  Achieving information-theoretic security using explicit coding scheme in
which unlimited computational power for eavesdropper is assumed, is one of the
main topics is security consideration. It is shown that polar codes are
capacity achieving codes and have a low complexity in encoding and decoding. It
has been proven that polar codes reach to secrecy capacity in the binary-input
wiretap channels in symmetric settings for which the wiretapper's channel is
degraded with respect to the main channel. The first task of this paper is to
propose a coding scheme to achieve secrecy capacity in asymmetric
nonbinary-input channels while keeping reliability and security conditions
satisfied. Our assumption is that the wiretap channel is stochastically
degraded with respect to the main channel and message distribution is
unspecified. The main idea is to send information set over good channels for
Bob and bad channels for Eve and send random symbols for channels that are good
for both. In this scheme the frozen vector is defined over all possible choices
using polar codes ensemble concept. We proved that there exists a frozen vector
for which the coding scheme satisfies reliability and security conditions. It
is further shown that uniform distribution of the message is the necessary
condition for achieving secrecy capacity.
