On sending one bit of information over an AGWN channel with noiseless feedback

We study the problem described by the title under the real-time constraint that no block coding is allowed. Three separate schemes, including the well known center-of-gravity scheme, and their performance are compared.The research reported in this paper was made possible through support from the Office of Naval Research under the Joint Services Electronics Program by Contract No. N00014-75-C-0648 and Contract No. N00014-77-C-0531, and by the National Science Foundation, Grant No. ENG-76-11824.The formulation of this problem took place when the first author was SRC Senior Fellow at Imperial College during the summer of 1977. He appreciates discussions with M. Davis and D. Mayne of Imperial College.