Comment on “Improved Analysis of List Decoding and Its Application to Convolutional Codes and Turbo Codes”

In a recent paper (Bai et al, IEEE Trans. Inf. Theory, 2007) an improved analysis concerning the analysis of List Decoding was presented. The event that the correct codeword is excluded from the list is central. For the additive white Gaussian noise (AWGN) channel an important quantity is the in (Bai et al, IEEE Trans. Inf. Theory, 2007) called effective Euclidean distance. This was earlier considered in (Aulin, IEEE Trans. Commun., 1999) under the name Vector Euclidean Distance, where also a simple mathematical expression for this quantity was easily derived for any list size. In (Bai et al, IEEE Trans. Inf. Theory, 2007), a geometrical analysis gives this when the list size is 1, 2 or 3