Fountain Codes With Nonuniform Selection Distributions Through Feedback

One key requirement for fountain (rateless) coding schemes is to achieve a high intermediate symbol recovery rate. Recent coding schemes have incorporated the use of a feedback channel to improve the intermediate performance of traditional rateless codes; however, these codes with feedback are designed based on uniformly at random selection of input symbols. In this paper, on the other hand, we develop feedback-based fountain codes with dynamically adjusted nonuniform symbol selection distributions, and show that this characteristic can enhance the intermediate decoding rate. We provide an analysis of our codes, including bounds on computational complexity and failure probability for a maximum likelihood decoder; the latter is tighter than bounds known for classical rateless codes. Through numerical simulations, we also show that the feedback information paired with a nonuniform selection distribution can highly improve the symbol recovery rate, and that the amount of feedback sent can be tuned to the specific transmission properties of a given feedback channel.

[1]  Jianfei Cai,et al.  Joint Unequal Loss Protection and LT Coding for Layer-Coded Media Delivery , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[2]  A. Beimel,et al.  RT Oblivious Erasure Correcting , 2004, IEEE/ACM Transactions on Networking.

[3]  Jingming Kuang,et al.  LT Codes with Limited Feedback , 2014, 2014 IEEE International Conference on Computer and Information Technology.

[4]  Amin Shokrollahi,et al.  On-line fountain codes for semi-random loss channels , 2011, 2011 IEEE Information Theory Workshop.

[5]  Petar Popovski,et al.  On the Role of Feedback in LT Codes , 2010, ArXiv.

[6]  Joong Bum Rhim,et al.  Fountain Codes , 2010 .

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

[8]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[9]  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.

[10]  Morteza Hashemi,et al.  CDP: a coded datagram transport protocol bridging UDP and TCP , 2015, SYSTOR.

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

[12]  Michael Luby,et al.  A digital fountain approach to reliable distribution of bulk data , 1998, SIGCOMM '98.

[13]  Morteza Hashemi,et al.  Near real-time rateless coding with a constrained feedback budget , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[14]  Toshiaki Koike-Akino,et al.  Rateless feedback codes , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[15]  Nazanin Rahnavard,et al.  Robust LT codes with alternating feedback , 2014, Comput. Commun..

[16]  Morteza Hashemi,et al.  Delete-and-Conquer: Rateless coding with constrained feedback , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[17]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

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

[19]  Matteo Sereno,et al.  An optimal partial decoding algorithm for rateless codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[20]  Nazanin Rahnavard,et al.  Rateless Codes With Unequal Error Protection Property , 2007, IEEE Transactions on Information Theory.

[21]  Jon Feldman,et al.  Growth codes: maximizing sensor network data persistence , 2006, SIGCOMM.

[22]  Sheldon M. Ross.  Introduction to Probability Models. , 1995 .

[23]  Nazanin Rahnavard,et al.  Rateless Codes with Optimum Intermediate Performance , 2009, GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference.

[24]  Sachin Agarwal,et al.  Rateless Coding with Feedback , 2009, IEEE INFOCOM 2009.