Study on AR4JA Code in Deep Space Fading Channel

Transcription

1 01 7th International ICST Conference on Communications and Networking in China (CHINACOM) Study on AR4JA Code in Deep Space Fading Channel Hui Li 1, Jianan Gao,Mingchuan Yang 1 *, Member, IEEE, Gu Lv 1, Ming Li 1, Qing Guo 1 1. Communication Research Center, Harbin Institute of Technology, Harbin, Heilongjiang Province,150001,China. Dept. of Environmental Engineering, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu Province,1003,China Abstract Because of good systematicness of its parity check matrix, linear relationship between the minimum distance and code length, and inheritance of punching property of ARA(accumulate repeat accumulate) code, AR4JA (accumulate-repeat-4-jagged-accumulate) code is thought to be the most suitable error correction channel code for deep space reliable communication in the future. Given that the accurate channel model of deep communication environment is lacked, in the paper, the absorption, reflection or other uncertain effects of different kinds of particles in aerospace were described with Rician fading model. Then the performance of AR4JA code in deep space Rician fading channel with BP algorithm and Min-Sum algorithm were studied in the paper. Simulation results show that in Rician fading channel, compared with BP algorithm, Min-Sum algorithm declines decoding complexity with few gain loss, which is beneficial to realize miniaturization of deep space communication receiver. Through further analysis, relationship of iteration times of Min-Sum algorithm and SNR is also given for the better use of decoding AR4JA codes by Min-Sum algorithm. Index Terms deep space communication; AR4JA code; Rician fading channel; Min-Sum decoding algorithm I. INTRODUCTION Deep space exploration is exploration activities to universe in the deep space environment whose distance from earth is greater than or equal to 10 6 km.. As critical parts in deep space exploration, deep space communication system has a great influence. Feature of deep space communication channel is that received SNR (signal to noise ratio) is very low, while the available channel bandwidth is relatively wide. In order to communicate reliably in this power limited channel, using channel error correction coding technology to improve system gain is indeed necessary. At present, Turbo code and LDPC (Low Density Parity Check) code are the latest and most important kinds of channel error correction coding [1]. ESA (European Space Agency) used data transmission equipment based on Turbo code in its first lunar detector SMART-1 which was launched in Sep 003 []. And its Rosetta program used Turbo code too. However, compared with Turbo code, a well designed LDPC code s performance is superior to that of Turbo code in the case of long code [3]. LDPC code has several good characters such as supporting parallel processing, far decoding speed, high design freedom in order to get a balance between decode threshold and error smooth layer. Therefore, LDPC code is more suitable for deep space communication field. In 007, CCSDS (Consultative Committee for Space Data System) published a LDPC code encoding standard, among which an AR4JA code group including three code rates and three code lengths was suggested to be used in deep space environment [4]. AR4JA code is a subclass of LDPC who has several advantages. Such as, it has a good systematicness, and it can encode easily, improve code rate by punching, increase minimum distance linearly [5]. Accordingly, using AR4JA code as deep space communication channel error correction coding is a kind of trend. However, the research on the AR4JA code is just in the start stage. And nearly all the analysis on AR4JA code focused on AWGN channel. In fact, the absorption, reflection or other uncertain effect of different kinds of particles in aerospace must cause a certain extent signal fading. So in this paper, Rician fading channel is used as the model of deep space fading channel. And the characteristic of AR4JA code is studied in the paper. II. AR4JA CODE CHARACTERISTIC ANALYSIS A. AR4JA protogragh analysis AR4JA code originated in RA(Repeat-Accumulate) code and IRA(Irregular-Repeat-Accumulate) code. At present, it is proved that binary IRA code can achieve the same superior performance with irregular LDPC code [6]. While, its coding complexity is much lower than LDPC code. But in order to achieve good performance, IRA code usually has a high demand of nodes, thus increases the decoding complexity requirements. ARA(Accumulate-Repeat-Accumulate) code which was invented by A.A bbasfar in 004 can encode easily, improve the code rate through punching, and get good performance even the requirements of node degree is not high [7]. However, the minimum distance of this kind of code does not grow linearly with the code length. In order to solve this disadvantage, ARJA code and its subclasses are generated. Fig. 1 is the protogragh of AR4JA code, where refer to variable nodes, + refer to check nodes, refer to variable nodes that will be removed, connection between variable nodes and check nodes represents the degree of nodes. *Corresponding author: Mingchuan Yang; mcyang@hit.edu.cn /1/$ IEEE

2 n C D E F. Fig. 1 AR4JA code group protograph. In the protogragh of ARA code, the number of variable nodes whose degree is is equal to the number of inside check nodes who are connected with those variable nodes. If using variable nodes whose degree is 3 to take the place of parts of variable nodes whose degree is in the protogragh of ARA code, the resulting code is ARJA (Accumulate-Repeat-Jagged- Accumulate) code. This kind of code is the improvement of ARA code, and the minimum distance of it grows linearly with the code length. For example, in Fig. 1, the degrees of variable node A and B are both in the protogragh of ARA code, while the degree of variable node A becomes 3 in the protogragh of ARJA code. If the repeat time after precoding is 4, ARJA code becomes AR4JA code. For example, in Fig. 1, the degrees of variable node C, D, E and F are all 4, which mean the repeat time is 4. By inference, if the degrees of them turn into 3, then ARJA code becomes AR3JA code. From Fig. 1, it can also be obtained that the code rate of AR4JA code is R (n+1)/(n+), that is, AR4JA code can get 1/ or higher code rates. (a) (c) (b) Fig. (a) code rate 1/ AR4JA code protogragh, (b) code rate/3 AR4JA code protogragh, (c) code rate /3 AR4JA code parity check matrix diagram. Fig. (a) is the protogragh of AR4JA code whose code rate is 1/, Fig. (b) is the protogragh of AR4JA code whose code rate is /3, and Fig. (c) is the parity check matrix diagram of AR4JA code whose code rate is /3 referred to Fig. (b). Seen as Fig. (a), AR4JA code whose code rate is 1/ is the simplest one in the AR4JA code group. And by comparing it with AR4JA code whose code rate is /3, it is clear to get the AR4JA code characteristics. By contrasting (a) and (b), it can be drawn that variable node 1 and are new nodes, that is, add nodes. Then comparing with Fig. 1, when n each increases by 1, add nodes are increased in the protogragh. So it can draw a conclusion that AR4JA code has a good systematicness. In Fig. (c), it can be seen that variable nodes in AR4JA code protogragh correspond to the columns in the parity check matrix, check nodes correspond to the rows in the A B parity check matrix, and the intersection point of each column and row is the degree between corresponding variable nodes and check nodes. For instance, if the degree is 0, it corresponds to the zero matrix; if the degree is 1, it corresponds to indentity matrix; if the degree is, it corresponds to interwoven matrix whose degree is, and so on. Considering Fig. (a), (b), (c) together, it concludes that when n increases by 1, add nodes are increased, then columns are increased in the left of the original parity check matrix corresponding to the add nodes. Then it can draw that the parity check matrix structure of AR4JA code also has a great systematicness, which means using only one encoder and one decoder can achieve the encoding and decoding work of AR4JA code whose code lengths and code rates are different. And when the code rate increases, iterative decoding threshold does not change much. B. CCSDS recommended AR4JA code structure In the orange book released by CCSDS in 007, nine kinds of AR4JA codes used in deep space environment are defined. The parity check matrix of the simplest one is given as (1). OM OM IM OM IM 1 (1) H1/ IM IM OM IM 3 4 IM 5 6 OM 7 8 I M where, O M means the M M dimension zero matrix, I M means the M M dimension indentity matrix. TABLE I shows the detail of the value of sub matrix size M. TABLE I AR4JA CODE PARITY CHECK MATRIX SUB MATRIX SIZE M Information Sub matrix size M bits length k r1/ r/3 r4/ Using (1) and the characteristics of AR4JA code parity check matrix which was analyzed in part A, it is clearly to get the formula of H /3, H 3/4, and H 4/5. Fig. 3 is parity check matrix when the information bits length is 104, code rate is 4/5. From Fig. 3, it can be seen that the parity check matrix structure of AR4JA code has a great systematicness, which was analyzed in part A. H 4/5 H /3 H 1/ H 3/4 Fig. 3 parity check matrix H 4/5 of AR4JA code. III. DEEP SPACE CHANNEL MODEL AND DECODING ALGORITHM 151

3 Deep space channel was first described as AWGN channel by Shannon in And most channel error correcting codes are merely discussed in AWGN channel. In fact, the absorption, reflection or other uncertain effect of different kinds of particles in aerospace must cause a certain extent signal fading. So in this paper, Rician fading channel is used as the model of deep space fading channel. The probability density function of Rice distribution is given in (). r ( r + β ) β r exp I 0 0 r < p( r) σ σ σ () 0 r < 0 where, β is the maximum amplitude of the direct wave, σ is the root-mean-square value of received voltage signal before envelope detection. α Fig.4 Rician fading channel model. Fig. 4 shows the Rician fading channel model [8]. In Fig. 4, y k is the received signal, x k is the send signal, α k is the Rician fading factor, n k is the Gauss white noise, which obeys the normal distribution. From Fig. 4, the Rician fading channel model can be described as (3) y α x + n (3) k k k k Since fully interleaved Rician fading factors α k are statistically independent, they can be simulated as Rician random variables. α i ( i ) a + b + γ ( γ + ) 1 where, a i and b i are independent and identically distributed Gauss variables whose means are 0, variances are 1. γ is the ratio of channel reflection energy and scattering energy, and γ β / σ. Since AR4JA code is a kind of LDPC, typical decoding algorithms of LDPC are used to decode AR4JA codes in this paper. Soft decision decoding algorithm is a kind of algorithm based on message passing. In the ideal case, when quantization level of the message passing algorithm tends to infinity, the algorithm becomes BP (Belief Propagation) algorithm. BP algorithm is a continuous algorithm with the highest complexity, while it shows the best performance. The concrete step of BP algorithm is easy to get. However, in the case of Rician fading channel, the method of initial information calculation change, which is shown in (5) qmn fn (5) yα 1+ exp σ (4) where, m, n are the row number and column number of parity check matrix H, α is the Rician fading factor, and σ is the rootmean-square value. If the BP algorithm is mapped into the logarithmic domain, it is called LLR BP algorithm. And the initial information is calculated as (6) [9]. yα λmn Ln (6) σ Although BP algorithm has the best performance, it is too complex to be used for hardware implementation. A kind of improved algorithm whose name is Min-Sum algorithm is used to decode AR4JA code in the paper. Min-Sum algorithm simplifies the check node update part of the LLR BP algorithm. In other words, Min-Sum algorithm uses addition instead of multiplication in the same step of LLR BP algorithm. So it is less complex for Min-Sum to be realized by hardware. Also in the case of Rician fading channel, the first step of the algorithm is changed, which is shown in (7). λ L yα (7) mn IV. SIMULATION AND DISCUSSION Through the analysis above, Rician fading channel is used as the deep space fading channel model, and three different fading degrees are described by the situations of γ -10dB, γ 0dB, γ 10dB. Since the communication link between MSL (Mars Science Laboratory) and MRO (The Mars Reconnaissance Orbiter) in the Mars local area network will use AR4JA code whose information bits length is 104, three kinds of AR4JA codes whose information bits lengths are 104, code rates are 1/, /3, 4/5 are structured and simulated in the paper. And the other simulation parameters can be seen in TABLEⅡ. TABLE Ⅱ AR4JA CODE SIMULATION PARAMETERS IN RICIAN FADING CHANNEL Information Code Code Decoding Coding bits length rate length Soft decision decoding 104 1/ 048 / /5 180 BPSK n BP algorithm Min-Sum algorithm Iteration times 50 Fig. 5 is the error performance comparing curve that using BP algorithm and 50 times iteration Min-Sum algorithm to decode AR4JA code whose information bits length is 104, code rates are 1/, /3, and 4/5 in the case of Rician fading channel whose γ 10dB. Compared with the BER in AWGN channel which was given in [10], Fig. 5 shows that the overall error performance of AR4JA code in Rician fading channel declines. While the overall trend of the AR4JA code error performance curve is the same as that in AWGN channel. From Fig.5, it is easy to get that soft decision decoding algorithm is still a rational solution for AR4JA decoding in Rician fading channel. In these algorithms, BP algorithm has a better performance, but as analyzed in part III, it is hard to realize by hardware; while, by losing few gain, Min-Sum algorithm declines the compulational complexity in order to meet hardware realization. 15

4 stable, the closest iteration time can be chosen to realize the balance of decoding overhead and decoding efficiency BER BP r1/ BP r/3 BP r4/5 Min-Sum r1/ Min-Sum r/3 Min-Sum r4/ Fig.5 AR4JA code BER using Min-Sum algorithm and BP algorithm in Rician fading channel. Since Min-Sum is a better choice for AR4JA code in engineering realization, it is useful to analyze the character of Min-Sum algorithm. BER Rician -10dB Rician 0dB Rician 10dB Gauss Channel Fig.6 AR4JA code BER in different Rician fading channels and Gauss channel. Fig. 6 is the error performance comparing curve that using 50 times iteration Min-Sum algorithm to decode AR4JA code whose information bits length is 104, code rates are 1/ in Rician fading channel whose γ -10dB, γ 0dB, γ 10dB and Gauss channel. The influence of channel fading degree can be seen clearly in Fig.6. From Fig.6, it can be obtained that like other error correction channel codes, AR4JA code is directly influenced by channel fading degree. However, when γ - 10dB, the channel condition is similar to that of Rayleigh fading channel. While in this case, about 4.3dB SNR is needed to achieve 10-4 BER. It is to say, AR4JA code is still suitable to be used in deep space fading channels that have different fading degrees. Fig.7 shows the changes of iteration times of Min-Sum decoding algorithm in Rician fading channel when channel SNR changes. Maximum iteration times in one time decoding algorithm is set as 50. From Fig.7, it is clear to see that, for AR4JA code of certain code rate, there is a SNR threshold. When SNR is lower than the threshold, AR4JA code is not completely decoded. But when SNR is higher than the threshold, iteration times decreases with the increase of SNR. Based on this conclusion, if the channel SNR is relatively Iteration times Rician -10dB r1/ 15 Rician 0dB r1/ Rician 10dB r1/ 10 Rician 10dB r/3 Rician 10dB r4/ Fig.7 Iteration times of Min-Sum algorithm in Rician fading channel. The analysis above gave the AR4JA performance in Rician fading channel. Through the simulation, it proved that AR4JA code can be also used in the deep space Rician fading channel application scene of different channel fading degrees and relationship between code rate and BER should be considered seriously in practical application. Using Min-Sum algorithm of suitable iteration times can decline the hardware realization complexity to meet the need of deep space detection receiver miniaturization while losing few gain. VI. CONCLUSION This paper analyzed the importance of deep space communication system in deep space exploration mission. And since deep space communication system has several characteristics of low received SNR, wide available channel bandwidth, and intermittent communication, channel error correction coding technology becomes one of the most important technologies for deep space communication system. AR4JA code recommended by CCSDS is very suitable for this kind of environment. Therefore, systematic and deep analysis on AR4JA code is undertook in the paper. On the basis of analysis on AR4JA code performance characteristics, Rician fading channel is chosen as the model of deep space channel. Then BP algorithm and Min-Sum algorithm are used to decode AR4JA code whose code length is 104, code rates are 1/, /3, 4/5. By comparing the simulation results, it is obtained that in Rician fading channel, channel fading degree influences BER much. Compared with BP algorithm, Min- Sum algorithm declines decoding complexity with few gain loss. And suitable iteration times of Min-Sum algorithm can be chosen from the simulation result to obtain the largest gain. ACKNOWLEDGMENT The paper is sponsored by National Natural Science Foundation of China (No ), and the Fundamental Research Funds for the Central Universities (Grant No.HIT.NSRIF.0101). The authors are grateful to Yu Fangyuan and Zhou Dawei for providing thorough comments on the previous version of the paper. Their suggestions have considerably improved the quality of the paper. 153

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