On the Outage Theorem and its Converse for Discrete Memoryless Channels

We prove both the outage theorem and its converse for block fading discrete memoryless channel. If Pout is the outage probability for the rate R, then any transmission rate below R, together with any average error probability greater than Pout is achievable. Conversely, for any code with rate slightly greater than R, the error probability is greater than any number smaller than Pout, for large codeword lengths. Two cases are considered depending on whether the transmitter has channel state information (CSI) or not.