Performance analysis of systematic linear codes over AWGN channels

Abstract

In this paper, amended truncated union bounds on the bit error probability of systematic linear codes over additive white Gaussian noise (AWGN) channels are proposed. The proposed bounds are based on Gallager's first bounding technique (GFBT), where the “good” region is defined by a suboptimal list decoding algorithm. The proposed bounds require only the knowledge of partial input output weight enumerating function (IOWEF) with truncated information weight, which can also be adapted to the codes when the IOWEF is not available and difficult to calculate but the weight spectrum is known. The proposed amended truncated union bounds improve the conventional union bounds and the recently proposed Ma bounds but have a similar complexity since they involve only the Q-function.