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arXiv:2205.01503 · Globecom

Uniform vs. Non-Uniform Coarse Quantization in Mutual Information Maximizing LDPC Decoding

Philipp H. Mohr, Gerhard Bauch

Published Dec 4, 2022• 4 citations
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Abstract

Recently, low-resolution LDPC decoders have been introduced that perform mutual information maximizing signal processing. However, the optimal quantization in variable and check nodes requires expensive non-uniform operations. Instead, we propose to use uniform quantization with a simple hardware structure, which reduces the complexity of individual node operations approximately by half and shortens the decoding delay significantly. Our analysis shows that the loss of preserved mutual information resulting from restriction to uniform quantization is very small. Furthermore, the error rate simulations with regular LDPC codes confirm that the uniform quantization causes only minor performance degradation within 0.01 dB compared to the non-uniform alternative. Due to the complexity reduction, especially the proposed 3-bit decoder is a promising candidate to replace 4-bit conventional decoders.

DOI
10.1109/globecom48099.2022.10001452

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Recently, low-resolution LDPC decoders have been introduced that perform mutual information maximizing signal processing. However, the optimal quantization in variable and check nodes requires expensive non-uniform operations. Instead, we propose to use uniform quantization with a simple hardware structure, which reduces the complexity of individual node operations approximately by half and shortens the decoding delay significantly. Our analysis shows that the loss of preserved mutual information resulting from restriction to uniform quantization is very small. Furthermore, the error rate simulations with regular LDPC codes confirm that the uniform quantization causes only minor performance degradation within 0.01 dB compared to the non-uniform alternative. Due to the complexity reduction, especially the proposed 3-bit decoder is a promising candidate to replace 4-bit conventional decoders.
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For improving coarsely quantized decoding of LDPC codes, we propose a check node aware design of the variable node update. In contrast to previous works, we optimize the variable node to explicitly maximize the mutual information preserved in the check-to-variable instead of the variable-to-check node messages. The extended optimization leads to a significantly different solution for the compression operation at the variable node. Simulation results for regular LDPC codes confirm that the check node aware design, especially for very coarse quantization with 2- or 3-bit messages, achieves performance gains of up to 0.2 dB - without additional hardware costs. We also show that the 2-bit message resolution enables a very efficient implementation of the check node update, which requires only 2/9 of the 3-bit check node's transistor count and reduces the signal propagation delay by a factor of 4.
We enhance coarsely quantized LDPC decoding by reusing computed check node messages from previous iterations. Typically, variable and check nodes update and replace old messages every iteration. We show that, under coarse quantization, discarding old messages entails a significant loss of mutual information. The loss is avoided with additional memory, improving performance by up to 0.23 dB. We optimize quantization with a modified information bottleneck algorithm that considers the statistics of old messages. A simple merge operation reduces memory requirements. Depending on channel conditions and code rate, memory assistance enables up to 32% better area efficiency for 2-bit decoding.
We enhance coarsely quantized LDPC decoding by reusing computed check node messages from previous iterations. Typically, variable and check nodes update and replace old messages every iteration. We show that, under coarse quantization, discarding old messages entails a significant loss of mutual information. The loss is avoided with additional memory, improving performance by up to 0.23 dB. We optimize quantization with a modified information bottleneck algorithm that considers the statistics of old messages. A simple merge operation reduces memory requirements. Depending on channel conditions and code rate, memory assistance enables up to 32 % better area efficiency for 2-bit decoding.
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.