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Suppose is a family of discrete memoryless channels. An unknown member of will be available, with perfect, causal output feedback for communication. We study a scenario where communication is carried by first testing the channel by means of a training sequence, then coding according to the channel estimate. We provide an upper bound on the maximum achievable error exponent of any such coding scheme. If we consider the Binary Symmetric and the Z families of channels this bound is much lower thandoi:10.1109/tit.2005.864468 fatcat:qtgtku2nurbxxpxt5g7bvantom