Abstract
Luby Transform (LT) code is the first practical implementation of digital fountain code. The coding behavior of LT code is mainly decided by the degree distribution which determines the relationship between source data and codewords. Two degree distributions are suggested by Luby. They work well in typical situations but not optimally in case of finite encoding symbols. In this work, the degree distribution optimization algorithm is proposed to explore the potential of LT code. Firstly selection scheme of sparse degrees for LT codes is introduced. Then probability distribution is optimized according to the selected degrees. In image transmission, bit stream is sensitive to the channel noise and even a single bit error may cause the loss of synchronization between the encoder and the decoder. Therefore the proposed algorithm is designed for image transmission situation. Moreover, optimal class partition is studied for image transmission with unequal error protection. The experimental results are quite promising. Compared with LT code with robust soliton distribution, the proposed algorithm improves the final quality of recovered images obviously with the same overhead.
Funding statement: Funding: This work is supported by the National Natural Science Foundation of China (NSFC, 61401269, 61371125, 61205081), the Natural Science Foundation of Shanghai (14ZR1417400), Shanghai Technology Innovation Project (10110502200, 11510500900), Innovation Program of Shanghai Municipal Education Commission (12ZZ176, 13YZ105), Project of Science and Technology Commission of Shanghai Municipality (10PJ1404500), Leading Academic Discipline Project of Shanghai Municipal Education Commission (J51303).
References
1. Byers JW, Luby M, Mitzenmacher M, Rege A. A digital fountain approach to reliable distribution of bulk data. Proceedings of the ACM SIGCOMM’98, 1998, pp. 56–67.10.1145/285243.285258Search in Google Scholar
2. Universal Mobile Telecommunications System (UMTS): Mobile Broadcast/Multicast Service (MBMS): Protocols and Codecs, 3GPP TS 26.346, Version 6.3.0, Release 6, December 2005.Search in Google Scholar
3. Digital Video Broadcasting (DVB): Transmission system for handheld terminals (DVB-H), ETSI EN 302 304 V1.1.1, 2004.Search in Google Scholar
4. Luby M. LT codes. Proceedings of IEEE Symposium on Foundations of Computer Science, Vancouver, Canada, 2002, pp. 271–80.Search in Google Scholar
5. Hyytiä E, Tirronen T, Virtamo J. Optimal degree distribution for LT codes with small message length. INFOCOM, Anchorage, AK, 6–12, May, 2007, pp.2576–80.10.1109/INFCOM.2007.324Search in Google Scholar
6. Yen KK, Liao YC, Chen CL, Chang HC. Modified robust soliton distribution (MRSD) with improved ripple size for LT codes. IEEE Commun Lett 2013;17:976–9.10.1109/LCOMM.2013.040913.130136Search in Google Scholar
7. Hussain I, Xiao M, Rasmussen L. Regularized variable-node LT codes with improved erasure floor performance. IEEE Information Theory and Applications (ITA) Workshop, San Deigo, USA, 10–15,Feb. 2013.Search in Google Scholar
8. Jafarizadeh S, Jamalipour A. An exact solution to degree distribution optimization in LT codes. IEEE WCNC’14 Track 1 (PHY and Fundamentals), Istanbul, 6–9, April, pp. 764–8, 2014.Search in Google Scholar
9. Bodine EA, Cheng MK. Characterization of Luby Transform codes with small message size for low-latency decoding. Proceedings of the IEEE International Conference on Communications, Beijing, China, 19–23, May, 2008, pp. 1195–9.10.1109/ICC.2008.233Search in Google Scholar
10. Hyytia E, Tirronen T, Virtamo J. Optimal degree distribution for LT codes with small message length. Proceedings of the 26th IEEE International Conference on Computer Communications (INFOCOM 2007), Anchorage, AK, 6–12, May, 2007, pp. 2576–80.10.1109/INFCOM.2007.324Search in Google Scholar
11. Hyytia E, Tirronen T, Virtamo J. Optimizing the degree distribution of LT codes with an importance sampling approach. Proceedings of the 6th International Workshop on Rare Event Simulation (RESIM 2006), Bamberg, Germany, 8–10, Oct. 2006, pp. 64–73.Search in Google Scholar
12. Chen C-M, Chen Y-P, Shen T-C, Zao JK. On the optimization of degree distributions in LT code with covariance matrix adaptation evolution strategy. Proceedings of the IEEE Congress on Evolutionary Computation, Barcelona, 18–23 July, 2010, pp. 3531–8.10.1109/CEC.2010.5586202Search in Google Scholar
13. Chen C-M, Chen Y-P, Shen T-C, Zao JK. Optimizing degree distributions in LT codes by using the multiobjective evolutionary algorithm based on decomposition. Proceedings of the IEEE Congress on Evolutionary Computation, Barcelona, 18–23 July, 2010, pp. 3635–42.10.1109/CEC.2010.5586340Search in Google Scholar
14. Tsai P-C, Chen C-M, Chen Y-Ping. Sparse degrees analysis for LT codes optimization. IEEE World Congress on Computational Intelligence,Brisbane, QLD, June 10–15, 2012, pp. 1–6.Search in Google Scholar
15. Hansen N, Ostermeier A. Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. Proceedings of the IEEE International Conference on Evolutionary Computation, Nagoya, 2–22, May, 1996, pp. 312–17.Search in Google Scholar
16. Auger A, Hansen N. Performance evaluation of an advanced local search evolutionary algorithm. Proceedings of the 2005 IEEE Congress on Evolutionary Computation (CEC 2005), Edinburgh, UK, 2–5, Sept. 2005, pp. 1777–84.Search in Google Scholar
17. Auger A, Hansen N. A restart CMA evolution strategy with increasing population size. Proceedings of the 2005 IEEE Congress on Evolutionary Computation (CEC 2005), Edinburgh, UK, 2–5 Sept. 2005, pp. 1769–76.Search in Google Scholar
18. Vukobratovic D, Stankovic V, Sejdinovic D, Fagoonee L, Xiong Z. Scalable data multicast using expanding fountain codes. IEEE Trans Multimedia 2009;11:1094–104. Special Issue: Quality-Driven Cross-Layer Design for Multimedia.10.1109/TMM.2009.2026087Search in Google Scholar
19. Hellge C, Schierl T, Wiegand T. Receiver driven layered multicast with layer-aware forward error correction. Proceedings of the IEEE International Conference on Image Processing (ICIP), SanDeigo, CA, 12–15, Oct. 2008, pp. 2304–7.10.1109/ICIP.2008.4712252Search in Google Scholar
20. Cataldi P, Grangetto M, Tillo T. Sliding-window raptor codes for efficient scalable wireless video broadcasting with unequal loss protection. IEEE Trans Image Process 2010;vol. 19:1491–503.10.1109/TIP.2010.2042985Search in Google Scholar PubMed
21. Bogino M, Cataldi P, Grangetto M, Magli E, Olmo G, Sejdinovic D, et al. Expanding window fountain codes for unequal error protection. Proc. 41st Asilomar Conf., Pacific Grove, Xi’an, China, 14-16, Sept, 2007, pp. 1020–4.Search in Google Scholar
©2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Editorial
- Peer Review and Plagiarism
- Amplifiers
- Performance Analysis of an EDFA Utilizing a Partially Doped Core Fiber (PDCF)
- Devices
- Design and Analysis of Ultra-Fast All-Optical Modulator Based on Photonic Crystal
- Networks
- A New Wavelength Optimization and Energy-Saving Scheme Based on Network Coding in Software-Defined WDM-PON Networks
- Hierarchical Supervisor and Agent Routing Algorithm in LEO/MEO Double-layered Optical Satellite Network
- A Self-Driven and Adaptive Adjusting Teaching Learning Method for Optimizing Optical Multicast Network Throughput
- Analysis of SDWDM Ring Network and Enhancement Using Different Hybrid Optical Amplifiers and Modulation Formats
- Systems
- Optical Generation of 12-Tupling Millimeter-Wave Signal without Optical Filtering
- A Degree Distribution Optimization Algorithm for Image Transmission
- Theory
- Performance Enhancement of Multichannel Gigabit Rate Bidirectional WDM-PON Using RSOA and Optimized Modulation Format
- A Simple but Accurate Method for Analytical Estimation of Splice Loss in Single-Mode Triangular Index Fibers for Different V Numbers Including the Low Ones
- News
- News
Articles in the same Issue
- Frontmatter
- Editorial
- Peer Review and Plagiarism
- Amplifiers
- Performance Analysis of an EDFA Utilizing a Partially Doped Core Fiber (PDCF)
- Devices
- Design and Analysis of Ultra-Fast All-Optical Modulator Based on Photonic Crystal
- Networks
- A New Wavelength Optimization and Energy-Saving Scheme Based on Network Coding in Software-Defined WDM-PON Networks
- Hierarchical Supervisor and Agent Routing Algorithm in LEO/MEO Double-layered Optical Satellite Network
- A Self-Driven and Adaptive Adjusting Teaching Learning Method for Optimizing Optical Multicast Network Throughput
- Analysis of SDWDM Ring Network and Enhancement Using Different Hybrid Optical Amplifiers and Modulation Formats
- Systems
- Optical Generation of 12-Tupling Millimeter-Wave Signal without Optical Filtering
- A Degree Distribution Optimization Algorithm for Image Transmission
- Theory
- Performance Enhancement of Multichannel Gigabit Rate Bidirectional WDM-PON Using RSOA and Optimized Modulation Format
- A Simple but Accurate Method for Analytical Estimation of Splice Loss in Single-Mode Triangular Index Fibers for Different V Numbers Including the Low Ones
- News
- News