Adaptive Error-Correction Coding Scheme for Underwater Acoustic Communication Networks

Transcription

1 Adaptive Error-Correction Coding Scheme for Underwater Acoustic Communication Networks 1 Roee Diamant and Lutz Lampe University of British Columbia, Vancouver, BC, Canada, {roeed,lampe}@ece.ubc.ca Abstract Underwater acoustic communication networks (UWAN) has recently attracted much attention in the research community. The long propagation delay and the possible sparsity of the network topology offer opportunities to increase throughput through time- and spatial-reuse. In this paper, we focus on time-slotted scheduling protocols, which are a practical solution for contention-free and interferencefree access in small-scale UWANs. A disadvantage of slotted scheduling compared to contention-based protocols is the need for a guard interval in every time slot to account for the maximal propagation delay in the channel. Since, however, for many links the actual propagation delay is shorter than the guard interval, in this paper we propose an adaptive channel coding technique that exploits the surplus guard time for improving transmission reliability. In particular, using link distances as side information, transmitter adapt their code rate such as to fill the instantaneously available portion of the time slot. For practical implementation of this adaptive coding scheme we consider punctured and rateless codes, either with explicit knowledge of the instantaneous code rate at the receiver or in the form of incremental redundancy automatic repeat request (IR-ARQ). Simulation results demonstrate the gains achieved by our coding scheme over fixed-rate error-correction codes in terms of both throughput and consumption of transmitted energy per successfully delivered packet. We also report results from a sea trial conducted at the Haifa harbor, which corroborate the simulations. Index Terms Underwater acoustic communication, Adaptive coding, Rate-less codes, Hybrid ARQ

2 2 I. INTRODUCTION Reliable underwater acoustic communication networks (UWAN) is challenging due to the limited available transmit power and bandwidth, large channel attenuation and long channel delay, as well as time-varying channel conditions with large Doppler spread [1]. The set of possible applications including sharing of navigation information, control of autonomous underwater vehicles (AUV), and undersea command and control, where the number of network nodes is relatively small, transmission distance is large, and frequent packet exchange allows distance estimation. A practical example we have in mind is a system called Deep-Link, which is used for command and control, surveillance, and diver-safety purposes in three navies. Nodes in the Deep-Link system operate in a spatial-reuse time-division-multiple-access (TDMA) network and periodically broadcast navigation packets to nodes up to 5 km away (see system specification in [2]). In this paper, we present an adaptive coding scheme for time-slotted UWANs. Slotted scheduling is especially attractive in UWANs, where networks are often small and possible clock drifts are negligible compared to the time slot duration [3]. Adaptive coding can be done by transmitterside adjustment of code rate or by receiver-initiated request of additional transmissions, i.e., automatic repeat request (ARQ), to ensure successful data delivery. With regards to the latter, incremental redundancy HARQ (IR-HARQ) is particularly efficient as it does not suffer from a coding loss due to repetition of the same parity symbols [4]. The application of IR-HARQ using modern rateless codes for UWAN has recently been studied in [5]. However, despite the coding efficiency of IR-HARQ, it suffers from high latency due to retransmission requests and retransmissions. This disadvantage is particularly pronounced in UWAN due to the long propagation delay of sound transmission. Furthermore, each time slot includes a sizeable guard interval, usually dimensioned according to the modem s maximal transmission range (which for UWANs corresponds to a propagation delay in the order of a few seconds for transmission range of few km [1]), and thus each retransmission adds extra guard overhead. Considering that actual propagation delay for specific communication links is often notably shorter than the maximal expected delay, in this paper we suggest improving link reliability by utilizing the often over-sized guard intervals in the time slot. In particular, assuming that the propagation delays to nodes within the interference range of a transmitting node are known, our

3 3 scheme opportunistically includes extra parity symbols in the data packet if the guard interval is longer than needed for interference-free transmission. The extra parity symbols, corresponding to a lower code rate, reduce the packet error probability and thus also the number of packet retransmissions. We note that compared to conventional adaptive coding, where channel-stateinformation (CSI) usually is given in the form of a link quality parameter like signal-to-noise ratio (SNR), a one novel aspect of our approach lies in the use of ranging information as CSI. Furthermore, while several approaches have been suggested to utilize the long propagation delay in the channel by transmitting more data in the channel (e.g., [6],[7]), the adaptation of coding rate based on delay has not been considered before. We present two possible implementations for our approach, one based on a bank of codes and another one based on rateless codes. Furthermore, we include the case of ranging CSI being available only at the transmitter side, which leads to range-based adaptive coding, such that similar to IR-ARQ, acknowledgment is not required. We present simulation results for typical underwater acoustic environments as well as results from a sea trial. The results demonstrate that, when ranging information is available (e.g., the Deep-Link application), our protocol provides significant gains compared to the performance of fixed coding schemes in both reliability and transmission energy consumption. The remainder of this paper is organized as follows. The details of the system model are introduced in Section II. In Section III, we describe our adaptive coding scheme. Simulation and experimental results are presented and discussed in Section IV, and conclusions are drawn in Section V. II. SYSTEM MODEL We consider slotted UWANs where nodes transmit in designated time slots. The considered scenario can accommodate both unicast or broadcast transmission, and we set no limitation on the scheduling protocol. Due to the large attenuation in the underwater acoustic channel (cf. [1]) we assume the per-link interference range 1 can be bounded by the detection range of synchronization signals, whose energy is usually much larger than that of information bearing 1 Link interference range is defined as the distance up to which remote transmissions significantly affect the signal-to-noiseplus-interference-ratio (SINR) at the receiver.

4 4 signals. We assume periodic packet exchange between nodes, such that by estimating the timedifference-of-arrival or time-of-arrival [8], [9] of received synchronization signals, each node is aware of the distance to nodes located within its interference range. Let d max be the maximal interference range of the system, which is determined by the detection range of the modem. Furthermore, for time slot t, let d actual be the maximum distance of node i to nodes within its interference range which are scheduled to receive in the next time-slot, t + 1. Clearly, d actual d max, (1) and this thus often the guard interval could be reduced while still ensuring that packets are received interference-free. Using knowledge of d actual, our goal is to maximize time slot utilization by allowing node i to increase its error correction capability as described next. III. THE ADAPTIVE CODING SCHEME At a transmitting node i, K information symbols are encoded into a minimum number of N min coded symbols. N min is determined assuming d actual = d max and thus the full guard interval is needed for interference-free scheduling. Assuming that node i has an accurate estimate of the range difference = d max d actual, (2) the guard interval can be shortened however. That is, during its designated time slot t, node i can transmit N actual = N min + T s c (3) symbols to a receiver j, where T s and c are the symbol period and propagation speed, respectively, N min N actual N max and N min = N max dmax T s c. (4) While node i has knowledge of and thus can calculate N actual, this may not the case for its receiver j. This is because is a determined by the distances of node i to nodes within its interference range, and this information may not be available at j. However, node j has a-priori knowledge of K, N min, and N max. Considering this problem, one possibility is to transmit the value N actual as part of the data packet. Then, the receiver j can decode the (K, N actual ) code. If

5 5 Fig. 1. Illustration of decoding for the adaptive coding scheme.. it is undesirable to transmit this side information, which of course takes away from the available guard time for sending extra parity symbols, in the following we suggest the iterative decoding scheme illustrated in Figure 1. A. Implementation The receiver makes multiple decoding attempts with the first attempt starting after receiving N min samples. If decoding fails (e.g., the cyclic-redundancy check (CRC) did not pass), receiver j makes another attempt after having obtained at least one more sample. Hence, at most M try = N max K decoding attempts are made. Next, we suggest two implementation examples for our adaptive coding approach. 1) Bank-of-Codes: The first implementation uses a pre-defined bank of N max N min codes, which can be a set of either optimized codes for different rates or punctured codes. For the latter, we apply a (K, N) mother code, where N is pre-defined at both transmitter and receiver and N N max. At its designated time slot t, node i transmits N actual N N actual symbols of the codeword, following a pre-defined puncturing pattern. symbols by puncturing 2) Rateless Codes: The second implementation example is based on the Fountain codes [10]. At time slot t, the transmitter generates a codeword whose length corresponds to N actual transmit symbols. Due to the rateless nature of Fountain codes, generation of any number of parity symbols

6 6 is easily facilitated. No side information is needed at the receiver assuming that a common seed for the random generation of the columns of the generator matrix is used. Using Fountain codes has an additional benefit if the transmitter-receiver link can be modeled as an erasure channel. In this case, message passing decoding is alike successive cancelation, and additionally demodulated symbols available at the m-th decoding attempt can be used directly to improve the result from the m 1-st decoding stage (see [11]). Here, decoding with and without knowledge of N actual in fact identical, and thus there is no complexity overhead due to the iterative decoding procedure from Figure 1. When the channel cannot be modeled as an erasure channel, the integration of newly arrived samples into message-passing decoding is somewhat more complicated. For this case, favorable decoding schedules are described in [12] and [13]. The same adaptive coding and successive decoding procedure can be applied to variants of Fountain codes, most notably Raptor codes [14]. For Raptor codes, we use an (K, N outer ) outer error-correction code and an inner (N outer, N actual ) Fountain code, where N outer = δ N min and δ is a design parameter controlling the maximal probability of the inner Fountain decoding failure. Since in underwater acoustic communication transmission rate is in the order of few kbps and packets are small [15], we expect K to be in the order of hundreds to thousands symbols. Therefore, while in IR-HARQ, Fountain codes are commonly implemented using the LT codes presented in [10], LT codes, which reaches capacity only asymptotically, may not be a good fit for our adaptive coding scheme. Instead, we apply the fixed-rank windowed random matrix coding scheme described in [16], where good results are obtained for as low as K = 100 symbols at the cost of complexity. 3) Discussion: Comparing the above Bank-of-Codes and Rateless codes schemes, we note that for the former since often there are restrictions over the design of a code 2, N may be much bigger than N max, and complexity may be greater than that of the Rateless scheme. However, in the Bank-of-Codes scheme, the punctured or pre-defined code can be designed to achieve better performance than the rateless codes. In the following we discuss the gain achieved by our adaptive coding scheme in terms of both packet-error-rate (PER) and energy consumption for transmission. are 2 For example, for Reed-Solomon codes N must be equal to 2 n 1 for some integer n [17].

7 7 B. PER Gain As a specific example for the first implementation type, i.e., a bank of pre-defined codes, we consider a punctured (K, N) Reed-Solomon (RS) block code [17]. Let p RS be the RS coded symbol error probability before decoding. The packet error probability (PER) after decoding is given by p RS packet(n, T (K, N)) = N k=t (K,N)+1 ( ) N (p RS ) k (1 p RS ) N k, (5) k where T (K, N) = N K for the erasure channel and T (K, N) = (N K)/2 otherwise. Let us consider PER when the receiver obtains N actual decoded symbols, and compare it to the case of a fixed (K, N min ) RS code. Here, by (5), the PER is p RS actual packet (K, N ). Thus, in terms of success rate, the gain of the adaptive punctured RS coding scheme over the fixed code is g coding = 1 prs actual packet (K, N ) 1 p RS packet (K, N min ). (6) In Figure 2, for T s = 0.01 sec, c = 1500 m/sec, and a non-erasure channel, we show gain g coding from (6) over a (54, 63) fixed RS code as a function of. Results are shown for several values of p RS from (5). We observe that even for such a slow transmission rate, g coding is significant and fast increasing with (2) and p RS. We note that starting from a certain value, the PER of the adaptive coding scheme becomes extremely small, which is the reason for the seemingly convergence of g coding observed in Figure 2. Next, we discuss energy consumption benefits of our approach. C. Energy Consumption for Transmission Since instead of N min symbols, we opportunistically transmit N actual symbols, the potential large gain of the adaptive coding scheme over the fixed code in terms of PER is achieved at the cost of higher energy consumption for per-packet transmission. This may seem to be a challenge for UWAC networks, where often energy resources at (battery-operated) network nodes are limited. However, considering the low reliability in UWAN links, and accordingly the energy spent for successfully received data packets, the improved error correction capability of the adaptive coding scheme may ultimately reduce energy consumption for transmission, as we discuss next.

8 p RS =0.05 p RS =0.08 p RS =0.12 p RS =0.15 g coding [m] Fig. 2. Gain g coding from (6) as a function of from (2). Non-erasure channel.. Let p packet (N, K) be the error rate of a packet transmitted using an (K, N) error-correction code. Then, a successful transmission requires on average n(k, N) = 1 1 p packet (N, K) packet re-transmissions. Denote E the energy consumption required for transmission of 1 sec. Also, let T h be the combined duration of the packet header and pre-ample sequence. Then, the total energy consumption for successful transmission is n(k, N)E (NT s + T h ), and the gain of our adaptive coding approach in terms of transmission energy consumption is g energy = n(k, N min ) (N min T s + T h ) n(k, N actual ) (N actual T s + T h ). (8) Clearly, gain (8) depends on the inversely proportional relation in (7) between n(k, N) and N, and will increase with T h. For the example of the punctured RS code given in Section III-B, in Figure 3 we show gain g energy from (8) as a function of (2) and T h for p RS = 0.05, 0.08, 0.12, 0.15, and the same set of parameters considered in Section III-B. As expected, we observe that g energy increases with T h. However, due to the low transmission rate, this increase is not significant. For p RS 0.08, we observe a significant gain increase in terms of transmission energy consumption. Since starting from a certain value, p packet (N, K) of the adaptive coding scheme becomes extremely small, (7)

9 9 p RS =0.05,T h =0.05 p RS =0.08,T h =0.05 g coding p RS =0.12,T h =0.05 p RS =0.15,T h =0.05 p RS =0.15,T h = [m] Fig. 3. Gain g energy from (8) as a function of T h and from (2). Non-erasure channel.. similar to the results in Figure 2, n(k, N) from (7) seem to converge. Thus, due to the tradeoff mentioned above, g energy does not monotonously increase with N actual, and there is an optimal value in terms of the transmitted energy consumption. This optimal value increases with p RS. IV. PERFORMANCE We now evaluate the performance of our adaptive coding scheme in terms of the PER and throughput. For simplicity, we consider the erasure channel and present simulation results for different symbol erasure probability. To show the affect of a realistic sea environment, we also present results from a sea trial, where we implemented the punctured RS scheme on an actual underwater acoustic modem (namely, the Deep-Link modem). A. Simulation Results B. Setting Our simulation setting includes a Monte-Carlo set of channel realizations. For each channel realization, four nodes are uniformly placed in a square area of m 2 at a fixed depth of 40 m for a 50 m long water column. The nodes operate for 100 sec in a simple TDMA

10 Average PER Bit Erasure Rate F RS (i.i.d) P RS (i.i.d) F RS (burst) P RS (burst) Fountain Raptor LDPC Raptor RS Fig. 4. Average PER as a function of bit-erasure-rate.. network with a time frame of four time slots, where the duration of the slot time is determined according to a maximal transmission range of 1000 m and a propagation speed of 1500 m/sec. Since in this paper our focus is on the possible gain of the adaptive coding scheme, for simplicity and results traceability we assume a perfect erasure channel and BPSK transmission. The biterasure-probability is determined based on the SNR according to the nodes positions. For each node pair, we calculate the SNR using the Bellhop ray-tracing model (cf. [18]) for a flat sand surface, carrier frequency of 15 khz, a common power source level of 135 db//µpa@1m, and a noise level of 50 db//µpa/hz. During the network operation, each node is assigned with short packets of K = 500 bits to transmit to its neighbor nodes with transmission rate of 1 kbps. Packets are retransmitted until successful reception in at least one neighbor node. For simplicity, we assume acknowledgments are always received. For the transmission parameters, we use T h = 0.1 sec, and an original coding rate of roughly 0.8. This scenario mimics the exchange of navigation packets in the Deep-Link system [2]. The adaptive coding scheme allows extension of this original coding rate. At best, i.e., for d actual = 0 m, this allows adding 83 coded symbols and extending the coding rate to roughly We demonstrate the gain of the adaptive coding scheme by comparing performance of different coding implementations: RS: fixed (F-RS) and punctured (P-RS), Fountain, and Raptor

11 Throughput range [m] P RS (i.i.d) P RS (burst) Fountain Raptor LDPC Raptor RS Fig. 5. Average throughput as a function of for bit-erasure-rate of for both RS and LDPC (cf. [19]) inner codes. As performance of the RS scheme is highly affected by the erasure pattern, we show performance for both i.i.d and burst distributed erasures. The former is motivated by the ambient noise in the channel, and the latter by temporarily correlated waves and ships-induced noises [1]. Finally, for the Raptor codes we use δ = 1.2 (see Section III). C. Simulation Results In Figure 4, we show the PER as a function of the bit-erasure-rate. Results are averaged for each transmitter-receiver pair. As expected, we observe that performance of the RS scheme for burst-type erasures are significantly better than for i.i.d.-type erasures. However, even for the former, performance of the different adaptive code schemes significantly outperform that of the fixed RS code. Compatible with the results in [14], compering the Fountain and the two Raptor code types, we observe that Raptor codes outperforms the former. Here, since the erasure pattern at the output of the outer Fountain code are i.i.d, LDPC-type Raptor are slightly better than RSbased Raptor. From Figure 4, we observe that best performance are achieved by the punctured RS code with burst-type erasures, which is optimal for this type of channel. Next, in Figure 5 we show the average throughput (i.e., number of successful packets in 1000 sec averaged for each transmitter-receiver pair) of the adaptive coding schemes for a biterasure-rate of roughly 0.28 and as a function of the range difference, from (2). Note that

12 12 Fig. 6. Satellite picture of the experiment location (picture taken from Google Earth on July 23, 2012.) The three locations of the nodes are marked.. since we consider 4 nodes and a simple TDMA, at most, throughput can be 1. However, it can 4 considerably degrade if retransmissions are made. For example, as also shown by the results in Figure 4, for the considered bit-erasure-rate only a few packets were properly decoded using the fixed RS code and throughput is almost zero. From Figure 5, we observe that throughput performance improves as increases. As in Figure 4, best performance is achieved by the punctured RS scheme with burst-type erasures. In fact, we observe that for the latter scheme, starting from 150 m, throughput is maximal, i.e., no retransmissions are required. D. Sea Trial Results On Nov we conducted an experiment in the Haifa harbor, Israel, to measure performance of our adaptive scheme in a realistic error and erasure pattern. The experiment included three Deep-Link modems, statically deployed from the harbor docks as shown in Figure 6. The distance between nodes 1 and 2 was 910 m, between nodes 1 and 3 was 780 m, and between nodes 2 and 3 was 340 m. The modems include RS codes with flexible parameters, where erasures are detected as decoded symbols with energy below a certain threshold. Using this capability, we tested both the fixed and punctured RS coding schemes. During the experiment, the three nodes periodically broadcasted short navigation packets of 200 bits at rate of 300 bps in a simple TDMA scheduling scheme. Each packet included a header of 0.67 sec for a synchronization

13 Punctured RS Fixed RS 0.9 P success range [m] Fig. 7. Packet success rate vs. range. Results from the sea trial.. signal and preamble sequence, as well as a guard interval accounting for possible clock drifts and a maximal propagation delay of 1 sec. The latter was determined according to the size of the harbor, which was roughly 1500 m. We compared the performance of the punctured RS scheme with a fixed RS code of rate 4/5, such that the duration of the time slot was 2.5 sec. This allowed an adaptive change of the coding rate up to 2/5. The experiment included two parts each lasting for one hour. In the first part we measured performance of the fixed RS, and in the second part the punctured RS scheme was tested. Signals were transmitted at a low source level of 130 db//µpa@1m to allow significant packet failure rate at the noisy harbor environment, and thus a better comparison between performance of the two schemes. In Figure 7, for the three nodes, we show the packet success rate, P success, as a function of the range difference range (see (2)). Corroborating the results in Figure 4, we observe that a significant gain of 14% on average for the punctured RS scheme over the fixed one. This gain increases with range. From these results and the results in Figures 4 and 5, we conclude that the possible difference between the maximal propagation delay and the actual one offers significant performance gain in slotted UWANs.

14 14 V. CONCLUSIONS In this paper, we suggested an adaptive coding approach to improve the packet error rate in a time-slotted UWAC network. Different than IR-HARQ, our approach uses range information as CSI to extend the code rate and fully exploit the temporal range difference between the assumed propagation delay, used as a guard interval in the time slot, and the actual one. We described two implementation schemes for our approach. One that is based on a bank of pre-defined codes, and another based on rateless codes. By means of analysis and simulation results, we demonstrated the gain achieved by our adaptive coding scheme over a fixed-rate error correction code in terms of packet error rate, transmission energy consumption, and throughput. The simulation results were verified in a sea trial. Further work would combine the suggested method in an IR-HARQ scheme. REFERENCES [1] W. Burdic, Underwater Acoustic System Analysis. Los Altos, CA, USA: Peninsula Publishing, [2] Specifications of the Deep-Link system. Rafael Ltd., STORAGE/FILES/5/995.pdf. [3] M. Chitre, S. Shahabudeen, L. Freitag, and M. Stojanovic, Recent advances in underwater acoustic communications and networking, in IEEE Oceans Conference, sep. 2008, pp [4] C. Lott, O. Milenkovic, and E. Soljanin, Hybrid arq: Theory, state of the art and future directions, in IEEE Information Theory Workshop on Information Theory for Wireless Networks, Jul. 2007, pp [5] M. Chitre and M. Motani, On the use of rate-less codes in underwater acoustic file transfers, in IEEE OCEANS, Jun [6] X. Guo, M. Frater, and M. Ryan, Design of a propagation-delay-tolerant MAC protocol for underwater acoustic sensor networks, IEEE J. Oceanic Eng., vol. 34, no. 2, pp , Apr [7] H. H. Ng, W. S. Soh, and M. Motani, ROPA: A MAC protocol for underwater acoustic networks with reverse opportunistic packet appending, in IEEE Wireless Communications and Networking Conference (WCNC), Sydney, Australia, Apr [8] M. Erol, H. Mouftah, and S. Oktug, Localization techniques for underwater acoustic sensor networks, IEEE Commun. Mag., vol. 48, no. 12, pp , Jun [9] R. Diamant and L. Lampe, Underwater localization with time-synchronization and propagation speed uncertainties, IEEE Trans. Mobile Comput., vol. PP, no. 99, p. 1, [10] M. Luby, LT codes, in The IEEE Symposium on Foundations of Computer Science, 2002, pp [11] D. MacKay, Fountain codes, IEE Proceedings-Communications, vol. 152, no. 6, pp , Dec [12] K. Hu, J. Castura, and Y. Mao, Reduced-complexity decoding of Raptor codes over fading cannels, in IEEE Global Commun. Conf. (GLOBCOM), San Francisco, CA, USA, Nov [13] A. AbdulHussein, A. Oka, and L. Lampe, Decoding with early termination for Raptor codes, IEEE Communications Letters, vol. 12, no. 6, pp , Jun [14] A. Shokrollahi, Raptor codes, IEEE Transactions on Information Theory, vol. 52, no. 6, pp , Jun

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