  ABS polar codes were recently proposed to speed up polarization by swapping
certain pairs of adjacent bits after each layer of polar transform. In this
paper, we observe that applying the Arikan transform $(U_i, U_{i+1}) \mapsto
(U_{i}+U_{i+1}, U_{i+1})$ on certain pairs of adjacent bits after each polar
transform layer leads to even faster polarization.
  In light of this, we propose ABS+ polar codes which incorporate the Arikan
transform in addition to the swapping transform in ABS polar codes. In order to
efficiently construct and decode ABS+ polar codes, we derive a new recursive
relation between the joint distributions of adjacent bits through different
layers of polar transforms. Simulation results over a wide range of parameters
show that the CRC-aided SCL decoder of ABS+ polar codes improves upon that of
ABS polar codes by 0.1dB--0.25dB while maintaining the same decoding time.
Moreover, ABS+ polar codes improve upon standard polar codes by 0.2dB--0.45dB
when they both use the CRC-aided SCL decoder with list size $32$. The
implementations of all the algorithms in this paper are available at
https://github.com/PlumJelly/ABS-Polar
