Error exponents of discrete memoryless channels and AWGN channels with noisy feedback

In this paper, Yamamoto-Itoh scheme, which is a blockwise variable length coding scheme originally proposed to the case of noiseless feedback, is generalized to the case of noisy feedback, and some lower bounds of the error exponent of the generalized Yamamoto-Itoh scheme are derived for discrete memoryless channels and additive white Gaussian channels. Furthermore, it is shown that error exponent can be improved by the generalized Yamamoto-Itoh scheme even if a feedback channel is noisy, and the error exponent of the generalized Yamamoto-Itoh scheme tends to the one of the original Yamamoto-Itoh scheme as the feedback noise becomes small.