, 2007.
