- Research
- Open Access
Rateless coding transmission over multi-state dying erasure channel for SATCOM
- Shushi Gu^{1},
- Jian Jiao^{1}Email authorView ORCID ID profile,
- Qinyu Zhang^{1} and
- Xuemai Gu^{2}
https://doi.org/10.1186/s13638-017-0964-6
© The Author(s) 2017
- Received: 4 July 2017
- Accepted: 15 October 2017
- Published: 30 October 2017
Abstract
Satellite communication (SATCOM) systems have attracted great attention from academic and industrial communities in recent years, and huge amount of data delivery over satellite downlinks is considered as a promising service in emerging 5G networks, such as multimedia broadcasting. Nevertheless, due to intermittent connections from LEO or MEO satellite to earth station, and high dynamic channel conditions over downlinks, satellites may not be able to transmit the large data files to the ground station on time. In this paper, we propose a new rateless coding transmission for multi-state dying erasure channels (MDEC) with random channel life span and time-varying packet error rates, to improve the transmitting capability over SATCOM downlinks. Firstly, a heuristic approach for suboptimal degree distributions based on AND-OR tree technique is presented to achieve higher intermediate performance and lower symbol error rate of our proposed rateless codes. Furthermore, the appropriate code length of the connective window is derived and analyzed for enhanced average throughput on MDEC that is also optimized by maximum problem solving. Simulations have been conducted to evaluate the effectiveness of our rateless coding transmission for large file delivery on dynamic channel conditions. The results demonstrate that our proposed transmission scheme outperforms existing conventional rateless codes with significantly better intermediate performance and throughput performance over unreliable SATCOM downlinks, under time-varying packet error rates and unpredictable occurrences of exhausted energy or cosmic ray attacks.
Keywords
- Satellite communication
- Multi-state dying erasure channel
- Rateless codes
- Degree distribution
- Optimal code length
1 Introduction
Satellite communication (SATCOM) systems have attracted great attention from academic and industrial communities in recent years, which have been widely used for many military and civil services, e.g., weather forecast, environment monitoring, multimedia service, positioning system, and emergency rescue [1–4]. In comparison to terrestrial communication, SATCOM systems have the advantages of larger bandwidth and wider coverage, for providing the huge amount of data services in the emerging fifth generation (5G) networks, such as hybrid satellite-terrestrial communication systems [5, 6].
Nevertheless, satellite systems have significantly different link characteristics than terrestrial links [7]. Firstly, since low earth orbit (LEO) or medium earth orbit (MEO) satellites (SA) fly along their own orbits and have very limited contact time with earth stations (ES), there is no sufficient contact time between SA and ES to download all data information [8]. Besides, the satellite downlink channel conditions are indeed time-varying due to atmospheric precipitation impacting high-frequency bands, so the time invariance assumption no longer holds [9]. Furthermore, the telecommunication systems on satellite may be subjected to serious effects, including the lack of battery energy and the attack of solar winds or cosmic rays, so that the communication links between SAs and ESs would randomly break down unpredictably. The above situations make great difficulties for the large amount of data transmitted back to the ground on the downlink channels. Therefore, it is necessary to give a theoretical channel model to describe the extremely dynamic characteristics on SATCOM channel, as well as to design an efficient and reliable transmission technique for large satellite data service downloading.
In [10], the authors firstly investigate a special type of channel with a finite and random channel length, termed dying channel. This type of channel may suddenly terminate due to communication links subjected to random fatal impacts, e.g., the sensor node may run out of power or be destroyed by fire attacks of military equipments in hostile environment, and the communication systems embedded in biological cells that may disappear unpredictably, due to excretion and digestion. It is critical to quantify how fast and reliably the information can be collected over this attacked channels with finite channel life span. Dying channels are modeled as the finite-state semi-Markov channels in [11]. It proves that lower Shannon limit which is very close to zero is almost reached on discrete memoryless channel that dies, so that arbitrarily small probability of error is not achievable. The authors optimize the sequences of finite block-length channel coding, to maximize the transmission volume communicated at fixed maximum message error probabilities by dynamic programming. Furthermore, the notion of the channel death is similar to the outage over fading channels. The outage capacity and the outage probability over dying channels are both given and derived in [12]. It also gives the optimization over the frame length and the power allocation over the constituting data blocks to minimize the outage probability. In consequence, the literatures above have motivated us to model the time-varying downlink between SA and ES subjected to unknown random blockages as a special form of dying channel.
Meanwhile, rateless codes, e.g., LT codes [13] and Raptor codes [14], as well-known erasure coding approaches, have attracted considerable interest in the areas of computing and communications. Unlike other error-correcting codes, i.e., RS and LDPC codes, rateless codes do not need a predetermined code-rate and have on-the-fly encoding and decoding property. It means that the encoder could continuously generate encoded symbols, while the decoder could gradually recover the original data files in real time. Rateless codes also have the following properties. (1) They can totally recover the original message from any subset of the encoded symbols of the length slightly larger than the original message that also can be seen as the near-MDS codes. (2) They allow very efficient encoding and decoding complexities, even as the logarithmic or linear number of the input symbols. In recent years, rateless codes have been widely used in vehicular networks for data dissemination by their high speed broadcasting ability [15]. Besides, based on unequal error protection (UEP) property, rateless codes are also employed for multimedia streaming service in terrestrial networks, and the adaptive recovery of the layered multimedia progressively improves the quality of experience (QoE) of the receivers [16]. Therefore, it can be confirmed that the flexible adaptation and capacity-achieving make rateless codes natively appropriate for the large data bulk transmission on the satellite downlinks. There have been some studies about rateless codes used in SATCOM systems for burst error resistance and DVB-S file delivery [17, 18].
For rateless codes over the dying channel, the topic of good intermediate performance of rateless codes would be widely studied. The author of [19] firstly investigated the intermediate performance of LT codes through deriving the asymptotic error probability and provided a tight outer bound on the proportion of recoverable symbols. Building on the basis of [19], the authors in [20] presented two new methods (degree distribution optimization and encoded symbol sorting) to maximize the intermediate symbol recovery rate of rateless coding. However, in their work, the different degree distributions were needed to match the different numbers of received encoded symbols, which may cause the transmitting system more complex. The investigation on rateless codes over dying channel was firstly presented in [21]. The authors optimized the degree distribution of LT codes for both partial and full recovery situations, aiming to match the stochastic channel life span. But their model failed to consider a constituting procedure of large file transmission over multiple connections or multiple channel states over the dying channels. The authors of [22] proposed a new rateless code, named the growth codes, to improve intermediate performance and to maximize video transmission quality over error resilient channels. The transmitter continuously adapts the degree of the encoded symbols to guarantee that each received encoded packet has the highest instantaneous recoverable probability. The online fountain codes [23] is another class of rateless codes designed for higher intermediate performance. The lower redundancy overhead of online fountain codes is the most important improvement over the growth codes, and the feedback cost is roughly half that of growth codes. But the common drawback of growth codes and online codes is that feedback signal is required to inform the alterations of the decoding states in transmission process, in order to change an optimal encoding strategy at the transmitter, which may not be easily employed in some practical SATCOM networks.
In this paper, we consider a multi-state dying erasure channel (MDEC) model different from [21], which is window-connected with dynamic variation of the packet error rates and channel life spans. Different channel death distributions of MDEC are considered to describe the unpredictable effect factors on SATCOM links, such as device exhaustion or random attacks of cosmic radiation. Three channel states (good, bad and dead) on downlinks between SA and ES are modeled due to the influences by atmospheric precipitation for high-frequency carrier waves, with a semi-Markov chain following time changes. The objective of this work is to improve the throughput of the large bulk files delivering over this multi-state dying erasure channel, through proposing a rateless coding transmission with appropriate degree distributions and code lengths for lower symbol error rate.
Our major contributions are summarized as three aspects: (i) we give the throughput expression of this multi-state dying erasure channel to describe intermittent and time-varying characteristic on SATCOM links, and also indicate the essential methods for rateless transmission designing over this channel model; (ii) we propose the sub-optimal degree distributions by a heuristic approach based on And-OR tree technique to minimize the symbol error rate over MDEC; and (iii) we analyze and derive the appropriate code lengths to improve the intermediate performance and throughput by a maximizing problem solving.
The remainder of this paper is organized as follows. Section 2 introduces the multi-state dying erasure channel modeling, presents the rateless transmission, and gives the throughput analysis. Relying on this model and problem statement, Section 3 proposes a certain degree distribution design method and optimizes the code length by solving a maximization problem. The simulation experiments and results are presented in Section 4, and Section 5 concludes the paper.
2 System model and performance analysis
2.1 Multi-state dying erasure channel
where λ _{ G } indicates the probability that the channel transits from bad state to good state, while λ _{ B } indicates the probability that the channel transits from good state to bad state.
In summary, MDEC channel in Fig. 1 has three channel states, good, bad, and dead. Good and bad states (available) mean the channel is available for data transmission, but the transmitter cannot know the accurate state is good or bad of every window and just knows the statistical erasure probabilities of the two states and Markov transition matrix. The occurrence of dead state (unavailable) is also unknown by transmitter, and the duration of channel life span is random. MDEC model exhibits extremely quick dynamics, so SATCOM system cannot provide availability of reliable communications. Since limited contact time with ESs, satellite may not have sufficient contact time to download all its data to the ground.
2.2 Rateless coding transmission over MDEC
In order to resist the packets discarded and damaged, an appropriate transmission method is desired to improve the data reliability and efficiency over the MDEC with finite and random channel lifespan L and time-varying erasure probability p. It is important to note that automatic repeat-request (ARQ) is not suitable for MDEC. Since the connection time is limited, frequent retransmissions of lost or erroneous packets waste many opportunities of large data volume delivery from SA to ES. In addition, the feedback information is hard to inform channel state information (CSI) to the transmitter due to the dynamic channel conditions and the random channel death, which makes the advantages of ARQ mechanism degrade significantly.
Firstly, denote by k as the code length, which is the number of input symbols to be sent in one connective window. Secondly, the number of output symbols actually transmitted by SA is denoted as l. Apparently, l is a random variable decided by the channel lifespan L and length of window K, i.e., \(l=\min \left (K,\left \lfloor \frac {L}{\tau }\right \rfloor \right)\). Once the channel switches to the dead state unpredictably, the transmitting flow of output symbols would break off at this moment, as \(l=\left \lfloor \frac {L}{\tau }\right \rfloor \). If the channel state sustains available in one connective window, the transmitting flow of output symbols can be continuous until the end of connection, as l=K. Lastly, the number of output symbols successfully received by the ES (l after erased with probability p) in one window is denoted as a random variable n, so the decoding overhead at the decoder is given by \(\gamma =\frac {n}{k}\). If the channel dies or connective window finishes, the receiver will start to decode the output symbols and recover the original data. The decoder may partially or fully recover the original data in one window, which means that intermediate performance of rateless codes is necessarily considered.
2.3 Throughput performance analysis
where Pr(n) is the probability of n output symbols successfully received by the receiver in one window, and as we know that \(\mathop {\sum }\limits _{n=1}^{K} \Pr (n)=1\). Furthermore, we can also express the probability that output symbols erased on MDEC, named as the output symbol error rate S E R _{ o u t }. The detailed derivation about the relationship between Pr(n), S E R _{ o u t } and channel parameters will be given in Section 3 of this paper.
In Eq. (2), z _{ a v g } provides a reasonable measurement for the average input symbol recovery ratio over MDEC, conditioned upon two crucial parameters about the code length k and the encoding degree distribution Ω. We define the input symbol decoding error rate at the receiver as SER, which can be easily expressed as S E R=1−z _{ a v g }(k,Ω). Therefore, larger k means less redundancy, and \(\gamma =\frac {n}{k}\) decreases, resulting in reduced z _{ a v g } and raise SER. Besides, the intermediate performance z _{ a v g } and input symbol error rate SER are affected by the degree distribution Ω selections. When the average degree is higher (e.g., robust soliton distribution of LT codes), the rateless codes are suitable for the case that γ>1, as full recovery. When the average degree is lower (i.e., only degree-one and degree-two encoded packets), rateless coding is suitable for the case that γ<1, as partial recovery. Consequently, one of the objectives of our work is to find the most appropriate k and Ω(x) under certain channel conditions, in an effort to maximize the intermediate performance z _{ a v g } and minimize input symbol error rate SER at the receiver.
As can be easily seen that, if K is fixed, throughput in Eq. (4) improves by increasing k, which implies more input symbols can be transmitted. But as the above description, larger k makes lower intermediate performance z _{ a v g } and higher input symbol error rate SER, so the throughput reduces especially when the lifespan L is shorter or the channel erasure probability p is higher. In addition, z _{ a v g } and SER are both closely decided by Ω in the decoding process. Therefore, for our final objective in this work, we need to maximize the throughput in Eq. (4), maximize the intermediate performance z _{ a v g } in Eq. (2), and minimize the input symbol error rate SER using the optimization method to tradeoff appropriate code lengths k and appropriate degree distributions Ω(x), based on the time-varying and dying channel conditions of MDEC model.
3 Degree distribution design and code length optimization
The sequence y _{ h } converges with respect to the number of decoding iterations h. Consequently, as mentioned in Section 2, the average intermediate performance z _{ a v g } is the proportion of input symbols recovered in one window, which can be expressed as z _{ a v g }=1−S E R. We will give the SER performances of our codes after degree distribution and code-length optimized, compared to those of LT and Raptor codes in the following sections.
3.1 Linearly combined degree distribution Ω _{LC}
The first two degree distributions are chosen in consideration of the dead and bad states of MDEC, while the weak robust soliton distribution accounts for relatively general cases as well as the good state.
The above heuristic degree distribution exhibits two notable advantages. Firstly, this linear combination approach only needs three weighting coefficients to generate a practical degree distribution with sub-optimum intermediate performance z _{LC}, which is able to save enormous computational power in hardware equipments of SA. Secondly, the three weighting coefficients are all related to the probability intervals of the decoding overhead γ. If the three weighting coefficients are set properly in accordance with the random distribution of lifespan L and the Markov transition probabilities λ _{ G } and λ _{ B }, the proposed rateless codes can dynamically adapt the degree distribution Ω _{LC}(x) to the random channel conditions.
3.2 Optimization of the code length k
It is not difficult to see that k and ω in Ω _{LC}(x) are not independent. Because the weighting vector ω is defined as the probability distribution of \(\gamma =\frac {n}{k}\) in different decoding overhead intervals. That is, the choice of k affects the value of weighting vector ω. As a result, ω _{1}, ω _{2}, and ω _{3} can be transformed to functions of k. Therefore, we attempt to transform the above maximum problem with multiple variables into a single variable optimization problem. We derive the relationship between ω and k over the MDEC with an exponentially distributed channel life span, while the derivation with a non-negative Gaussian distributed channel life span is similar.
where the coefficients q _{ B } and q _{ G } can be expressed as \(q_{B}=\frac {\lambda _{G}}{\lambda _{G}+\lambda _{B}}\) and \(q_{G}=\frac {\lambda _{B}}{\lambda _{G}+\lambda _{B}}\).
It can be easily seen that the output symbol error rate S E R _{ o u t } is only relevant to the channel conditions of MDEC, including erasure probabilities p _{ G } and p _{ B }, transition probabilities λ _{ G } and λ _{ B }, and channel lifespan L(t). Hence, S E R _{ o u t } describes the dynamic switching of the MDEC states.
The initial value y _{LC,0}=1. The intermediate performance z _{LC}=1−y _{LC,h } converges roughly with respect to a constant number of decoding iterations h (according to the following simulations, h=40 is adequate for convergence). Because of the on-the-fly encoding and decoding property, the iteration time delay will not severely impact the throughput performance at the receiver. We can ignore the decoding delay in our analysis.
Furthermore, it is easy to see that the complexity of problem (18) is O(K ^{2}) with exhaustive search algorithm used, since the feasible set of the optimum solution k _{ o p t } is finite and integer. Due to the computing capability of SA and ES, the complexity of O(K ^{2}) is reasonable for practical SATCOM scenarios. Once the value of k _{ o p t } is attained, the linear combined degree distribution Ω _{LC}(x) can be obtained. The optimization results of the code length and degree distribution for various channel conditions will be stored in several databases. As similarly as above, this optimization method of k _{ o p t } can also be applied in the situation where the channel lifespan follows a Gaussian distribution \(\mathcal {N}(\mu,\sigma ^{2})\). Although this approach is heuristic, the numerical results in Section 4 show that it could achieve a significant performance improvement over the conventional rateless codes.
4 Simulation and discussion
4.1 Symbol error rate and intermediate performance of proposed degree distribution
We will evaluate the symbol error rate SER and the intermediate performance z _{LC} of the linear combined degree distribution Ω _{LC}(x) obtained via the heuristic approach.
Furthermore, in order to evaluate the intermediate performance z _{LC} of our designed degree distribution Ω _{LC} on SATCOM channel model, the parameters of the simulated MDEC are set as follows. The connective window length K=3000. The channel lifespan L follows exponential distributions with means 1/λ=3000 and 5000, or non-negative Gaussian distributions with means μ=2000 and 3000, σ=400 and 1600. The two transition probabilities of the Markov channel are set λ _{ G }=0.1 and λ _{ B }=0.2, and the erasure probabilities of good and bad states are p _{ G }=0.01 and p _{ B }=0.2, respectively. The asymptotic intermediate performance in [19] is taken as the upper bound, which is calculated under the assumption that the decoding overhead γ in every window can be accurately estimated by the SA. We give the fixed range of the code length k from 1500 to 2850, so the Ω _{LC}(x) (named LC for short) with ω _{1},ω _{2},ω _{3} can be calculated by Eqs. (8) and (17).
4.2 Average throughput of proposed transmission scheme
Next, we compare the throughput of the proposed coding scheme with that of the conventional rateless codes. MDEC lifespans with both exponential and non-negative Gaussian distributions are used to model the scenarios of energy exhaustion of the device and random attacks by radiation, respectively. We give three and four cases for the above two channel lifespan distributions with different means and variances.
Optimal code length k _{ o p t } and weighting vector ω over the MDEC with an exponentially distributed channel lifespan
Case | 1/λ | k _{ o p t } | ω= [ω _{1},ω _{2},ω _{3}] | d _{ a v g } |
---|---|---|---|---|
1 | 3000 | 2050 | 0.4006, 0.0555, 0.5439 | 5.58 |
2 | 5000 | 2280 | 0.2894, 0.0456, 0.665 | 6.59 |
3 | 10000 | 2550 | 0.1725, 0.0303, 0.7972 | 7.68 |
Optimal code length k _{ o p t } and weighting vector ω over the MDEC with a non-negative Gaussian distributed channel lifespan
Case | μ | σ | k _{ o p t } | ω= [ω _{1},ω _{2},ω _{3}] | d _{ a v g } |
---|---|---|---|---|---|
1 | 2000 | 400 | 2850 | 0.6241, 0.2584, 0.1176 | 2.24 |
2 | 3000 | 400 | 2150 | 0.0005, 0.0062, 0.9933 | 9.29 |
3 | 3000 | 1600 | 2100 | 0.1905, 0.0515, 0.758 | 7.37 |
4 | 5000 | 1600 | 2250 | 0.0207, 0.0114, 0.9679 | 9.08 |
5 Conclusions
In this paper, we considered the problem that large data file transmission over the connective-window and dynamic downlinks in SATCOM systems. Due to atmospheric precipitation and other emergency situations, such as energy exhausted and cosmic ray attacks, the channel state dramatically changes and unpredictably breaks off. A type of multi-state dying erasure channel model, named MDEC, is presented and characterized by a time-varying erasure probabilities and random channel lifespan. Moreover, a rateless coding transmission method with proper degree distribution and optimal code length was proposed to improve the average throughput and reduce the symbol error rate over MDEC. We firstly used a heuristic approach to design a weighted degree distribution based upon the AND-OR tree analysis technique to increase the intermediate performance. In addition, we have given the optimal code lengths by numerical analyses and calculations, to solve a maximize problem of throughput under random channel death probability distributions. We evaluated our transmission schemes by simulation based on different SATCOM channel conditions. The results demonstrated that our proposed rateless coding transmission attained better intermediate performance and throughput than LT and Raptor codes with different channel state transitions and random distributions of unpredictable attacks.
Declarations
Acknowledgements
This work has been supported in part by the National Natural Sciences Foundation of China NSFC) under Grants 61525103, 61701136, 61771158, and 61371102, and Shenzhen Basic Research Program under Grants JCYJ 20160328163327348 and JCYJ 20150930150304185.
Competing interests
The authors declare that they have no competing interests.
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