3 research outputs found
Algebraic matching techniques for fast decoding of polar codes with Reed-Solomon kernel
We propose to reduce the decoding complexity of polar codes with non-Arikan
kernels by employing a (near) ML decoding algorithm for the codes generated by
kernel rows. A generalization of the order statistics algorithm is presented
for soft decoding of Reed-Solomon codes. Algebraic properties of the
Reed-Solomon code are exploited to increase the reprocessing order. The
obtained algorithm is used as a building block to obtain a decoder for polar
codes with Reed-Solomon kernel.Comment: Accepted to ISIT 201
Window Processing of Binary Polarization Kernels
A decoding algorithm for polar (sub)codes with binary
polarization kernels is presented. It is based on the window processing (WP)
method, which exploits the linear relationship of the polarization kernels and
the Arikan matrix. This relationship enables one to compute the kernel input
symbols probabilities by computing the probabilities of several paths in Arikan
successive cancellation (SC) decoder.
In this paper we propose an improved version of WP, which has significantly
lower arithmetic complexity and operates in log-likelihood ratios (LLRs)
domain. The algorithm identifies and reuses common subexpressions arising in
computation of Arikan SC path scores.
The proposed algorithm is applied to kernels of size 16 and 32 with improved
polarization properties. It enables polar (sub)codes with the considered
kernels to simultaneously provide better performance and lower decoding
complexity compared with polar (sub)codes with Arikan kernel.Comment: Final version to appear in IEEE Transactions on Communications. The
source code is available at https://github.com/gtrofimiuk/SCLKernelDecode
Efficient decoding of polar codes with some 1616 kernels
A decoding algorithm for polar codes with binary 1616 kernels with
polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented.
The proposed approach exploits the relationship of the considered kernels and
the Arikan matrix to significantly reduce the decoding complexity without any
performance loss. Simulation results show that polar (sub)codes with
1616 kernels can outperform polar codes with Arikan kernel, while
having lower decoding complexity.Comment: This is the extended version of the conference paper. Minor typos are
fixed, arithmetical complexity computations are refine