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Reverse Convolutional Precoding of Polar Codes: Design, Analysis, and Decoding Algorithms
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DOI：10.1109/OJCOMS.2025.3644338.png)
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Abstract
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Convolutionally precoded polar codes known as polarization-adjusted convolutional (PAC) codes are a promising variant of polar codes for short block lengths. The precoding in PAC codes has demonstrated an effective reduction in the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This reduction potentially improves the error correction performance significantly. From a codeword formation perspective, this reduction has limitations. Capitalizing on the understanding of the decomposition of minimum-weight codewords, this paper proposes a new coding scheme called reverse PAC (RPAC) codes that can effectively reduce minimum-weight codewords more than in PAC codes. Additionally, we propose a look-ahead list decoding for the RPAC codes, which maintains the same order of complexity as list decoding in PAC codes. Numerical results demonstrate that RPAC codes achieve significant improvements in block error rate over polar and PAC codes, especially in high-rate short-code scenarios where existing schemes are less effective.
Keywords:
Polar codes
PAC codes
convolutional codes
sphere decoding
ordered statistics decoding
minimum weight codewords
precoding
pre-transformation
error coefficient
minimum-weight codewords
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6.1
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478
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