  Most existing works of polar codes focus on the analysis of block error
probability. However, in many scenarios, bit error probability is also
important for evaluating the performance of channel codes. In this paper, we
establish a new framework to analyze the bit error probability of polar codes.
Specifically, by revisiting the error event of bit-channel, we first introduce
the conditional bit error probability as a metric to evaluate the reliability
of bit-channel for both systematic and non-systematic polar codes. Guided by
the concept of polar subcode, we then derive an upper bound on the conditional
bit error probability of each bit-channel, and accordingly, an upper bound on
the bit error probability of polar codes. Based on these, two types of
construction metrics aiming at minimizing the bit error probability of polar
codes are proposed, which are of linear computational complexity and explicit
forms. Simulation results show that the polar codes constructed by the proposed
methods can outperform those constructed by the conventional methods.
