Abstract
In this paper, we analysis the maximum likelihood (ML) decoding failure probability (DFP) of finite length RaptorQ codes with a high-order low density generator-matrix (LDGM) code as the pre-code. By investigating the rank of the product of two random coefficient matrices, we derive upper and lower bounds of DFP on the RaptorQ codes under ML decoding algorithm. Finally, we verify the accuracy of derived theoretical bounds through the Monte Carlo simulations with different degree distributions. The high accuracy bounds can be used to design near-optimum RaptorQ codes with short and moderate lengths.
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Acknowledgment
This work was supported in part by the National Natural Sciences Foundation of China (NSFC) under Grant 61771158, 61701136, 61525103 and 61371102, and the Shenzhen Basic Research Program under Grant JCYJ20160328163327348 and JCYJ20150930150304185.
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Zhang, K., Jiao, J., Gu, S., Wu, S., Zhang, Q. (2019). Bounds on the Finite-Length RaptorQ Codes Under Maximum Likelihood Decoding. In: Liang, Q., Mu, J., Jia, M., Wang, W., Feng, X., Zhang, B. (eds) Communications, Signal Processing, and Systems. CSPS 2017. Lecture Notes in Electrical Engineering, vol 463. Springer, Singapore. https://doi.org/10.1007/978-981-10-6571-2_101
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DOI: https://doi.org/10.1007/978-981-10-6571-2_101
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