Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes

Understand

Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2.

• The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely.
• Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of Eve's equivocation ratio.
• Wyner showed that the situation is characterized by a single constant C_s, called the secrecy capacity, which has the following meaning: for all $\epsilon > 0$, there exist coding schemes of rate $R \ge C_s - \epsilon$ that asymptotically achieve both the reliability and the security objectives.