Variable Packet-Error Coding: the Point-to-Point Case

We consider a communication system with one encoder, one decoder, and an omniscient adversary that can potentially alter the message received by the decoder in a way that maximizes the realized distortion. We are interested in the tradeoff between the rate of the message, the distortion when the packet is not altered, and the distortion when it is. We present an achievable scheme, which illustrates a particular mechanism for designing the codebook so as to limit the harm that can be done by the adversary, and an impossibility result. A binary example is solved exactly over a certain range of rates.