Channel Capacity

After receiving a word through a communication channel, we hope to recover the original message. We use a Decoding rule and analyse some properties of the channel.

We define two concepts: Operational Channel Capacity Information Channel Capacity

We prove they are the same in Shannon’s noisy coding theorem (2nd coding theorem)

Example

A Binary Symmetric Channel (BSC) with error probability has capacity .

Proof

Calculate Information Channel Capacity.