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New Direction on Low Complexity Implementation of Probabilistic Gradient Descent Bit-Flipping Decoder

Abstract : Probabilistic Gradient Descent Bit Flipping (PGDBF) algorithm have been recently introduced as a new type of hard decision decoder for Low-Density Parity-Check Code (LDPC) applied on the Binary Symmetric Channel. By following precisely the decoding steps of the deterministic Gradient Descent Bit-Flipping (GDBF) decoder, PGDBF additionally incorporates a random perturbation in the flipping operation of Variable Nodes (VNs) and produces an outstanding decoding performance which is better to all known Bit Flipping decoders, approaching the performance of soft decision decoders. We propose in this thesis several hardware implementations of PGDBF, together with a theoretical analysis of its error correction capability. With a Markov Chain analysis of the decoder, we show that, due to the incorporation of random perturbation in VN processing, the PGDBF escapes from the trapping states which prevent the convergence of decoder. Also, with the new proposed analysis method, the PGDBF performance can be predicted and formulated by a Frame Error Rate equation as a function of the iteration, for a given error pattern. The analysis also gives a clear explanation on several phenomenons of PGDBF such as the gain of re-decoding (or restarting) on a received error pattern. The implementation issue of PGDBF is also addressed as a main part in this thesis. The conventional implementation of PGDBF, in which a probabilistic signal generator is added on top of the GDBF, is shown with an inevitable increase in hardware complexity. Several methods for generating the probabilistic signals are introduced which minimize the overhead complexity of PGDBF. These methods are motivated by the statistical analysis which reveals the critical features of the binary random sequence required to get good decoding performance and suggesting the simplification directions. The synthesis results show that the implemented PGDBF with the proposed probabilistic signal generator method requires a negligible extra complexity with the equivalent decoding performance to the theoretical PGDBF. An interesting and particular implementation of PGDBF for the Quasi-Cyclic LDPC (QC-LDPC) is shown in the last part of the thesis. Exploiting the structure of QC-LDPC, a novel architecture to implement PGDBF is proposed called Variable-Node Shift Architecture (VNSA). By implementing PGDBF with VNSA, it is shown that the decoder complexity is even smaller than the deterministic GDBF while preserving the decoding performance as good as the theoretical PGDBF. Furthermore, VNSA is also shown to be able to apply on other types of LDPC decoding algorithms.
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Khoa Le Trung. New Direction on Low Complexity Implementation of Probabilistic Gradient Descent Bit-Flipping Decoder. Signal and Image Processing. université de cergy-pontoise, 2017. English. ⟨tel-01731019⟩

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