  Convolutional precoding in polarization-adjusted convolutional (PAC) codes is
a recently introduced variant of polar codes. It has demonstrated an effective
reduction in the number of minimum weight codewords (a.k.a error coefficient)
of polar codes. This reduction has the potential to significantly improve the
error correction performance. From a codeword formation perspective, this
reduction has limitations. Capitalizing on the understanding of the
decomposition of minimum-weight codewords, this paper studies reverse precoding
that can effectively reduce minimum-weight codewords more than in PAC codes. We
propose a look-ahead list decoding for the reverse PAC codes, which has the
same order of complexity as list decoding in PAC codes. Through numerical
analysis, we demonstrate a notable reduction in error coefficients compared to
PAC codes and polar codes, resulting in a remarkable improvement in the block
error rate, in particular at high code rates.
