This note is meant to address the case where your serial communication becomes unsynchronized and ANT misses bytes from a message sent from the host. The idea is to keep sending zeroes (just zeroes, not a particular message) if you have not received a confirmation that ANT has received a complete message, in order to flush out its receive buffer.
This is a rare situation, and generally, it is recommended to use the reset pin instead to reset ANT. However, since you are working on a USB library, and do not have access to performing a hardware reset, this solution would work for you.
