When is noisy state information at the encoder as useless as no information or as good as noise-free state?

摘要

For any binary-input channel with perfect state information at the decoder, if the mutual information between the noisy state observation at the encoder and the true channel state is below a positive threshold determined solely by the state distribution, then the capacity is the same as that with no encoder side information. A complementary phenomenon is revealed for a similarly defined quantity.