Optimized Non-Surjective FAIDs for 5G LDPC Codes With Learnable Quantization

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.