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Journal of Physics Conference Series

Non-uniform Quantization of Soft Information for 5G LDPC Codes

Xiaohua Chang, Yu Zhang

Published Aug 1, 2020• 0 citations
Publisher

Abstract

Abstract This paper proposes a non-uniform quantization algorithm of soft information based on density evolution for the decoding of low-density parity check (LDPC) codes, which applies a non-linear transform function to soft information, and provides good block error rate performance. The transform function is obtained by minimizing weighted mean square quantization error for every combination of modulation type and LDPC codes and has an analytical expression of distribution of soft information. It can be realized as look-up table via quantization of transform function and has low complexity of implementation. Simulation results show that the error performance of proposed algorithm is close to no quantization condition and has a gain of around 0.3 dB compared to uniform quantization algorithm for 5G’s rate 2/3 LDPC codes with APSK modulation over additive white Gaussian noise (AWGN) channel.

DOI
10.1088/1742-6596/1606/1/012014

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Abstract This paper proposes a non-uniform quantization algorithm of soft information based on density evolution for the decoding of low-density parity check (LDPC) codes, which applies a non-linear transform function to soft information, and provides good block error rate performance. The transform function is obtained by minimizing weighted mean square quantization error for every combination of modulation type and LDPC codes and has an analytical expression of distribution of soft information. It can be realized as look-up table via quantization of transform function and has low complexity of implementation. Simulation results show that the error performance of proposed algorithm is close to no quantization condition and has a gain of around 0.3 dB compared to uniform quantization algorithm for 5G’s rate 2/3 LDPC codes with APSK modulation over additive white Gaussian noise (AWGN) channel.
Very high data rates and decoding computational complexity place strict constraints in 5G and 6G communications. In this paper, non-uniform Quantized Decoding algorithm is proposed for Low-density Parity Check codes (LDPC). In the proposed algorithm, the check node updating process is carried out using quantization, which reduces complexity. The Sum Product Algorithm (SPA) is iterative message passing decoding techniques offer the optimal performance for LDPC codes. Implementations use message-passing decoding with more precision, results extremely high complexity. In Iterative, message-passing (MP), trapping sets and absorbing sets causes low error floor. In this article non-uniform quantization proposed to overcome dynamic range of values over uniform quantization. Simulation results provide coding gain increases closer to of 0.5 dB in higher SNR and has good error floor at 10−5.
This paper proposes an adaptive normalized min-sum algorithm for the decoding of low-density parity check (LDPC) codes, which utilizes an adaptive normalization factor to improve the accuracy of the soft information transferred during the iterative decoding process, and provides superior performance accordingly. This adaptive normalization factor can be adjusted dynamically and adaptively at each decoding iteration according to a look-up table obtained via training and simulation. Its implementation facility and independence from the channel characteristics make the proposed adaptive normalized min-sum algorithm expect a wide application. Simulation results show that the proposed algorithm can achieve performance much closer to the sum-product algorithm and a coding gain of around 0.2dB compared to the conventional normalized min-sum algorithm for DVB-S2's rate 2/5 and 3/5 LDPC codes over the additive white Gaussian noise (AWGN) channel.
It is proved that hard decision algorithms are more appropriate than a soft decision for low-density parity-check (LDPC) decoding since they are less complex at the decoding level. On the other hand, it is notable that the soft decision algorithm outperforms the hard decision one in terms of the bit error rate (BER) gap. In order to minimize the BER and the gap between these two families of LDPC codes, a new LDPC decoding algorithm is suggested in this paper, which is based on both the normalized min-sum (NMS) and modified-weighted bit-flipping (MWBF). The proposed algorithm is named normalized min sum- modified weighted bit flipping (NMSMWBF). The MWBF is executed after the NMS algorithm. The simulations show that our algorithm outperforms the NMS in terms of BER at 10-8 over the additive white gaussian noise (AWGN) channel by 0.25 dB. Furthermore, the proposed NMSMWBF and the NMS are both at the same level of decoding difficulty.
This letter proposes a novel approach for designing non-surjective (NS) finite alphabet iterative decoders (FAIDs) for quasi-cyclic low-density parity-check (LDPC) codes, especially 5G LDPC codes. We employ recurrent quantized neural networks to optimize the look-up tables used in NS-FAIDs, the design of which is the kernel of FAIDs. During the optimization of LUTs, the quantized message alphabets and quantization thresholds are jointly designed. To cope with the untrainable problem of quantization thresholds in the existing neural-network-based linear FAIDs, we use softmax distribution to soften the implied one-hot distribution of quantization thresholds, making it trainable in the neural network. The proposed decoders offer enhanced universality compared to existing neural network-based linear FAIDs, making them directly applicable to 5G LDPC codes with support for 2-bit quantization over the additive white Gaussian noise channel. Additionally, they significantly outperform the original NS-FAID in terms of performance.
In order to improve the performance of non-binary low-density parity check codes (LDPC) hard decision decoding algorithm and to reduce the complexity of decoding, a sum of the magnitude for hard decision decoding algorithm based on loop update detection is proposed. This will also ensure the reliability, stability and high transmission rate of 5G mobile communication. The algorithm is based on the hard decision decoding algorithm (HDA) and uses the soft information from the channel to calculate the reliability, while the sum of the variable nodes’ (VN) magnitude is excluded for computing the reliability of the parity checks. At the same time, the reliability information of the variable node is considered and the loop update detection algorithm is introduced. The bit corresponding to the error code word is flipped multiple times, before this is searched in the order of most likely error probability to finally find the correct code word. Simulation results show that the performance of one of the improved schemes is better than the weighted symbol flipping (WSF) algorithm under different hexadecimal numbers by about 2.2 dB and 2.35 dB at the bit error rate (BER) of 10−5 over an additive white Gaussian noise (AWGN) channel, respectively. Furthermore, the average number of decoding iterations is significantly reduced.
This paper extends the work on density evolution for binary low-density parity-check (LDPC) codes with Gaussian approximation to LDPC codes over GF(q) . We first generalize the definition of channel symmetry for nonbinary inputs to include q-ary phase-shift keying (PSK) modulated channels for prime q and binary-modulated channels for q that is a power of 2. For the well-defined q-ary-input symmetric-output channel, we prove that under the Gaussian assumption, the density distribution for messages undergoing decoding is fully characterized by (q-1) quantities. Assuming uniform edge weights, we further show that the density of messages computed by the check node decoder (CND) is fully defined by a single number. We then present the approximate density evolution for regular and irregular LDPC codes, and show that the (q-1) -dimensional integration involved can be simplified using a dimensionality reduction algorithm for the important case of q=2p. Through application of approximate density evolution and linear programming, we optimize the degree distribution of LDPC codes over GF(3) and GF(4). The optimized irregular LDPC codes demonstrate performance close to the Shannon capacity for long codewords. We also design GF(q) codes for high-order modulation by using the idea of a channel adapter. We find that codes designed in this fashion outperform those optimized specifically for the binary additive white Gaussian noise (AWGN) channel for a short codewords and a spectral efficiency of 2 bits per channel use (b/cu).