AIAA 2013-5655 International Communications Satellite Systems Conferences (ICSSC) October 14-17, 2013, Florence, Italy 31st AIAA International Communications Satellite Systems Conference
Partial Decode-and-Forward of LDPC codes for Onboard Processing Satellite Platform
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Hang LI1, Zhen GAO, Wen PAN, Ming ZHAO and Jing WANG Research Institute of Information Technology, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China There is a contradiction between high processing complexity and limited processing resources when LDPC codes are used in the onboard processing satellite platform. To solve this problem, we present a partial Decode-and-Forward method for LDPC codes used in satellites. Simulation results show that the proposed method can effectively decrease the complexity of on-board processing while achieve most of the decoding gain. I. Introduction
Satellite communication system, with its large coverage, is an effective supplement for terrestrial cellular system. Satellite platforms can be divided into two patterns: transparent forwarding and on-board processing, which correspond to Amplify-and-Forward (AF) mode and Decode-and-Forward (DF) mode, respectively, in the view of relay strategy [1]. In AF mode, the satellite directly amplifies the received waveforms and then forwards them to the destination, whereas in DF mode, the satellite first decodes the received data, and then re-encodes the decoded bits before sending to the destination. Both forwarding strategies have their disadvantages [2]. On the one hand, in AF mode, the satellite just simply forwards the signal received without using channel coding for error control. As a result, the noise in the uplink will be amplified and added to the downlink, causing cumulatively spreading. On the other hand, in DF mode, the processing complexity of satellite is higher. Besides, the satellite makes hard decision of the received waveforms, which contains soft information presents reliability. This causes performance loss. For satellite communication system, on-board processing platform [3] provides processing gain by eliminating the effect of the uplink noise. Besides, on-board processing can realize single-hop T2T communication, which decreases the communication delay by half. For the GEO based mobile satellite communication systems, this improves the user experience obviously. As a result, satellite communication system based on on-board processing platform is widely discussed in recent years. LDPC code [4][5] is a kind of effective channel coding technology, which can improve power efficiency and increase the system capacity if it is used in the on-board 1
Student, Department of Electronic Engineering,
[email protected], Non-member.
Copyright © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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processing satellite platform. However, because decoding algorithm of LDPC code contains a large number of iteration, the decoding complexity is so high that the limited on-board processing resource cannot afford for large throughput. If the code is completely decoded and re-encoded by the satellite, the processing throughput on the satellite is decreased. Therefore, it is essential to study that how to obtain the decoding gain as much as possible, with limited processing resource on satellite. To solve this problem, this paper proposes the Partial Decode-and-Forward (PDF) method to decrease the complexity of the on-board processing while achieving most of the decoding gain. The remainder of the paper is organized as follows. Section 2 introduces the system model and gives a brief introduction of the proposed PDF method. Section 3 describes the PDF method in detail. Section 4 shows the simulation results, which verify the effectiveness of the proposed method. And section 5 is the conclusion of this paper. II. System Model
For simplicity, we consider a basic scene in satellite communication, where user 1 sends messages to user 2 via the satellite as depicted in Fig. 1. We suppose the two users are far apart so that there is no direct link between them. The uplink and downlink are independent. Satellite
Uplink
Downlink
User1
User2
Figure 1 System Model In this scene, the proposed PDF method is described as follows. Step 1. User 1 sends K-bit message s i 0,1 , i 0,1, K 1 . s i is BPSK modulated and then encoded by a LDPC encoder. The encoded N-bit signal is denoted as xS i 1, 1 , i 0,1, , N 1 . And the satellite receives the signal
rS , R i hS , R ES , R xS i nS , R i
(1)
Step 2. The satellite partial decodes the signal received. To be specific, the satellite performs limited iterations, and get a rough estimation of the soft information of xs . And then forwards the soft information to User 2. Step 3. User 2 received this soft information with noise rR , D i hR , D ER , D xR i nR , D i (2) and decoded the received signal with hard decision.
In Eq. (1) and Eq. (2), hS , R and hR , D are the fading coefficients and are equal 1 for AWGN channel. ES , R and ER , D are transmit power of the source and relay respectively.
nS , R and nR , D are modeled as zero-mean white Gaussian additive noise. The above process is summarized in Fig.2. rS , R i
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s i
sˆ i
rR , D i
Figure 2 III.
Process of the proposed PDF method
Detailed Partial Decode-and-Forward Method
A. A Brief Introduction of the Concept of LDPC Code and its Decoding Algorithm LDPC code is a kind of linear block code defined by its parity check matrix H which is sparse. In order to realize parallel decoding algorithm in hardware, QC_LDPC code is proposed [6]. In QC_LDPC code, the base parity check matrix is defined as
In Eq. (3), Pi , j
P0,1 P0, nb 1 P0,0 P1,1 P1, nb 1 P1,0 HB (3) Pmb 1,0 Pmb 1,1 Pmb 1,nb 1 represents a block matrix of size z z , and z is called expansion
factor. If Pi , j 1 , the block matrix is obtained by circular right shift of an unit matrix, and the offset is defined by Pi , j . If Pi , j 1 , it represents a z z zero matrix. Therefore, the parity matrix H, with size mb z nb z , can be canculated from the base parity check matrix H B with size mb nb . LDPC code is often decoded by BP algorithm or improved BP-Based algorithms [7][8]. In general, BP algorithm use iterative decoding and each time of iteration contains two steps: bit nodes message processing and check nodes message processing. For binary LDPC code, the message transfered in BP algorithm is represented as log likelihood ratio (LLR) in order to decrease the complexity of canculation. This kind of decoding algorithm is called LLR BP algorithm, and is widely used for LDPC decoding. In LLR BP algorithm, the soft message transfered between bit nodes and check nodes is log likelihood ratio. When the iteration ends, the bit nodes canculated the soft
information which is used for hard desicion. In the proposed PDF method, the soft information for hard desicion is forwarded.
B. Partial Decode-and-Forward Method In traditional DF mode, the satellite platform completely decodes LDPC codes with maximum iterations before making hard decision. Then the satellite forwards the reencoded message to the destination. However, the iteration time is usually large especially in case of low SNR condition, as Fig.3 shows, which makes it unpractical for satellite platform with limited on-board processing resources. 100
80 Average Iteration Times
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90
70 60 50 40 30 20 10 0
0
0.5
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2 Eb/N0
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Figure 3 Average Iteration Times for LDPC Codes In PDF scheme, the on-board processing platform only performs limited iterations according to the processing resources limitation and throughput requirements, and soft information is forwarded. For LDPC codes, the soft information, which can be obtained using BP-based algorithm, is the log-likelihood of posteriori probability. It can be written as P xs i 1| r (4) L xs i ln , i 0,1, , N 1 P xs i 0 | r In Eq. (4), r is the signal received by satellite, and soft information L is the log likelihood ratio, which represents the reliability of the message sent by the source. As introduced above, LDPC code employs iterative decoding algorithm, so the soft information of N bit nodes is refreshed after iteration. However, it is necessary to iterate for enough times to get a relatively accurate estimation of the soft information. For traditional algorithm, the decoder stops either when the hard decision satisfies the parity matrix or when the iteration time gets the maximum value, which makes the decoder very computational complex. To make matters worse, the decoder usually stops at maximum iteration in the low SNR condition, and the performance gets worse if it iterates without enough times. Therefore, the decoder has to iterate many times to get a good performance in traditional method.
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However, in the resource limited system, such as the on-board processing platform, it is unpractical for the decoder to iterate too many times. By limiting the iteration time, the partial iterative decode-and-forward method can be used to decrease the decoding complexity. In PDF method, the satellite platform forwards the soft information of N bit nodes to the destination only after limited iteration.
C. The Method of Forwarding Soft Information Current solution for soft information forwarding is to quantify the soft information as digital signals and then re-encode them before sending to the destination [9]. The drawback of the scheme is that the transmission bandwidth increases a lot. In the proposed PDF scheme, soft information is forwarded as analog signal, so no re-encoding is needed. Since the magnitude range of the soft information is very large, but the on-board transmit power is limited, so the soft information needs to be limited and normalized before forwarding. It should be noted that the threshold of the limiter seriously affects the performance of the system. We propose two types of limiter. The first type is static limiter. In this type, the threshold is set statically as a constant A. The second type is dynamic limiter. In this type, the threshold is currently calculated after iteration according to the statistics of the value of soft information. The first method is to set the threshold based on the average of magnitude of soft information, as N 1
a ai
N
(5)
i 0
In Eq. (5), ai is the soft information of each bit node, N is code length, and is scaling factor. The optimal scaling factor is determined by simulation. The output of the limiter is ai a a , (6) bi ai , a ai a , i 0,1, , N 1 a , ai a The second method is based on tanh function. The output of the limiter is (7) bi tanh( ai ), i 0,1,...N 1 In Eq. (7), the symbols have the same meaning as in Eq. (5). The optimal is also determined by simulation. Then the soft information is normalized as bi , i 0,1, , N 1 (8) ci N 1
b i 0
2 i
N
and forwarded to the destination. IV.
Performance Evaluations
To verify the effectiveness of the proposed PDF method, we compared it with DF and AF mode by simulation. In the simulation, two rates of LDPC codes defined in 802.16e [10] are employed, and the maximum decoding iterations is set to be 16. BPSK is applied.
Both of the uplink and downlink channels are modeled as AWGN channel with same SNR. 10
10
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DF PDF AF 3.5
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a) LDPC code with rate 5/6 0 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 10 -7 10 1
DF PDF AF 1.5
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b) LDPC code with rate 1/2 Figure 4 Simulation Results The first graph shows the simulation results of (2304, 1920) code, for BER = 10-4, the performance of PDF with 4 iterations is only 0.5dB worse than that of DF mode, and outperforms AF mode by 2.5dB. The second graph shows the simulation results of (3840, 1920) code. With a lower code rate, the gap between DF and AF becomes further due to more noise propagation in
AF mode. In this case, the performance of PDF with 4 iterations is only 1dB worse than that of DF mode, and outperforms AF mode by 2.5dB. Both results tell that PDF can provide most of the processing gain with only 25% of the decoding complexity that DF requires.
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V. Conclusion
The complexity of LDPC decoding algorithm is too high to be applied in on-board processing satellite platform. To solve this problem, a partial decode-and-forward method is proposed. In this method, the satellite first performs limited iterations to get the soft information of bit nodes by decoding algorithm. Then the soft information is limited and normalized, and forwarded to the destination. Simulation results show that this method can achieve most of the processing gain with only 25% of the decoding complexity that DF requires. How to apply this PDF method in higher order modulation and in a cooperative way needs further investigation. References [1] T. M. Cover and A. A. El Gamal, “Capacity theorems for the relay channel”, IEEE Transactions on Information Theory, Vol. IT-25, No. 5, Sep. 1979, pp. 572-584. [2] U. Bhat and T. M. Duman, “Decoding Strategies at the Relay with Physical-Layer Network Coding”, IEEE Transactions on Wireless Communications, Vol. 11, No. 12, Dec. 2012, pp. 4503-4513. [3] Ananasso Fulvio and Bennion I., “Optical technologies for signal processing in satellite repeaters”, IEEE Communications Magazine, Vol. 28, No. 2, Feb. 1990, pp. 55-64. [4] R. G. Gallager, “Low Density Parity Check Codes”, IRE Transactions on Information Theory, Vol. 8, No. 1, 1962, pp. 21-28. [5] David J. C. Mackay and R. M. Neal, “Near Shannon Limit Performance of Low Density Parity Check Codes”, Electronic Letters, Vol. 32, No. 18, 1996, pp. 1645-1646. [6] Lei Chen, Jun Xu, Djurdjevic I. and Shu Lin, “Near-Shannon-limit quasi-cyclic low-density parity-check codes”, IEEE Transactions on Communications, Vol. 52, No. 7, July. 2004, pp. 1038-1042. [7] David J. C. Mackay, “Good Error-Correcting Codes Based on Very Sparse Matrices”, IEEE Transactions on Information Theory, Vol. 45, No. 2, 1999, pp. 399-432. [8] J Chen, and MPC Fossorier, “Near optimum universal belief propagation based decoding of low-density parity check codes”, IEEE Transactions on Communications, Vol. 50, No. 3, 2002, pp. 406-414. [9] Younes Hairej, Andreas Darmawan and Hiroyuki Morikawa, “Cooperative Diversity using Soft Decision and Distributed Decoding”, Mobile and Wireless Communications Summit, 2007. [10] IEEE Std. 802.16e, “IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, Amendment 2: Physical and Medium Access Control Layer for C ombined Fixed and Mobile Operation in Licensed Bands”, 2006
