  Polarization-adjusted convolutional (PAC) codes are special concatenated
codes in which we employ a one-to-one convolutional transform as a precoding
step before the polar transform. In this scheme, the polar transform (as a
mapper) and the successive cancellation process (as a demapper) present a
synthetic vector channel to the convolutional transformation. The numerical
results in the literature show that this concatenation improves the weight
distribution of polar codes which justifies the superior error correction
performance of PAC codes relative to polar codes. In this work, we explicitly
show why the convolutional precoding reduces the number of minimumweight
codewords. Further analysis exhibits where the precoding stage is not
effective. Then, we recognize weaknesses of the convolutional precoding which
are unequal error protection (UEP) of the information bits due to rate
profiling and lack of cross-segmental convolution. Finally, we assess the
possibility of improving the precoding stage by proposing some irregular
convolutional precodings.
