Chapter 9: Channel Capacity for Discrete Memoryless Channels

Learning Objectives

• Define the discrete memoryless channel (DMC) model and the channel coding problem
• State and prove the channel coding theorem: $C = \max_{P_X} I(X;Y)$
• Prove achievability via random coding and joint typicality decoding, using the packing lemma
• Prove the converse via Fano's inequality and the chain rule for mutual information
• Compute the capacity of the BSC, BEC, symmetric channels, and additive noise channels
• Prove that feedback does not increase the capacity of a DMC and explain the Schalkwijk-Kailath scheme
• State the source-channel coding theorem and the capacity-cost function
• Describe the Blahut-Arimoto algorithm for computing capacity