Selective Reverse PAC Coding for Sphere Decoding

by   Xinyi Gu, et al.

Convolutional precoding in polarization-adjusted convolutional (PAC) codes can reduce the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This can result in improving the error correction performance of (near) maximum likelihood (ML) decoders such as sequential decoders and sphere decoders. However, PAC codes cannot be decoded by sphere decoding. The reason is twofold: 1) Sphere decoding of polar codes is performed from the last bit - due to the lower rectangular shape of the polar transform. Whereas the shape of PAC codes generator matrix is no longer triangular. 2) One may modify the precoding matrix to get a lower-triangular shape. However, this may reduce the minimum distance of the code due to the formation of unwanted cosets. This work proposes a selective convolutional precoding scheme with transposed precoding matrix to reduce the error coefficient while avoiding the reduction in the minimum distance. The numerical results show the improvement of block error rate by 0.2-0.6 dB, depending on the code rate, in medium and high SNR regimes.


page 1

page 2

page 3

page 4


On Convolutional Precoding in PAC Codes

Polarization-adjusted convolutional (PAC) codes are special concatenated...

Error Coefficient-reduced Polar/PAC Codes

Polar codes are normally designed based on the reliability of the sub-ch...

List Decoding of Arikan's PAC Codes

Polar coding gives rise to the first explicit family of codes that prova...

A Monte-Carlo Based Construction of Polarization-Adjusted Convolutional (PAC) Codes

This paper proposes a rate-profile construction method for polarization-...

Application of Guessing to Sequential Decoding of Polarization-Adjusted Convolutional (PAC) Codes

Despite the extreme error-correction performance, the amount of computat...

A Novel SCL Bit-Flipping Decoding Of Polarization-Adjusted Convolutional (PAC) Codes

Polar codes have attracted the attention of numerous researchers in the ...

Optimized Rate-Profiling for PAC Codes

The polarization-adjusted convolutional (PAC) codes concatenate the pola...

Please sign up or login with your details

Forgot password? Click here to reset