Decoding of NonBinary LDPC Codes using the Information Bottleneck Method Recently, a novel lookup table based decoding method for binary lowdensity paritycheck codes has attracted considerable attention. In this approach, mutualinformationmaximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to nonbinary codes. This is not a straightforward extension but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the logmax decoding algorithm and operates close to sumproduct decoding.

The Probabilistic Finite Alphabet Iterative Decoder for LowDensity ParityCheck Codes We propose in this paper a new approach of applying the NonSurjective Finite Alphabet Iterative Decoder (NSFAID) for the LowDensity ParityCheck (LDPC) decoding. Differently from the NSFAID which applies a fixed nonlinear function by using a fixed LookUpTable (LUT) on the variable node messages, the proposed method, called Probabilistic FAID (PFAID), uses more than one LUT in a probabilistic way. By using the density evolution, we show that this method provides a significant improvement in performance compared to the NSFAID and the traditional MS. The advantage of PFAID is shown by the fact that, a PFAID with low message quantization level can reach or even surpass the performance of the higher level quantization MS decoder. Furthermore, we show that PFAID can be efficiently implemented with no hardware overhead compared to MinSum (MS) or NSFAID with the same message quantization level. The hardware complexity analysis and decoding simulation performance are provided as superiority evidences of PFAID over the referenced benchmarks.