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International Workshop on Signal Design and its Applications in Communications

A new class of parity-check concatenated polar codes using belief propagation decoding

Inseon Kim, Hong‐Yeop Song

Published Oct 1, 2019• 0 citations
Publisher

Abstract

In this paper, we propose a construction of parity-check equations for Low Density Parity-Check (LDPC) based Parity-Check Concatenated (PCC) polar codes in order to (i) increase the minimum Hamming weight and (ii) correct some errors using belief propagation decoding. We simulate some experiment to show that the proposed LDPC base PCC polar codes have coding gain in the sense of block error rate compared with existing PCC polar codes.

DOI
10.1109/iwsda46143.2019.8966111

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In this paper, we propose a construction of parity-check equations for Low Density Parity-Check (LDPC) based Parity-Check Concatenated (PCC) polar codes in order to (i) increase the minimum Hamming weight and (ii) correct some errors using belief propagation decoding. We simulate some experiment to show that the proposed LDPC base PCC polar codes have coding gain in the sense of block error rate compared with existing PCC polar codes.
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Bit-channels of finite-length polar codes are not fully polarized, and the negative influences from semi-polarized channels are not negligible. In this letter, we consider the concatenated system of an inner polar code and an outer low-density parity-check (LDPC) code to improve the error correction performance of finite-length polar code with belief propagation (BP) decoding. We propose a bit mapping method between LDPC coded bits and polarized channels, aiming to match the coding protection of LDPC codes with polarization of polar codes. Simulation results show that, the concatenated polar codes with bit mapping outperform the pure polar codes with BP decoding and concatenated polar codes with traditional consecutive bit mapping.
Nowadays concatenated codes are actively developed for different applications of error-correcting theory. In this paper we propose a new method for constructing concatenated codes consisting of some outer error-correcting code and a particular designed inner low-density parity-check (LDPC) code. We consider polarization-adjusted convolutional (PAC) code and LDPC code as outer code of suggested construction. A specialized optimization algorithm was developed to generate inner code with particular error-reducing properties. By using the woven codes decoder with this design, the complexity of the decoding procedure is reduced compared to traditional polar and LDPC codes decoders, while still providing error-correcting characteristics. Additionally, we enhance the performance of our system by puncturing the encoded symbols. The resulting concatenated constructions outperform low-rate LDPC code from the 5G standard and polar code. Furthermore, we demonstrate the performance of code with a special paritycheck matrix which consists of parity-check matrices of inner and outer codes from our proposed construction.