The input to a channel Q is a word of 8 bits. The output is also a word of 8 bits. Each time it is used, the channel flips exactly one of the transmitted bits, but the receiver does not know which one. The other seven bits are received without error. All 8 bits are equally likely to be the one that is flipped. Derive the capacity of this channel.
Show, by describing an explicit encoder and decoder that it is possible reliably (that is, with zero error probability) to communicate 5 bits per cycle over this channel.