On Computationally Bounded Adverserial Capacity

The main reason behind the complexity of codingdecoding scheme is the randomness in the source or channel noise. We model source or channel noise as pseudo-random to study the limitation of coding-decoding schemes in the presence of an adversary. In this adverserial model, we characterize the limitations of computationally bounded source and channel coding-decoding schemes in terms of classical Information theoretic quantities such as shannon capacity and entropy. It is well-known that from a small amount of truly random bits, a very large amount of pseudo-random bits can be generated (under certain hypothesis). Subsequently, we find that in our adverserial model with computationally bounded schemes, the channel capacity becomes arbitrarily smaller compared to the classical shannon capacity or compressible source becomes incompressible. As a byproduct, our results will lead to novel (negative) characterization of pseudo-random generators.