Bounds on the error probability of finite-length RaptorQ codes

Abstract

Massive machine-to-machine (mM2M) communication requires data transmission in short packets, but at present, the theory of short length code design and optimazation is still incompletely. In this paper, we analyze the maximum likelihood (ML) decoding failure probability (DFP) of finite length RaptorQ codes, and propose a theoretical performance bound of DFP on the RaptorQ codes under ML decoding algorithm by investigating the rank of the product of two random coefficient matrices. Moreover, we verify the accuracy of derived theoretical bounds through the Monte Carlo simulations over varied Galois field order. The high accuracy bounds can be used to design near-optimum RaptorQ codes with short and moderate lengths.