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An analytical approach to error detection and correction for onboard nanosatellites
EURASIP Journal on Wireless Communications and Networking volume 2023, Article number: 49 (2023)
Abstract
Nanosatellites are persistently progressing and creating global communication and data transmission. It builds up a colossal request for more progressed and dependable frameworks to transmit faster and more reliable information. A syntactic machine learning approach has been distinguished as a good plot for anticipating singlebit and multiplebit errors that influence onboard nanosatellites. In this paper, we have proposed an analytical approach to error detection and correction for onboard nanosatellites. We have planned the framework separately with three distinct parts: encoding, error checking, and decoding. It has created an amid information exchange from satellite to the ground station. It has analyzed six camera pictures simultaneously with the assistance of field programmable gate array and EDAC strategies. We have presented the progressed turbo mechanics EDAC for unprecedented transfer speeds of satellite communication and execution & examination with the AWGN and Rayleigh channels to extend the proficiency. EDAC strategies codes have been implemented in MATLAB. This method is straightforward and accomplishes unwavering quality and exactness compared to comparable strategies.
1 Introduction
A nanosatellite is a device that moves in an elliptical way around a planet. Earth observation (EO) satellite is one of the fundamental devices for investigating the environment [1]. EO satellites apply highresolution image sensors from the earth’s surface to watch and get data. It utilizes infrared for underneath observation. By watching the ground from space, EO satellites give fundamental data on climate observation, urban and rural development, natural disasters, natural monitoring, etc. [2]. During data transmission usually we miss valuable data due to interference.
Nanosatellite’s error detection and correction devices aim to transmit secured and errorless information between the satellite and the ground station [3]. They are subject to unsteady and unstable data corruption because of thermal noise, high energy particle impact, or other noise [4]. Singlebit and burst errors are common satellite data communication errors [5]. A singlebit error implies one bit changed from 0 to 1, and a burst error suggests more than one conjugated bit degraded [6]. The mistake discovery handle is the primary step to error redress, which is subordinate to adding extra bits to the first information [7].
Excess bits are accomplished through two basic coding plans: convolution and block coding. Error correction can be classified as a forward error correction (FEC) and automatic repeat request (ARQ). Sometimes ARQ and FEC can be combined [6]. This strategy is called a hybrid automaticrepeat request program. There are numerous frameworks outlined to distinguish and redress mistakes. We have introduced this core error detection and correction (EDAC) algorithm with lowdensity parity check (LDPC), Turbo code, Bose Chaudhuri Hocquenghem (BCH) code, Convolutional code, and Shannon’s theorem to our system for increasing the proficiency of EDAC. We have also analyzed their combined form. We have presented a progressed turbo component with two interleaved, five encoding and interpreting forms. All the mechanisms have been implemented in MATLAB with additive white Gaussian noise (AWGN) and Rayleigh channel.
The main contributions of this paper are as follows:

We have proposed an innovative architecture that consists of the EDAC method for the nanosatellites. It has analyzed six camera images simultaneously with the assistance of FPGA.

We have analyzed, and compared the satellites’ error detection and correction algorithms. We have also developed our proposed hybrid approach for EDAC.

We have identified the number of erroneous bits. Based on that, we have developed a syntactic analysis for the error correction method.

We have implemented the scheme for the LDPC, BCH, Turbo, Convolutional, and Shannon’s theorem. The scheme shows that the BER ratio gradually decreases from 10^{−1} to 10^{−6}; on the other hand, system performance increases significantly.

We have discussed the limitations of existing error detection and correction algorithms. We have proposed future work to introduce an advanced error detection method based on satellitetransmitted data using machine learning techniques and to implement the ASIC architecture in Spartan 6 FPGA, a novel approach to improving the accuracy and reliability of nanosatellite data transmission systems.

Finally, we have analyzed the performance of five different EDAC algorithms with AWGN and Rayleigh channels in MATLAB.
The rest of the paper has been organized in the following ways. Section 2 discusses the literature reviews. Section 3 depicts the architecture of the nanosatellite. Section 4 shows the algorithmic investigation and performance analysis of EDAC Mechanism V1.1. Sections 5 and 6 describe the EDAC Mechanism V1.2 and EDAC Mechanism V1.3. Section 7 shows the performance evaluation graphs. Section 8 describes the limitation and future work of EDAC. Finally, Sect. 9 concludes the paper.
2 Related works
Mamun et al. [1] proposed a Hamming Code to prevent parity and singlebit error onboard satellites in low earth orbit (LEO). The focus is to work on EDAC via generating a Hamming Code matrix [4, 11, 16]. MATLAB is used for the implementation process of both singlebit and doublebit errors. Pakartipangi et al. [8] proposed a technique for obtaining more comprehensive coverage area images for low dimensions satellites. The system handles all the error bits using the XULA2 LX9 field programmable gate array board, and the camera array was designed so that overlapping areas cannot be found. Ahmed Hanafi et al. [9] proposed an SRAMbased FPGA technology that implements an onboard computer system and uses lowearth orbit nanosatellites. The system was designed to develop payload architecture and an inherent space environment. Ibrahim et al. [10] proposed a satellite system designed with acceptable accuracy in a lowpower system. This paper presents a concept to establish avionics systems by utilizing crucial features with the available FPGAs. Scrubbing keeps the FPGA data configurations safe with frame calculation and backtracking methods.
Daniel et al. [11] proposed a technique that describes a guideline for simulating the system’s accuracy providing the necessary statistics to support the decision system regarding the necessary methodology to be implemented [11]. The system is designed to monitor air pollution in Mexican and Latin American cities. Wilson at el. [12] proposed two major supervised themes, hybrid computing and reconfigurable computing [12]. The system survey of the imposition and convenience of small satellites also focuses on new technologies, methods and implementation for the next generation [12]. Banu et al. [13] proposed an encryption method to secure terrestrial communication via a small satellite. Increased quantity of sending valuable and sensitive data, a satellite can bring risks of providing access to unauthorized data. An advanced encryption standard method is used to protect data from such threats. Banu et al. [14] proposed a commercial algorithm called Advanced Encryption Standard (AES). To protect sensitive data and prevent unauthorized access in terrestrial communication, 5 modes of AES in satellite imaging have been used. To prevent the fault from noisy channels and the effect of SEUs, the 5 modes were analyzed and observed using Hamming error correction code.
Hiler et al. [2] proposed a parity check matrix and a calculated syndrome of EDAC onboard nanosatellites. The scheme can selfdetect and selfcorrect any single event effect errors during transmission. BENTOUTOU et al. [15] proposed an onboard EDAC method to protect data transmission between the AISAT1 CPU and its memory. Wang et al. [16] mentioned a comparison of correction codes for correcting colossal burst data ruins. Colossal burst errors happen in communication driving to different chosen bit errors. They compare the CCSDS codes, such as RS codes convolution, turbo, and LDPC codes. Gao et al. [17] give thought to LDPC codes for the joint attendant and characteristic broadcasting framework. In this paper, they highlighted an earthbound broadcasting framework called time broadcastingwireless which encompasses China and some other parts of Asia. This framework gives excellent execution results, especially for combined deciphering.
3 Methods
Satellite onboard command data handling structures are shown in Fig. 1. For a lowcost framework of the nanosatellite, a single chip executed onboard command data handling (OBCDH) was proposed for a mixedmode applicationspecific integrated circuit (ASIC) [9]. Future Nano Satellites, which have information handling and control capacities with information collecting and further detecting capabilities for Soil perception Missions, result from ASIC detail. Square graph Fig. 1 comprises 4 subsystems where a 32bit RISC processor center is adjusted for space utilization, a subsystem of picture dealing with the unit, a communication association for the satellite, and a supporting fringe subsystem. OBC is the most component of two scaleddown OBCDH frameworks. To serve an introductory model of the advanced portion of the OBCDH ASIC, this onboard computer framework on a chip Fig. 1. Within the OBCDH, our fundamental need is to upgrade the EDAC framework to have errorfree information on disciple communication.
In EDAC, mechanisms V1.1, V1.2 and V1.3 describe the different approaches to solving the satellite communication error and analyze the performance of different channels. Different EDAC Mechanisms have different bit error rates (BER). If we combine multiple encoding methods in a single one, the BER will be reduced, and the system's performance will be much higher than the single encoding method. We have proposed an architecture comprising the top 5 EDAC methods for the nanosatellites.
4 EDAC mechanism V1.1
Nanosatellites that transmit information to the ground station from their blunders be checked with the assistance of a few calculations. Within the ground station, CRC checks blunder information. After that step, with a sort of blunder, able to get the information indicated by detection methods. Within the location strategies, we figure out whether blunders are shown in our data in case of able to distinguish using three steps like information word codeword generator at that point able to recognize the erroneous bit within the input stream appeared in Fig. 2. We ought to alter our calculations based on our mistakes, agreeing to the measure of mistakes. In these adjustment strategies like Hamming, CRC and Reed Solomon codes, we would present our less error information with the assistance of these adjustment strategies.
4.1 Hamming code
Hamming code could be a direct piece code for blunder location and redress. It can identify onebit or two bits mistakes at the same time and can rectify them as if they were singlebit mistakes. The fundamental concept of the hamming code is to include an equality bit after the stream of information to confirm that the ground station got the information and matches the comparing input information stream. Partisan ground stations check the transmitted information to distinguish where the mistake happened. The structure of the hamming code has a square length, message length, and separation. Square length characterizes as n = 2r − 1 where r > = 2 message length and remove the inclusion 2r − r − 1. Depending on the hamming code adaptation, remove the error bit that got changed. It includes more than one error bit, which can find the blunder’s position and selfcorrect it by altering the bit. Generally, three sorts of hamming codes are utilized in Nanosatellite communication as Hamming [3, 4, 7], Hamming [4, 4, 8], and Hamming [4, 11, 16].
4.2 Cyclic redundancy check
CRC is the method of accepting emerging alter blunders within the communication channel. Satellite information trade is based on CRC codes, and the EDAC process broadly utilized in advanced CRC code is additionally commonly alluded to as polynomial codes 1 on a thin wire. Working on a thin wire is characterized as polynomial checks. The kbit message is considered a polynomial condition list with the words k, from x^{(k−1)} to x^{0}. The most noteworthy arrangement is the coefficient of x^{(k−1)}, the proportionate of x^{(k−2)}, and so on. Test digits are created by rehashing the kbit message x^{n} and partly produced by rm(n + 1) bits polynomial code. The excite n bit adjust is passed as test digits. The same polynomial generator separates the total collection grouping. If the remaining pieces are zero, no mistakes have occurred. If the remaining pieces are not zero, an exchange blunder happens.
4.3 Reed Solomon
Reed Solomon codes work with a burst sort of information mistake. It is also used as a broadcast framework in adjustment code communication, capacity framework, etc. [18]. It recognizes the burst blunder of information transmission and amends those blunder information. If the Reed Solomon codes are utilized at that point, the likelihood of an error remaining within the decoded information will be much lower [19]. Reed Solomon codes are too appropriate for different burst blunder adjustment codes as a grouping of b + 1 sequential mistakes can influence up to 2 signals of measure excite b [20]. The exciting alternative goes to the coding architect and can be chosen over a wide range.
Reed Solomon’s mistake adjustment may be a forwardlooking blunder code [21]. It works with polynomial tests of information. Polynomials have been tried in a few places, and these numbers are either transmitted or recorded.
4.4 Performance analysis of EDAC structure
In this Fig. 3, we have outlined error bits to equality check lattice at that point generator lattice and last adjusted code. To begin with, characterize codeword bits per piece, knead bits per piece, equality submatrix, generator lattice, and paritycheck network. Encode the message and discover the position of the blunder in the code word (list). At that point, the code alters and adjusts the code. After all, evacuate blunder information at that point plot this Fig. 3.
In this Fig. 4, we have planned input and yield messages with the assistance of CRC. To begin with, we take the input and generate the network. At that point, we discover checksum values. After discovering the checksum, we include a checksum to message bits; at that point, we check yield if the update is nonzero, a transmission mistake has happened, and if the update is zero, no blunders happen, no blunders happen. At that point, the plot yield Fig. 4.
In this Fig. 5, we have outlined Reed Solomon code as input and yield messages. Reed Solomon code is utilized to adjust burst blunders related. This code is characterized by three parameters a letter set estimate t, square length excite n, and message length k. Decoder characterizes this area utilizing Reed Solomon’s code see of codeword as polynomial esteem is based on the message encoded. The decoder recovers the encoding polynomial from the gotten message information in Fig. 5.
5 EDAC mechanism V1.2
5.1 Turbo encoding mechanism
The turbo encoder block uses a parallel concatenated coding scheme to encode a binary input signal [22]. Three identical convolution encoders and two internal interleavers are used in this coding scheme Fig. 6. An interleaver is used between systematic convolution encoders, as In Fig. 6. Here, we can hit a rate of 1/3, without puncturing and 1/2, with a form of puncturing [23]. The process of puncturing also obtains other code rates.
5.2 Turbo decoding mechanism
A turbo decoder is applied when turboencoded data is applied to transmission over the AWGN channel via baseband. The LogMap decoding structure offers less complex output than the limit of Shannon with less complexity. The turbo decoder consists of interleaver and deinterleaver separated SISO decoders, as shown in Fig. 7.
5.3 Performance analysis of advance turbo mechanism
Turbo codes are better performance codes that result from the interaction of information between recursive codes and decoders of the constitution in Fig. 8.
Turbo code simulated for Rayleigh faded channel for frame size K = 40. Each SNR’s frame number is 500 to keep the simulation fast.
5.4 Additive white Gaussian noise channel (AWGN)
The AWGN channel is one of the most commonly utilized channels that are demonstrated by large used to show an environment with an exceptionally vast number of added substance noise sources. Most added substance commotion sources in modern electronics are a coordinate result of zeromean warm noise caused by random electron movement inside the resistors, wires, and other components. The AWGN channel may be a wellknown model to demonstrate the line of location (LOS) conditions.
5.5 Rayleigh channel
The Rayleigh blurring model is in a perfect world suited to circumstances with vast numbers of flag ways and reflections [24]. Common scenarios consolidate cellular broadcast communications where there’s a vast number of reflections from buildings and the like, conjointly HF ionospheric communications where the uneven nature of the ionosphere suggests that, in general, hail can arrive, having taken various assorted ways. This proposition uses a moderatelevel independent Rayleigh blurring channel demonstration for the blurring environment [25]. An autonomous Rayleigh blurring handle can be modeled as a steady irregular variable amid each image interim.
6 EDAC Mechanism V1.3
Five Identical EDAC algorithms are used as encoders LDPC, BCH, Turbo, Convolutional, and Shannon’s, and for all the algorithms, random interleavers are used in this coding scheme. Each constituent encoder is terminated by tail bits autonomously. An interleaver is used between five systematic encoders of convolution, as in Fig. 9.
Here, we can hit a rate of 1/3, without puncturing and 1/2, with a form of puncturing. Different EDAC Mechanisms have different bit error rates (BER). If we combine multiple encoding methods in a single one, the BER will be reduced, and the system's performance will be much higher than the single encoding method. We have proposed an architecture that consists of the top 5 EDAC methods for the nanosatellites. Based on communication data EDAC mechanism will be changed. For choosing the coding methods, we used the syntactic machine learning approach. As we know, syntactic analysis finds out the dictionary meaning of any sentence, just like finding the error sequence pattern in a stream of data.
The process of puncturing also obtains other code rates. The algorithm for decoding can be designed by either an A Probability posterior method or a method of maximum likelihood.
Decoder consists of five interleavers and deinterleavers separated SISO decoders, as shown in Fig. 10. Because of noise, encoded output data bit can get corrupted and enter the input of the decoder as r0 for the device bit, r1 for parity1, r2 for parity2, r3 for parity3, r4 for parity4, r5 for parity5. They are fed to the first SISO decoder with these inputs. SISO first, the decoder takes the obtained data bits as input, sequence r0 and parity sequence r1 got, which is RSC generated encoder 1, Sequence of output results.
6.1 Lowdensity parity check (LDPC)
6.1.1 Lowdensity paritycheck encoder
LDPC code design reversible data transmitted is used to LDPC encoder and decoder. A few design methods will be considered to lower the complexity of LDPC code encoding. The technique is to apply the stair code. The ladder structure can be encoded linearly compared to repetitive H decoders. Only a single calculation is required to make the encoder effective by general multiplication. Design circuits perform the aspect of the Tanner graph. The same circuits use the encoding and decoding part. Such functions transfer a lot of promise in a function where the circuit area is limited.
6.1.2 Lowdensity paritycheck decoder
The most effective decoders for LDPC codes can be realized by applying repeat messagepassing decoders [26]. LDPC code represents by parity check matrix H. Tanner’s graph is a graph presentation of LDPC, parity matrix. Tanner graph using defined sets of nodes. First variable nodes refer to a single bit of valid code word x with the length of the bits. The second set represents the checking node. Constraint a flexible agreement trust extension decoder transmits the probability between checks nodes and variable nodes. This is data transfer local data using finding solutions to a difficult overall complication with less complexity. However, for this type of application, it is necessary to save all the code words that search for 2K code words, which are increasing significantly [27]. Faith Promotion Decoder uses repeat messages to pass checks to search for code word X and bit nodes.
6.2 Performance analysis of LDPC
AWGN Channel is considered to perform in the best possible way; the only reason is to reduce the power of the channel [28]. The performance of LDPC on AWGN channel in 11. Performance of LDPC codes 10^{3} on AWGN channel at SNR = 0 dB and BRR 10^{−1} at the same SNR is not for any higher coding than the original. Rayleigh fading is considered the worstcase scenario as there is no effective way. Due to the functionality of the LDPC codes of the relay channel 12, multiple received signals are due to events such as reflection, scratching, and [29]. For example, a comparison of curves in SNR = 5 dB implies that the code is BER 10^{3} for coding and not BER 10^{−1} for no coding. Figure 11 and 12 show the effectiveness of LDPC codes on AWGN, Rayleigh channel. Here the curves are displayed at the same SNR = 2 dB BER, respectively 10^{−4}, 10^{−1}. The results show that the AWGN channel provides the best performance for the LDPC. It is almost impossible to encounter AWGN channels in reallife applications. In most cases, we have to consider the Rayleigh Fading system that should be built and keep in mind the effects of the Rayleigh channel.
6.3 Bose Chaudhuri Hocquenghem (BCH) codes
6.3.1 BCH encoder
Codewords are shaped by including the leftover portion after dividing the message polynomial with the generator polynomial. They are products of the generator polynomial. The generator polynomials are not ordinarily part of the encoding side because they will request more equipment and control circuitry. The polynomial is utilized as such for encoding [30]. The generator polynomial for BCH is given by 1 + x^{3} + x^{4} + x^{5} + x^{9} + x^{12} BCH codes are executed as efficient cyclic codes. Consequently, it can be effectively actualized, and the rationale which actualizes the encoder and decoder is controlled into move enrol circuits. The leftover portion can be calculated within the (n−k) straight arrange move registers with the input association at the coefficient of the generator polynomial. LFSR is initialized with seed esteem 0.
6.3.2 BCH decoder
The interpreting handle of the BCH codes comprises three steps. The disorder computation preparation creates 2t disorders from the gotten code word, which is the data information concatenated with the equality information. At that point, the blunder locator polynomial is computed from the disorders of which the roots point out the blunder positions. Inevitably, the mistakes are adjusted by thoroughly finding out the roots of it utilizing the look calculation. If there is no blunder within the square, we require not one or the other to assess the mistake locator polynomial nor conduct the chain look handle. In this way, to decrease the interpreting time, it is exceptionally important to recognize whether there’s any blunder or not as early as conceivable. Here, we propose to check the mistake event with a disorder polynomial by reusing the encoder, which, as it were, requires the GFD, whereas the routine blunder location strategy employments the disorder values, which require a much longer time for conducting a few diverse CGFMs.
6.4 Performance analysis of BCH code
Figure 13 and 14 show the BER plots vs. threshold SNR. For BCH code for two values of average SNR λ_{0}, 10 dB and 20 dB, with different Doppler frequencies. From the figures, it is clear that an increase in the performance of the BCH code occurs. For large values, the errors tend to be more random as the transition probabilities b and g increase leading to good performance since the BCH code is capable of correcting such random errors.
6.5 Convolutional codes
6.5.1 Convolutional encoder
Inside the encoder, data bits are input to a move enlist of length K, called the elemental length. As each bit enters at the cleared out of the select, the past bits are moved to the proper to show disdain toward the truth that the primary orchestrated bit inside the select is evacuated. Two or more twofold summing operations, let’s say r make code bits that leave inside the center of one data stream period.
In this way Fig. 15, the code bit rate is 1/r times the data rate, and the encoder is called a rate 1/r convolutional encoder of confinement length K. It also requires to completely characterize the encoder are the affiliations from stages inside the move select to the r summing squares. These generator vectors may be communicated on a very basic level as a push of K parallel digits.
6.5.2 State diagram
The convolutional encoder shows an outline with K = 3, r = 2, and the generator vectors are chosen accordingly. Discrete looking at times are labeled n. The data stream enters on the cleared out and the show bit at time n, the first afterward bit n − 1, and the taking after a most reliable bit at n − 2 have the move to enlist. Two balance bits are traded out inside the between times between n and n − 1 from the upper snake and, after that, the lower one. When the takingafterdata bit arrives, the move select moves its substance to the proper. The K − 1 earlier bit, in this case, two, choose the state of the encoder. They appeared in gray at 15. In convolutional encoder, there are 2K states. For each encoder state, there are two conceivable comes about of yield code bits, depending on whether the input bit is zero or one. At that point, the advancement of states in time can be a work of the information stream. The development of states in time, at that point, may well be a work of the information stream Fig. 15. Each state appears inside a circle, and the alteration from one state to another is shown up by a jar, recognized by the input bit, cut, and yield code bits.
6.5.3 Convolutional decoder
Convolutional codes are frequently alluded to as trellis codes due to the reality that trellis charts can effortlessly portray them. The code's trellis chart records the encoder's diverse states and how they are connected. The trellis structure for the state diagram of 16 state diagram appeared in Fig. 16. Trellis structure for a fourstate encoder. There exist two straightforward approaches to translating a transmitted arrangement of bits.
The Viterbi calculation can be utilized by utilizing two primary procedures. The direct approach employs the difficult choice of the received noisy data bits by thresholding the information to parallel digits and applying the calculation. In contrast, the moment approaches employments delicate choice to translate the lead by finding the way among all the ways of the trellis, which has the most significant matrix.
6.6 Performance analysis of convolutional code
For the event, at an SNR regard of 5 dB, a bit botch rate of 10^{−5} was gotten. In this regard, 1 bit got in a blunder for 100,000 bits sent. This was far off predominant when the SNR was 2 dB with a bit bumble rate of 10^{−1}. That’s 1 bit gotten in botch when 10 bits were sent. For the theoretical BER, the SNR ranges of 2 dB, 2.5 dB, and 3 dB had a bit botch rate of 10^{−1}, whereas, inside the mirrored BER, the SNR was observed to be of the expand 2 dB, 2.5 dB and had the same regard of BER of 10^{−1} whereas the SNR of 3 dB of the imitated BER had an advanced BER of 10^{−2}. This was a result of the convolution coding displayed. Another characteristic was obtained by considering the incline of the hypothetical and imitated regard gotten as in Figs. 17 and 18.
6.7 Shannon’s theorem
6.7.1 Shannon’s encoding
The included repetition increments the flag’s length but permits a more prominent location and adjustment of mistakes amid the translating preparation. Common causes of channel coding incorporate the utilization of equality check bits and redundancy codes. An equality check bit is essentially an additional bit that’s included in a twofold sequence such that there’s an indeed number of 1 s. If an arrangement with an odd number of 1’s is gotten, at that point, the decoder can identify that a blunder has happened amid transmission through the channel.
6.7.2 Shannon’s decoding
The yield of the channel is, at that point, gotten by a decoder, which attempts to change over the gotten flag back to the first message. At that point, at long last, the yield of the decoder is sent to the ultimate client or goal, which is alluded to as the data sink [31]. W speaks to a message. We’ll regularly consider that it is the yield of the compressor. The encoder gets W and encodes it to X_{n}. The encoder puts X_{n} into the channel, and Y_{n} is the yield the decoder gets. At long last, the decoder tries to appraise W through Y_{n}. W_{c} signifies the decoder’s appraisal. Our objective is to get what kind of encodings are such that W_{c} is the same as W with tall likelihood and n is as little as conceivable.
6.8 Performance evaluation of Shannon’s theorem
In Figs. 19 and 20, AWGN Channel and Rayleigh fading, we have used Shannon Theorem. The higher theory is a scale that can be loaded with a BER, with an enabled central signal above the B Hz bandwidth affected by the channel. The term “unfairly BER” means that it has provided conditions for the theorem to be met; in any given BER, no matter how small, we can find the coding process that benefits this BER. The smaller the BER given, the harder it will be processed. The least accessible bit rate is called channel capacity C. S/N is a square signal, meaning the sound ratio and logarithm are in base 2.
7 Results and discussion
In analytical Figs. 21 and 22, we apply two types of noise, Rayleigh Channel and AWGN channel, for all algorithms. AWGN Channel is considered to perform in the best possible way and the only reason to reduce the power of the channel. Rayleigh fading is considered the worstcase scenario as there is no effective way. Here, we can see that LDPC, Turbo, Convolutional, BCH, and Shannon’s Theorem and these algorithms are best performing for different types of data. Some algorithms are good for less data, and others are better for more data. LDPC works better when signal noise is increasing. Convolutional code works best when signal noise is medium, and the bit error ratio is 10^{−3}.
LDPC works better for the AGWN channel. We transmitted data continuously using machine learning techniques and which type of data was best for which algorithms and identified more error data and removed error data in less time.
8 Limitations and future works
We used multiple algorithms to reduce data transmission error, but these algorithms were limited like an LDPC cannot detect all types of bits errors. LDPC adds extra bits per conversation that have been transmitted through the satellite data transmission system. Turbo code affects singlebit error correction and also detects multiplebit errors. If numerousbit error detection is in this code, turbo code can only solve singlebit error correction. A BCH is not suitable for security purposes. BCH is more complex than a checksum and takes more processing. A strong BCH might run slowly in software. But Reed Solomon codes are not efficient as BCH codes. It cannot provide satisfying performance without BCH codes in BPSK modulation schemes.
In the future, we would like to introduce an advanced error detection method based on satellitetransmitted data. Detection algorithms will be changed depending on data size, type, and importance. It might reduce the time of the EDAC process and get reliable, safe data faster. Predicted the less error mechanism in a different type of data. We may use the machine learning technique to find fewer error paths. We implemented the ASIC architecture in Spartan 6 FPGA. After all, we collaborated on our system architecture with Bangabandhu Satellite1 to have a more secure and faster data transmission.
9 Conclusions
In this article, we have emphasized different EDAC techniques and code correlation. The proposed approach has attracted the research community. This paper also represents an analytical approach to EDAC algorithms for nanosatellite data transmission systems. Using more complicated error detection and correction codes, the prototype can be expanded for multibit errors. The ground station of nanosatellites is continuously maturing and growing impressively. Space technology is continuously evolving and growing in significant ways. All the methods and systems are updated day by day. The automation progress of satellite memory chip architecture is becoming more and more promising, principally with the evolution of nanotechnology.
Availability of data and materials
The data set used and/or analyzed during the current study are available from the corresponding author upon reasonable request.
Abbreviations
 EDAC:

Error detection and correction
 FPGA:

Field programmable gate array
 AWGN:

Additive white Gaussian noise
 EO:

Earth observation
 LDPC:

Low density parity check
 BCH:

Bose Chaudhuri Hocquenghem
 LEO:

Low earth orbit
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The Institute for Advanced Research Publication Grant Ref has supported this research. No. IAR/2021/P ub/013 from United International University.
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All authors contributed to the research conception and design. Data collection was done by MH. Methodology designs were done by MI and MH. Original draft preparation, including review, response and editing, have been done by MI, MH, ZAB. The research has been supervised by MI. All the authors have read and approved the final manuscript.
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Islam, M., Hasan, M. & Bhuiyan, Z.A. An analytical approach to error detection and correction for onboard nanosatellites. J Wireless Com Network 2023, 49 (2023). https://doi.org/10.1186/s1363802302259y
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DOI: https://doi.org/10.1186/s1363802302259y
Keywords
 Error detection and correction
 Lowdensity parity check
 Bose–Chaudhuri–Hocquenghem codes
 Turbo codes
 Convolutional codes
 Shannon’s theorem
 Earth observation
 Field programmable gate array
 Onboard command data handling