The problem of achieving the secrecy capacity of wiretap channels explicitly and with low complexity has been open since the work of Wyner in 1975. Recently, Mahdavifar and Vardy presented a solution to this problem, based on polar codes, for the class of symmetric and degraded wiretap channels. Their polar coding scheme achieves both security and reliability under the weak security criterion, but does not guarantee reliability under the strong security criterion. The main difficulty in providing both strong security and reliability using polar codes is the existence of a small number of bit-channels that are both unreliable and unsecure. In this paper, a multi-block polar coding scheme that resolves this difficulty is presented. It is shown that this coding scheme achieves the secrecy capacity of symmetric degraded wiretap channels while guaranteeing both reliability and strong security.
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