Performance Analysis of Raptor Codes under Maximum-Likelihood (ML) Decoding

Raptor codes have been widely used in many multimedia broadcast/multicast applications. However, our understanding of Raptor codes is still incomplete due to the insufficient amount of theoretical work on the performance analysis of Raptor codes, particularly under maximum-likelihood (ML) decoding, which provides an optimal benchmark on the system performance for the other decoding schemes to compare against. For the first time, this paper provides an upper bound and a lower bound, on the packet error performance of Raptor codes under ML decoding, which is measured by the probability that all source packets can be successfully decoded by a receiver with a given number of successfully received coded packets. Simulations are conducted to validate the accuracy of the analysis. More specifically, Raptor codes with different degree distribution and pre-coders, are evaluated using the derived bounds with high accuracy. Peng Wang is with the School of Electrical and Information Engineering, The University of Sydney, Australia and National ICT Australia (NICTA) Sydney (e-mail: [email protected]). Guoqiang Mao is with the School of Computing and Communication, The University of Technology Sydney, Australia and National ICT Australia (NICTA) Sydney (e-mail: [email protected]). Zihuai Lin is with the School of Electrical and Information Engineering, The University of Sydney, Australia (e-mail: [email protected]). Ming Ding is with the National ICT Australia (NICTA) (e-mail: [email protected]). Weifa Liang is with the Research School of Computer Science, The Australian National University, Australia (e-mail: [email protected]). Xiaohu Ge is with the School of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China (email: [email protected]). Zhiyun Lin is with the College of Electrical Engineering, Zhejiang University, China (email: [email protected]). This article has been submitted to IEEE Transactions on Communication. Submission information: TCOM-TPS-15-0052. January 30, 2015 DRAFT Index Terms Raptor codes; asymptotic analysis; maximum-likelihood (ML) decoding; decoding success probability.