Channel Coding for Multimedia Transmission on High-Speed Flying Devices

– Communication systems for high-speed ﬂying devices, such as drones and missiles, have performances with error-ﬂoor caused by the Doppler effect, which causes inter-carrier interference (ICI) and destroys real-time data transmission. Channel coding cannot reduce error-ﬂoors, but channel coding may still achieve performance with turbo-cliff. This paper proposes a broadband communication system for high-speed ﬂying devices using soft 4 quadrature amplitude modulation (4-QAM) modulations with the optimal threshold S for practical implementation assuming that the maximum/minimum log-likelihood ratio (LLR) values of ± 709 . We use orthogonal frequency division multiplexing (OFDM) with low-density parity-check (LDPC) codes as the channel coding scheme and minimum mean squared error (MMSE) equalization. To reduce the computational complexity and to keep the data rate high, we use only a single pilot for the channel estimation. Computer-based simulations for several high speeds are performed to evaluate the performance of the proposed high-speed ﬂying devices system. The bit error rate (BER) performance is evaluated based on LLR under additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. The results conﬁrmed that the proposed system with the optimal threshold S can avoid unstable jumping error with better turbo-cliff and lower error-ﬂoor. The maximum speed the system can achieve for BER of 10 − 2 is 400 km/h. The results of this paper are expected to contribute signiﬁcantly to the development of communication systems on ﬂying devices.


I. INTRODUCTION
Wireless communication is widely used for communication systems on mobile devices, such as high-speed flying devices like drone or missile. However, movement in a wireless communication system can cause the Doppler effect. The Doppler effect causes the frequency shifting, causing intercarrier interference (ICI), which is damaging the data. The frequency shift depends on the relative speed of the transmitter and receiver of the devices and the carrier frequency used. The greater carrier frequency and speed can make the shift of the frequency also greater, and vice versa [1]. The Doppler effect also causes channels to be timevarying or time-selective fading, i.e., channel that change rapidly time-by-time [1]. If the rapid change to this channel cannot be captured at the receiver, an error-floor appears. The error-floor appears because the captured signals are equalized using the wrong channel.
Some high-speed flying devices can receive and transmit multimedia data in real-time by utilizing broadband wireless communication systems, which have high data-rate. Broadband communication systems transmit data in multiple paths or multipath. However, the problem with multipath data transmission is multipath fading as shown in Fig. 1. Diffracted waves can also cause the waves that arrive late. These late waves can interfere with the other waves or vice versa, called inter-symbol interference (ISI) [2].
The multipath fading can be slightly overcome by parallel transmission. Orthogonal frequency division multiplexing (OFDM) is the most implemented multicarrier transmission scheme [3]. OFDM is widely used for digital transmission because it can correct errors due to multipath fading [4]. The use of the OFDM technique can still produce errors because OFDM is vulnerable to frequency shifts caused by the Doppler effect and phase noise called ICI [5] and causes error-floor. The uses of channel coding cannot reduce errorfloors, but channel coding may still achieve performance with turbo-cliff. Channel coding has various types, one of which is the low-density parity-check (LDPC) codes. Robet Gallager invented LDPC codes in his PhD thesis in 1962 [6]. After 30 years of neglect due to the lack of computing power, MacKay and Neal developed the LDPC codes [7].
LDPC codes is chosen because it has a better performance than Turbo codes which is known to have a performance close to Shannon limit [8]. LDPC is also widely used for high-throughput and real-time communications [8]. LDPC also has a good ability on moderate (∼400) and large block size (∼6144) [9]. To achieve bit error rate (BER) performances that are close to channel capacity, the LDPC codes must have thousands of bits of LDPC codes block length N LDPC [10].
We consider using LDPC codes with the structure of the second generation digital terrestrial television broadcasting system (DVB-T2) because this flying devices also have functions for sending and receiving multimedia data. However, DVB-T2 LDPC codes has a block length N LDPC = 16200 and N LDPC = 64800 and requires a long process and high complexity in the encoding and decoding process. Because flying devices has limited battery lifetime, the communi-cation system requires low computational complexity of the encoding and decoding process. Therefore, we consider downscaled DVB-T2 LDPC codes, which has a short block length. In research [11], they simplified the DVB-T2 LDPC codes with downscaling technique from N LDPC = 16200 to N LDPC = 270.
However, some devices have limitations in performing calculations. This limitation causes the LLR to be infinity and unstable jumping error. In [12], Hamdi et al. researched and proposed the best d p for fifth generation new radio (5G-NR) [12] communication to solve this problem.
In this paper, we proposes a broadband communication system for high-speed flying devices using soft 4 quadrature amplitude modulation (4-QAM) modulations with the optimal threshold S for practical implementation helped by DVB-T2 LDPC codes. The optimal threshold S is used to avoid the unstable jumping error with better turbo-cliff and lower error-floor.
The rest of this paper is organized as follows: Section II describes the materials and method that used in this paper. Section III describes the performance of the proposed system. Section IV concludes the paper. Fig. 2 shows a communication system model on a highspeed flying devices from the transmitter (T x ) to the receiver (R x ). We used downscaled DVB-T2 LDPC codes from [11] for the channel coding. We also used 4 quadrature amplitude modulation (4-QAM) modulation and OFDM as the transmission scheme. Fig. 2 shows information source b generated randomly. The bits are encoded by block "C" into block "V" with block interleaver Π x . The encoding process changes the bit information b to codeword c. The codeword enters the modulation process using the 4-QAM modulator "M", and forms a symbol χ. 4-QAM generates a modulation symbol that has a pair of information bits in each symbol χ [13]. After the symbol is modulated, the symbol is transformed from frequency domain to time domain using block "IFFT" and produces symbol κ κ κ. The block "CP" function is adding a cyclic prefix (CP), forms a symbol x. Then, The symbols are sent through the channel. This paper uses the additive white Gaussian noise (AWGN) and multipath Rayleigh fading channel models.

A. System Model
Received information symbol y experiences channel distortion and defines where n is noise vector, h is 1 for the AWGN channel and the random complex number for the multipath Rayleigh fading channel which can be expressed by where A and B are each normally distributed random numbers with zero mean and j = √ −1. The blok "CP removal" function is removing CP that has been added in the symbol y from block "CP" and forms a new symbolκ κ κ.
The symbolκ κ κ can be expressed bŷ where H c is circulant matrix. Then, the symbolκ κ κ is transformed using the block "FFT" to return the symbol to the frequency domain and create the symbol q before entering the equalizer block "EQ". Symbol q can be expressed by where F is fast Fourier transform (FFT) matrix, F H is inverse fast Fourier transform (IFFT) matrix. In the block "channel estimation", channel estimation is carried out using the pilot-assisted channel estimation technique, which producesĥ and become an input for the block "EQ". Furthermore, the equalization process on the equalizer uses minimum mean squared Error (MMSE) to produce the outputχ symbol for the equalizer. Theχ symbol can be expressed bŷ where w is coefficient of the equalizer and it can be expressed by whereψ * is complex conjugate of ψ and ψ can be expressed by This paper uses a soft decoding technique as decoding technique. Theχ symbol is demodulated with the 4-QAM demodulator "M −1 " to create the log-likelihood ratio (LLR) L and be the input for the LDPC codes decoder. The iterative decoding process in the LDPC decoder is carried out by block "V", deinterleaver block Π −1 y , block "C", and interleaver block Π y .
The method of decoding LDPC codes uses the sumproduct algorithm (SPA) algorithm. This step aims to return the L in the form of information bitsb and determine whether the received bits are the same as the transmitted bits, then the BER is obtained. BER calculation P b in AWGN with 4-QAM can be expressed with [2] where E b /N 0 is normalized signal-to-noise ratio (SNR). BER calculation P b in multipath Rayleigh fading with 4-QAM can be expressed with [2] Fig. 3 The illustration of the angle between the transmitter and the receiver that causes the Doppler shift.

B. Doppler Effect
The Doppler effect occurs when a transmitter or receiver experiences movement at a relative speed which causes the frequency shift. The frequency shift that happens f d can be calculated by where v is the relative velocity (m/s), c is the speed of light (m/s), f c is the carrier frequency (Hz), and θ is the angle between the transmitter and receiver. The shift also depends on the size of θ. If the θ is between 0°and 90°, the received frequency is positive and greater than the carrier frequency. When the θ and between 90°and 180°, the received frequency is negative and smaller than the carrier frequency, as shown in Fig. 3.
where T s is symbol duration and can be obtained by where B sc is subcarrier spacing and κ is sample. Then, f d T s can be expressed by

C. Low-Density Parity-Check (LDPC) Codes
The form of the parity check matrix matrix H LDPC codes are adjusted to the number of column (N ) in matrix H equals to codeword c, the number of row (K) in matrix H equals to messages bits b, redundancy bit (M ), degree of check node (d c ) (i.e., the number of "1" in one column of the matrix), and the degree of variable nodes (d v ) (i.e., the number of "1" in a row of the matrix) with then matrix H has the dimensions M × N . Each row in matrix H represents a Check Nodes (CN) and each column in H represents a Variable Nodes (VN). The encoder uses the Generator Matrix G LDPC codes to create the codeword. The matrix H is created based on where ∆ is binary matrix (N −K)×K and I N −K is identity matrix with order N − K. If the form of the matrix H has been obtained, then the matrix H is obtained with form [14] where ∆ T is transpose ∆. Then, the codeword c is obtained with LDPC codes come in two forms. Regular LDPC codes have a constant d c and d v in each row and column [15]. Irregular LDPC codes have a varied d c and d v in each row and column [15]. Irregular LDPC codes also have higher girth than Regular LDPC codes. It makes Irregular LDPC codes have better performance than regular LDPC codes.
The matrix H can be represented in a bipartite graph with a Tanner graph [16]. Tanner graph has an edge interleaver that connects VN and CN, if and only if VN and CN have a relationship that is indicated by a non-zero on the matrix, as shown in Fig. 4. VNs and CNs are connected if the element of matrix H is "1".

D. DVB-T2 LDPC codes
Based on [17], the parity check matrix H DVB-T2 LDPC codes has N LDPC = 16200 and N LDPC = 64800 that has the following characteristics: • The information section has a cyclic structure. This characteristic can be implemented in encoders and decoders based on partly parallel processing architecture • The parity section has a staircase structure. This characteristic can be used to form parity bits with an accumulator. DVB-T2 LDPC codes has code rates effective R e = The matrix H has a dimension that can be determined by The matrix H can also be represented by In this paper, we consider use downscaled DVB-T2 LDPC codes from N = 16200 to N = 270 [11]. Downscaled DVB-T2 LDPC codes is used because it has lower complexity than LDPC N = 16200. This is intended to speed up the encoding and decoding process. Table I shows the dimensions and bits of information that can be sent for each R e .
Degree distributions of downscaled DVB-T2 LDPC codes is denoted by Λ(x) and Ω(x) for each variable node degree (VND) and check node degree (CND). The degree distributions are used by this paper for each code rates are same like the degree distributions that used in [11].

E. Sum-Product Algorithm (SPA)
SPA has better performance compared to other decoding techniques in LDPC codes [18]. SPA works on connected VNs and CNs by sending messages over the connection [19]. Each VNs sends LLR to the connected CNs. CNs process the LLR that the connected VNs have sent, and the CNs can predict each VN. Each connected VN process and add all the predicted LLR by CNs to produce a more precise LLR. This is the first iteration. This iteration keep continues until it meets the stop criteria until the LLR for each VN approaches "+1" or "−1".
The output of each VNs and CNs can be called extrinsic LLR L E as shown in Fig. 5. L Ev is from VNs and L Ec is from CNs. After interleaver or deinterleaver, L E is sent to VNs or CNs as a priori LLR L A . L Av is sent to VNs and L Ac is sent to CNs.
The operation in VN as shown in Fig. 6(a) can be expressed by [11]  in the first iteration, the L Av is 0. Then the operation in CN as shown in Fig. 6(b) can be expressed by [11] L Ec i (n) = dc n j=1,j =n but (22) can be simplified by some mathematical manipulation, and can be written as [19] L Ec i (n) ≈ sgn L Ac j · sgn L Ac j+1 {} · min L Ac j , L Ac j+1 (23)
This can be a problem in (32) ifχ falls right on the boundary line because the σ approaches 0 which causes infinite LLR, as Fig. 7 shows. In [12], Hamdi et al. researched and proposed the best d p for fifth generation new radio (5G-NR) [12] communication to solve this problem. The d p obtained still has to be optimized, which aims to minimize the P b , with the function [12] −710 < d 2(d p ) 2 < 710. (34) In [12], the σ is d p if d < d p . However, the performances using d p have no improvement. This paper proposes threshold S to solve this problem. Equation (32) is proposed to be changed to , otherwise.
This method also applies to L c2 . Fig. 8 shows the process of finding the best threshold S at range 0.0001 − 1. Fig. 8 shows that the threshold S = {0.0001, 0.001, 0.01} experienced an increase in BER at SNR γ = 30 dB and the best performance is at S = 0.1. To find out if there is a threshold S that is better than threshold S = 0.1, then an observation for the threshold S is performed again with a narrowed range, at 0.1 − 1 as shown in Fig. 9. Fig. 9 shows that, at threshold S = 0.5 has a better performance than the performance of threshold S = 0.1. An observation like this applies to all code rates. The results show if the threshold S cannot be set too small closer to 0 because it causes infinite value of LLR. On the other hand, is the S value is set too high, e.g. S = 1, the demapper just introduce additional errors. Therefore, the optimal threshold S should be carefully searched. The threshold S is needed practically in the field, for example because of the limitations of hardware which cannot calculate exponent above +709 or below −709. Table II shows the proposed threshold S in this paper. Table III shows the parameters used in this paper. We simulate the system at a maximum speed of 2450 km/h, which means we also look maximum speed of this system can achieve BER 10 −2 . We also use only one pilot symbol, which is located at the first position. It aims to test the system in the worst conditions by using only one pilot symbol.

A. Performance of LDPC Codes
We simulate the performances of DVB-T2 LDPC codes N = 270 on the AWGN channel, as shown in Fig. 10. In this figure, the horizontal axis represents the SNR, and the vertical axis represents the BER of transmitted bits. We simulate with maximum SNR γ = 10 dB and maximum LDPC iteration at 50. The R e = 4 9 has the best performance. To obtained BER performance 10 −4 , R e = 4 9 at SNR γ = 2.615 dB and R e = 37 45 at SNR γ = 6.7 dB. Systems with the DVB-T2 LDPC codes N = 270 has a better performance of around 8.375 dB for R e = 4 9 and 4.65 dB for R e = 37 45 than systems without channel coding at BER 10 −4 .
As shown in Fig. 11, we simulate with maximum SNR γ = 30 dB and maximum LDPC iteration at 50 on the multipath Rayleigh slow fading. We assumed the channel  better performance of around 21.24 dB for R e = 4 9 and 11.74 dB for R e = 37 45 than systems without the channel coding at BER 10 −4 . Fig. 12 shows the BER performances against f d T s of the proposed system with DVB-T2 LDPC codes N = 270. We simulate the system with SNR γ = 20 dB and maximum     The system with LDPC codes cannot reduce the error when f d T s ≥ 0.195 and all the code rate have same perfomance with the system without channel coding. The results show channel coding cannot reduce the errors and error-floor if the system is experienced in high speed. Fig. 13 shows the performances of DVB-T2 LDPC codes N = 270 on a high-speed flying devices with a maximum speed of 2450 km/h. We simulate the system with a maximum SNR γ = 35 dB and maximum LDPC iteration at 50. We assumed the channel model h = [1 0.7 0.5 0.3]. When the system experienced at 70 km/h, the system wihout channel coding cannot achieve BER 10 −4 , but LDPC codes with R e = 37 45 can achieve BER 10 −4 and can reduce the error-floor. When the system experienced at 160 km/h, the system wihout channel coding cannot achieve BER 10 −3 , but LDPC codes with R e = 4 9 and R e = 37 45 can achieve BER 10 −3 and can reduce the error-floor. When the system experienced at 400 km/h, LDPC codes with R e = 4 9 and R e = 37 45 can achieve BER 10 −2 and can reduce the errorfloor. Systems with high speed such as 2450 km/h have high errors. Even systems with LDPC codes unable to fix errors significantly. The results show channel coding can reduce errors and error-floor when the system is moving with low speed. When the system is moving with high speed, e.g. 2450 km/h, the channel coding cannot reduce the errors and error-floor.
B. Performance with Threshold S Fig. 14 shows the performances of the DVB-T2 LDPC codes N = 270 with threshold S and without threshold S on multipath rayleigh slow fading and fast fading. In fast fading, we use a speed of v = 400 km/h. The curve of the system without S threshold is increasing at SNR γ = 15 dB and is unstable in slow fading. In fast fading, the system curve without using S threshold is increasing at SNR γ = 15 dB and continue to rise without decreasing. This is due to the σ is closer to 0, which produces infinite LLR and causes unstable jumping error.

IV. CONCLUSION
This paper has proposed a high-speed flying devices system with the optimal threshold S for practical applications helped by DVB-T2 LDPC codes such that multimedia transmission from the high-speed flying devices is possible for BER less than 10 −2 . This paper confirmed that the DVB-T2 LDPC codes N LDPC = 270 can provide good communication performances of flying devices with speed up to 2450 km/h. The proposed optimal threshold S with LDPC codes can improve performance and reduce errorfloor at f d T s below 0.055. The maximum achievable speed that cause error-floor less than 10 −2 is 400 km/h. This paper has also found that the optimal threshold cannot be set too small S < 0.1, because it causes the infinite value of the LLR. On the other hand, if the treshold S > 0.875, the demapper just introduce additional errors. Therefore, the optimal threshold S should be carefully searched. The results of this paper are expected to contribute to the development of communication systems in high-speed flying devices by sending multimedia data in real-time.