  Besides the determined construction of polar codes in BEC channels, different
construction techniques have been proposed for AWGN channels. The current
state-of-the-art algorithm starts with a design-SNR (or an operating SNR) and
then processing is carried out to approximate each individual bit channel.
However, as found in this paper, for fading channels, an operating SNR can not
be directly used in approximating the bit channels. To achieve a better BER
performance, the input SNR for the polar code construction in fadding channels
is derived. A selection of the design-SNR for both the AWGN and the fading
channels from an information theoretical point of view is studied. Also
presented in this paper is the study of sacrificing a small data rate to gain
orders of magnitude increase in the BER performance.
