Cyclically Equivariant Neural Decoders for Cyclic Codes
This work addresses decoding efficiency for cyclic codes in communication systems, representing an incremental improvement with specific gains.
The authors tackled the problem of decoding cyclic codes by introducing a neural decoder that enforces cyclic shift invariance, leading to consistent performance improvements over previous neural decoders. For high-rate codes, their list decoder reduced the gap to the Maximum Likelihood decoder to less than 0.1dB.
Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by training the neural network. In this work, we propose a novel neural decoder for cyclic codes by exploiting their cyclically invariant property. More precisely, we impose a shift invariant structure on the weights of our neural decoder so that any cyclic shift of inputs results in the same cyclic shift of outputs. Extensive simulations with BCH codes and punctured Reed-Muller (RM) codes show that our new decoder consistently outperforms previous neural decoders when decoding cyclic codes. Finally, we propose a list decoding procedure that can significantly reduce the decoding error probability for BCH codes and punctured RM codes. For certain high-rate codes, the gap between our list decoder and the Maximum Likelihood decoder is less than $0.1$dB. Code available at https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders