Error Correcting Codes Clause Samples

Error Correcting Codes. We now show how to construct codes for an arbitrary memoryless chan- nel with rate arbitrarily close to the capacity. Our constructions will work for any channel which achieves the capacity on the uniform input distri- bution, i.e., a channel from £ to 7 for which H(T) — H(T|S) is maximized for the uniform distribution over the input £. Given a channel C from £ to 7 , we write C(s) to denote the random variable over 7 given by PT|S=s as specified by the channel. Further, if sn n we write C(n)(sn ) to denote the corresponding random variable over n, i.e., we apply the channel independently n times.