Erasure Floor Analysis of Distributed LT Codes

We investigate the erasure floor performance of distributed Luby transform (DLT) codes for transmission within a multi-source, single-relay, and single-destination erasure-link network. In general, Luby transform (LT) codes exhibit a high erasure floor due to poor minimum-distance properties, which can be improved by maximizing the minimum variable-node degree. The same behavior is observed for DLT codes, and therefore a new combining scheme at the relay is proposed to maximize the minimum variable-node degree in the decoding graph. Furthermore, the encoding process at the sources and the combining scheme at the relay are coordinated to improve the transmission overhead. To characterize the asymptotic performance of the proposed DLT codes, we derive closed-form density-evolution expressions, considering both lossless and lossy source-relay channels, respectively. To support the asymptotic analysis, we evaluate the performance of the proposed DLT codes by numerical examples and demonstrate that the numerical results correspond closely to the analysis. Significant improvements in both the erasure floor and transmission overhead are obtained for the proposed DLT codes, as compared to conventional DLT codes.

[1]  Ming Xiao,et al.  Buffer-Based Distributed LT Codes , 2014, IEEE Transactions on Communications.

[2]  Wei Zhong,et al.  Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix , 2003, IEEE Communications Letters.

[3]  Thomas E. Fuja,et al.  The Design and Performance of Distributed LT Codes , 2007, IEEE Transactions on Information Theory.

[4]  Shahram Yousefi,et al.  Improved systematic fountain codes in AWGN channel , 2013, 2013 13th Canadian Workshop on Information Theory.

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

[6]  Robert J. Piechocki,et al.  AND-OR tree analysis of distributed LT codes , 2009, 2009 IEEE Information Theory Workshop on Networking and Information Theory.

[7]  Mehrdad Valipour,et al.  Left degree distribution shaping for LT codes over the binary erasure channel , 2014, 2014 27th Biennial Symposium on Communications (QBSC).

[8]  Il-Min Kim,et al.  Improved Low-Complexity Soliton-Like Network Coding for a Resource-Limited Relay , 2013, IEEE Transactions on Communications.

[9]  Cristina Comaniciu,et al.  Toward Increasing Packet Diversity for Relaying LT Fountain Codes in Wireless Sensor Networks , 2011, IEEE Communications Letters.

[10]  Il-Min Kim,et al.  Binary Soliton-Like Rateless Coding for the Y-Network , 2011, IEEE Transactions on Communications.

[11]  Ming Xiao,et al.  Design of LT Codes with Equal and Unequal Erasure Protection over Binary Erasure Channels , 2013, IEEE Communications Letters.

[12]  Robert J. Piechocki,et al.  Decentralised distributed fountain coding: asymptotic analysis and design , 2010, IEEE Communications Letters.

[13]  Michael Mitzenmacher,et al.  A digital fountain approach to asynchronous reliable multicast , 2002, IEEE J. Sel. Areas Commun..

[14]  Ian F. Akyildiz,et al.  A survey on wireless mesh networks , 2005, IEEE Communications Magazine.

[15]  John S. Thompson,et al.  Random Network Coding for Multimedia Delivery Services in LTE/LTE-Advanced , 2014, IEEE Transactions on Multimedia.

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

[17]  Jonathan S. Yedidia,et al.  Rateless codes on noisy channels , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

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

[19]  Panganamala Ramana Kumar,et al.  Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks, and Computation , 2009, Proceedings of the IEEE.