Why does my simulation of the binary symmetric channel disagree with theory?

1. How do you represent a binary symmetric channel?
2. How is the channel matrix of a binary erasure channel different from a binary symmetric channel?
3. What is binary symmetric channel and derive it's capacity?
4. What is binary asymmetric channel?

How do you represent a binary symmetric channel?

The Binary Symmetric Channel has input and output alphabets equal to 0, 1. The probability that a received symbol is actually equal to the transmitted symbol is given by 1 − p, while the probability that they are not equal to each other is p, for some 0 ≤ p ≤ 1.

How is the channel matrix of a binary erasure channel different from a binary symmetric channel?

The binary symmetric channel has a channel capacity of 1 − H(p), where is the Shannon entropy of a binary distribution with probabilities p and 1 − p. The erasure channel has a channel capacity p, where p is the probability that the transmitted bit is not erased.

What is binary symmetric channel and derive it's capacity?

The capacity of the binary symmetric channel is C = 1 − H(p) bits per transmission, and the capacity of the binary erasure channel is C = 1 − α bits per transmission.

What is binary asymmetric channel?

The binary asymmetric channel BAC(p, q) is the discrete memoryless channel with binary alphabet and transition probability given by Pr(1|0) = p, Pr(0|0) = 1 − p, Pr(0|1) = q and Pr(1|1) = 1 − q, where Pr(x|y) denotes the probability of receiving x if y was sent.