A modified design of Raptor codes for small message length

Raptor codes are a class of fountain codes which can get capacity-achieving performance over various channels. Traditional Raptor codes can obtain perfect performance for large message length. However, small message length can cause significant performance deterioration. In this paper, a modified design of Raptor codes for small message length is proposed. The proposed Raptor codes are obtained by pre-coding the information symbols by low rate low-density parity-check codes and utilizing a low constant average degree distribution with high intermediate symbol recovery rate. Simulation results demonstrate that, although traditional Raptor codes can get good asymptotical performance, our proposed Raptor codes outperform traditional Raptor codes for small message length over binary erasure channels and binary input additive white Gaussian noise channels.

[1]  Jianping An,et al.  Design of UEP-Raptor codes over BEC , 2010, Eur. Trans. Telecommun..

[2]  Xi Liu,et al.  Fountain codes over fading relay channels , 2009, IEEE Transactions on Wireless Communications.

[3]  Michael Luby,et al.  LT codes , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[4]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[5]  Rüdiger L. Urbanke,et al.  Modern Coding Theory , 2008 .

[6]  Jorma T. Virtamo,et al.  Optimal Degree Distribution for LT Codes with Small Message Length , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[7]  Nazanin Rahnavard,et al.  On the Intermediate Symbol Recovery Rate of Rateless Codes , 2012, IEEE Transactions on Communications.

[8]  D. J. C. Mackay.  Fountain codes : Capacity approaching codes design and implementation , 2005 .

[9]  Toshiaki Koike-Akino,et al.  Ripple Design of LT Codes for BIAWGN Channels , 2014, IEEE Transactions on Communications.

[10]  Sujay Sanghavi.  Intermediate Performance of Rateless Codes , 2007, 2007 IEEE Information Theory Workshop.

[11]  Meixiang Zhang,et al.  Soft decoding method for systematic raptor codes , 2015, IET Commun..

[12]  Evangelos Eleftheriou,et al.  Regular and irregular progressive edge-growth tanner graphs , 2005, IEEE Transactions on Information Theory.

[13]  Benshun Yi,et al.  Poisson Robust Soliton Distribution for LT Codes , 2016, IEEE Communications Letters.

[14]  Harry Leib,et al.  Fixed-Rate Raptor Codes Over Rician Fading Channels , 2008, IEEE Transactions on Vehicular Technology.

[15]  Heiko Schwarz,et al.  Overview of the Scalable Video Coding Extension of the H.264/AVC Standard , 2007, IEEE Transactions on Circuits and Systems for Video Technology.

[16]  Ian D. Marsland,et al.  A Comparison of Rateless Codes at Short Block Lengths , 2008, 2008 IEEE International Conference on Communications.

[17]  David Declercq,et al.  Jointly Decoded Raptor Codes: Analysis and Design for the BIAWGN Channel , 2009, EURASIP J. Wirel. Commun. Netw..

[18]  Petar Popovski,et al.  Design and Analysis of LT Codes with Decreasing Ripple Size , 2010, IEEE Transactions on Communications.

[19]  Omid Etesami,et al.  Raptor codes on binary memoryless symmetric channels , 2006, IEEE Transactions on Information Theory.

[20]  Michael Mitzenmacher,et al.  Analysis of random processes via And-Or tree evaluation , 1998, SODA '98.