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International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS)

On the Serial Concatenation of LDPC Codes

Fedor I. Ivanov, Aleksey Kuvshinov

Published Oct 25, 2023• 3 citations
Publisher

Abstract

Concatenated codes are effectively used in different approaches of error-correcting theory. We suggest new concatenated code construction that is composed of outer LDPC code and a particular designed inner LDPC code. Special optimization procedure was developed to obtain inner code with specific error-correcting characteristics. We apply the decoder of woven codes to this construction, while reducing the complexity of decoding procedure compared to a classic decoder of LDPC code. Furthermore, we improve the performance of our scheme with puncturing the code symbols. The resulting concatenated construction outperforms low-rate LDPC from the 5G standard. Besides this, we demonstrate the performance of code with a special parity-check matrix consisting of parity-check matrices of inner and outer codes from our suggested construction.

DOI
10.1109/telsiks57806.2023.10316146

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Concatenated codes are effectively used in different approaches of error-correcting theory. We suggest new concatenated code construction that is composed of outer LDPC code and a particular designed inner LDPC code. Special optimization procedure was developed to obtain inner code with specific error-correcting characteristics. We apply the decoder of woven codes to this construction, while reducing the complexity of decoding procedure compared to a classic decoder of LDPC code. Furthermore, we improve the performance of our scheme with puncturing the code symbols. The resulting concatenated construction outperforms low-rate LDPC from the 5G standard. Besides this, we demonstrate the performance of code with a special parity-check matrix consisting of parity-check matrices of inner and outer codes from our suggested construction.
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.
In this paper we consider the special construction of concatenated codes. Our scheme consists of outer LDPC code and a specially designed class of inner LDPC code with interleaver between inner and outer codes. An inner code in the proposed construction is obtained using a specific optimization algorithm that allows to minimize SNR for a given target frame error probability. The decoding of the proposed codes is based on the idea of woven codes decoding. Simulation results show that suggested code construction being decoded by woven-based decoding algorithm outperforms low-rate 5G LDPC codes.
In this paper, we propose a concatenated coding scheme involving an outer Reed-Muller (RM) code and an inner Finite Field low-density parity check (LDPC) code of medium length and high rate. It lowers the error floor of inner Finite Field LDPC code. This concatenation scheme offers flexibility in design and it is easy to implement. In addition, the decoding works in a serial turbo manner and has no harmful trapping sets of size smaller than the minimum distance of the outer code. The simulation results indicate that the proposed serial concatenation can eliminate the dominant trapping sets of the inner Finite Field LDPC code.
Low Density Parity Check(LDPC) Codes is a class of approaching limits error correction codes which has gained widely application in communications. The excellent performance, however, is the result of a large number of repeatedly conducting iterative decoding algorithm, and is apt to be seriously affected by small girth in the parity check matrix. In this paper we present a novel serial concatenated scheme for LDPC codes which utilize much smaller generation matrix and the interleaver to reduce possibilities of girth, thus reducing the number of iterations in decoding. Simulation shows that the new codes have better performance while less requirement of iterations.
Despite the performance of 5th Generation Low Density Parity Check (5G-LDPC) codes close to the capacity limit, the near-optimal floating-point BP decoding will lead to excessive use of hardware and high complexity of calculation. Thus, the quantized min-sum decoder with limited-precision is usually used in practical implementations. No matter using high or low precision quantization, some 5G-LDPC codes always suffer from the problem of high error floor, which affects their applications in future ultra-reliable scenarios. Using Reed-Solomon (RS) codes as the outer codes can significantly lower the error floor of 5G-LDPC codes due to their Hamming distance properties and excellent error-correction capability. In order to further improve the overall performance, an efficient iterative decoding algorithm of RS-LDPC concatenated codes is proposed in this paper. The proposed iterative algorithm of RS-LDPC codes can achieve noticeable gains over the 5G-LDPC codes at lower FER.
—Low-density parity-check (LDPC) codes have been shown to deliver capacity approaching performance; however, problematic graphical structures (e.g. trapping sets) in the Tanner graph of some LDPC codes can cause high error floors in bit-errorratio (BER) performance under conventional sum-product algorithm (SPA). This paper presents a serial concatenation scheme to avoid the trapping sets and to lower the error floors of LDPC code. The outer code in the proposed concatenation is the LDPC, and the inner code is a high rate array code. This approach applies an interactive hybrid process between the BCJR decoding for the array code and the SPA for the LDPC code together with bit-pinning and bit-flipping techniques. Margulis code of size (2640, 1320) has been used for the simulation and it has been shown that the proposed concatenation and decoding scheme can considerably improve the error floor performance with minimal rate loss