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International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON)

On the woven-like concatenation of LDPC codes

Fedor I. Ivanov, Aleksey Kuvshinov

Published Nov 11, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1109/sibircon56155.2022.10016964

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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.
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.
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.
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.
LDPC code shows a good performance with long-block codes. However, certain channels are constrained to use short-block codes due to latency. Therefore, concatenated LDPC codes with iterative decoding is a good choice to get a good performance. Concatenated binary LDPC codes were introduced as a class of concatenated codes in which the LDPC codes are irregular codes having different parameters. Although irregular LDPC codes are more efficient than regular codes, irregular LDPC codes have an error floor and a higher encoding complexity than regular code. In this paper, in order to get a good performance/complexity trade-off with a short-block code, we investigate a parallel concatenation of two identical regular binary LDPC codes, using an interleaver. Simulation results show that the proposed code outperforms a single LDPC code. The proposed code needs less time decoding delay than a single LDPC code with the same iteration number. Also, the proposed code needs a less number of iterations to achieve the same performance of a single LDPC code that leads to less decoding complexity and decoding delay. A simplified algorithm, the min-sum algorithm, that is used to decode the component codes shows a small performance loss with respect to the sum-product algorithm.