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The Probabilistic Finite Alphabet Iterative Decoder for Low-Density Parity-Check Codes

This paper proposes a new concept of applying the Non-Surjective Finite Alphabet Iterative Decoder (NS-FAID) for the Low-Density Parity-Check (LDPC) decoding. Differently from the NS-FAID which applies a fixed nonlinear function by using a fixed Look-Up-Table (LUT) on the variable node messages, the proposed method, called Probabilistic FAID (PFAID), uses more than one LUTs in a probabilistic way. By using the density evolution, we show that this method provides a significant improvement in performance compared to the NS-FAID 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 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.