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On Pre-transformed Polar Codes

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arxiv 1912.06359 v1 pith:WP3BPJA7 submitted 2019-12-13 cs.IT math.IT

Bin Li , Huazi Zhang , Jiaqi Gu This is my paper · ORCID
classification cs.ITmath.IT
keywords codespolarcodedistancematrixminimumpre-transformationpre-transformed
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In this paper, we prove that any pre-transformation with an upper-triangular matrix (including cyclic redundancy check (CRC), parity-check (PC) and convolution code (CC) matrix) does not reduce the code minimum distance and an properly designed pre-transformation can reduce the number of codewords with the minimum distance. This explains that the pre-transformed polar codes can perform better than the Polar/RM codes.

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  1. BiD Codes: Algebraic Codes from $3 \times 3$ Kernel

    cs.IT 2025-07 conditional novelty 7.0 of 10

    BiD codes, built from a 3x3 Kronecker kernel, have proven minimum distance growing at least as N^0.543 at any fixed rate, faster than Reed-Muller's N^0.5.

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