# Soft Iterative Decoding Algorithms for Rateless Codes in Satellite Systems

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## Abstract

**:**

## 1. Introduction

## 2. HARQ Transmissions with Rateless Codes

#### 2.1. Rateless Codes

**u**, with a length of k and forms a codeword,

**c**. The encoding process is performed using a predetermined degree distribution, and it can be continued infinitely, resulting in infinite length of

**c**.

**c**to modulation symbols and sends them through the channel, and this mapping and transmission processes also continue as more parities are generated. The decoder at the receiver starts its process if a sufficient number of received signals are collected. In this case, the demodulator produces the bitwise estimation vector,

**r**, for decoding. If the decoding is successfully completed with the given collected signal set, then the ACK signal is sent to the transmitter. Otherwise, the receiver collects more signals for increased parities, and the decoding is performed with increased length of the codeword.

#### 2.2. HARQ with Rateless Codes

## 3. Efficient Soft Iterative Decoding Algorithms for HARQ with Rateless Codes in Satellite Systems

#### 3.1. HARQ for Satellite Systems

#### 3.2. HARQ with Rateless LDPC Codes

#### 3.2.1. Operational Principle

**u**as the information word, and generates the codeword

**U**. For the LDPC code specified in the DVB-S2/S2X, the size of

**U**is 64,800 and 16,200 bits for normal and short frames, respectively. Then, an LDPC codeword,

**U**forms the systematic part of the inner LT code, and parity words, ${\mathbf{p}}_{1},{\mathbf{p}}_{2},\dots $ are generated infinitely by the LT encoder. In our application, we use the following RSD to generate the parity words [1].

**c**from the rateless LDPC encoder consists of

**U**and ${\mathbf{p}}_{i}$s, and ${\mathbf{p}}_{i}$s are accumulated in the buffer. A type-II HARQ scheme can be operated by using this rateless LDPC code as follows:

**U**is transmitted at the first transmission. If the decoding of

**U**fails, a part of the generated parity blocks, say ${\mathbf{p}}_{1}$, is transmitted in the second transmission. If the decoding of

**U**combined with ${\mathbf{p}}_{1}$ fails again, more parity blocks, ${\mathbf{p}}_{2},{\mathbf{p}}_{3},\dots $ are transmitted until the ACK for successful decoding is received or until the limited number of retransmissions is reached.

#### 3.2.2. Soft Iterative Decoding Algorithms

#### 3.3. HARQ with Cross-Layer Rateless Codes

#### 3.3.1. Operational Principle

**I**, with a size of k is encoded by the systematic LT code in the MAC layer, yielding an output bit stream

**u’**with an arbitrary size of n. To generate parity words of the LT code, we use the following polynomial degree distribution [17].

**u’**is divided into several packets each of length K; each packet represented by

**u**is encoded by an LDPC encoding module, yielding an LDPC codeword

**c**of length N which is modulated and transmitted through the channel.

#### 3.3.2. Soft Iterative Decoding Algorithms

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Luby, M. LT Codes. In Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, Vancouver, BC, Canada, 19 November 2002; pp. 271–280. [Google Scholar]
- Shokrollahi, A. Raptor Codes. IEEE Trans. Inf. Theory
**2006**, 52, 2551–2567. [Google Scholar] [CrossRef] - Thota, J.; Bulut, B.; Doufexi, A.; Armour, S. Performance Evaluation of Multicast Video Distribution with User Cooperation in LTE-A Vehicular Environments. In Proceedings of the 2017 IEEE 86th Vehicular Technology Conference (VTC-Fall), Toronto, ON, Canada, 24–27 September 2017. [Google Scholar]
- Zhu, H.; Li, G.; Xie, Z. Advanced LT codes in Satellite Data Broadcasting System. In Proceedings of the 11th IEEE Singapore International Conference on Communication Systems, Guangzhou, China, 19–21 November 2008; pp. 1430–1435. [Google Scholar]
- Hagh, M.J.; Soleymani, M.R. Constellation Rotation for DVB Multiple Access Channels with Raptor coding. IEEE Trans. Broadcast.
**2013**, 59, 290–297. [Google Scholar] [CrossRef] - Zhang, M.; Li, C.; Kim, S. Efficient Utilization of Rateless LDPC Codes for Satellite Broadcasting Services. In Proceedings of the 2016 International Conference on Wireless Communications & Signal Processing (WCSP 2016), Yangzhou, China, 13–15 October 2016. [Google Scholar]
- Wang, Z.; Wang, Z.; Gu, X.; Guo, Q. Cross-layer design of LT codes and LDPC codes for satellite multimedia broadcast/multicast services. Chin. J. Aeronaut.
**2013**, 26, 1269–1275. [Google Scholar] [CrossRef] [Green Version] - Eroz, M.; Sun, F.; Lee, L. DVB-S2 Low Density Parity Check Codes with Near Shannon Limit Performance. Int. J. Satell. Commun. Netw.
**2004**, 22, 269–279. [Google Scholar] [CrossRef] - Yao, W.; Yi, B.; Huang, T. Poisson robust soliton distribution for LT codes. IEEE Commun. Lett.
**2016**, 20, 1499–1502. [Google Scholar] [CrossRef] - Zhang, M.; Kim, S. An Efficient Encoding Scheme for LT codes with Soft Iterative Decoding. IET Commun.
**2018**, 12, 1624–1629. [Google Scholar] [CrossRef] - Hong, T.C.; Kang, K.-S.; Ku, B.-J.; Chang, D.-I. Receiver memory management method for HARQ in LTE-based satellite communication system. Int. J. Satell. Commun. Netw.
**2017**. [Google Scholar] [CrossRef] - Zhang, M.; Kim, S.; Chang, J.Y.; Kim, W.-Y. A New Soft Decoding Method for Systematic Raptor Codes. IET Commun.
**2015**, 9, 1933–1940. [Google Scholar] [CrossRef] - Wen, L.; Razavi, R.; Imran, M.A.; Xiao, P. Design of joint sparse graph for OFDM system. IEEE Trans. Wirel. Commun.
**2014**, 14, 1823–1836. [Google Scholar] [CrossRef] - Zhang, M.; Kim, S.; Kim, Y. Universal Soft Decision Demodulator for M-ary Adaptive Modulation Systems. In Proceedings of the 2012 18th Asia-Pacific Conference on Communications (APCC), Jeju Island, South Korea, 15–17 October 2012; pp. 574–578. [Google Scholar]
- Zhang, M.; Kim, Y. Universal Soft Demodulation Schemes for M-ary Phase Shift Keying and Quadrature Amplitude Modulation. IET Commun.
**2016**, 10, 316–326. [Google Scholar] [CrossRef] - Zhang, M.; Kim, S. A New Soft Decoding Method for Systematic LT Codes. In Proceedings of the 20th European Wireless Conference, Barcelona, Spain, 14–16 May 2014; pp. 1–6. [Google Scholar]
- Hu, K.; Castura, J.; Mao, Y. Performance-Complexity Tradeoffs of Raptor Codes over Gaussian Channels. IEEE Commun. Lett.
**2007**, 11, 343–345. [Google Scholar] [CrossRef] [Green Version] - Jenka, H.; Mayer, T.; Stockhammer, T.; Xu, W. Soft Decoding of LT-codes for Wireless Broadcast. Available online: https://www.eurasip.org/Proceedings/Ext/IST05/papers/390.pdf (accessed on 28 July 2019).
- Ma, Y.; Yuan, D.; Zhang, H. Fountain Codes and Applications to Reliable Wireless Broadcast System. In Proceedings of the Information Theory Workshop, Chengdu, China, 22–26 October 2006; pp. 66–70. [Google Scholar]
- Zhang, M.; Kim, S. A Statistical Approach for Dynamic Rain Attenuation Model. In Proceedings of the 29th AIAA International Communications Satellite Systems Conference, Nara, Japan, 28 November–1 December 2011. [Google Scholar]

**Figure 2.**Hybrid automatic repeat request (HARQ) transmissions with rateless low-density parity check (LDPC) codes in satellite systems.

**Figure 4.**The flow chart of the parallel soft iterative decoding algorithm for the proposed rateless LDPC used for the HARQ scheme.

**Figure 8.**Bit error rate (BER) performance of the proposed cross-layer rateless codes over an additive white Gaussian noise (AWGN) and rain fading channel.

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**MDPI and ACS Style**

Zhang, M.; Chan, S.; Kim, S.
Soft Iterative Decoding Algorithms for Rateless Codes in Satellite Systems. *Algorithms* **2019**, *12*, 151.
https://doi.org/10.3390/a12080151

**AMA Style**

Zhang M, Chan S, Kim S.
Soft Iterative Decoding Algorithms for Rateless Codes in Satellite Systems. *Algorithms*. 2019; 12(8):151.
https://doi.org/10.3390/a12080151

**Chicago/Turabian Style**

Zhang, Meixiang, Satya Chan, and Sooyoung Kim.
2019. "Soft Iterative Decoding Algorithms for Rateless Codes in Satellite Systems" *Algorithms* 12, no. 8: 151.
https://doi.org/10.3390/a12080151