Upper Bounding the Deletion Channel Capacity by Auxiliary Memoryless Channels

We present two upper bounds on the capacity of the binary deletion channel. Both bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined random processes. Since the closed-form expressions of the proposed bounds involve infinite series, we also introduce provable inequalities that lead to more manageable results. For most values of the deletion probability, these bounds improve the existing ones and significantly narrow the gap with the available lower bounds.