On Computationally Bounded Adverserial Capacity

Abstract—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.