Amended Truncated Union Bounds on the ML Decoding Performance of Binary Linear Codes over AWGN Channels

In this paper, simple upper bounds are derived on the frame and bit error probabilities of binary linear codes over Additive white Gaussian noise (AWGN) channels. The conventional union bound is first truncated and then amended, which can be justified by invoking Gal-lager's first bounding technique (GFBT). Different from most other works, the “good region” is specified by a sub-optimal list decoding algorithm. The error probability caused by the good region can be upper-bounded by the union bounds using pair-wise error probability and triplet-wise error probability, which can be further tightened by exploiting the independence between the error events and certain components of the receiving signal vector. The proposed bounds are simple since they involve only the $Q$-function. The proposed bounds improve our recently proposed bounds. Numerical results are also presented to compare the proposed bounds with the Divsalar bound, which is a simple tight upper bound with closed-form, and the Tangential-sphere bound (TSB), which is considered as one of the tightest upper bounds.