An upper bound for the block coding error exponent with delayed feedback

The issue of whether feedback can significantly increase reliability in the fixed-length channel code setting is further investigated. This paper considers the problem of error exponents for block codes with noiseless, delayed feedback used over discrete memoryless channels (DMCs) - including asymmetric channels with and without zeros in their transition matrix. We show that when output feedback is given to the encoder with a delay of T symbols, the error exponent is upper bounded by E_sp(R - O((log T)/T )) + O((log T)/T ), where E_sp denotes the sphere-packing exponent.