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Circuits Systems and Signal Processing

Architecture of Generalized Bit-Flipping Decoding for High-Rate Non-binary LDPC Codes

Francisco García-Herrero, María José Canet, Javier Valls

Published Aug 30, 2012• 7 citations
Publisher
DOI
10.1007/s00034-012-9481-3

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The Probabilistic Gradient Descent Bit-Flipping (PGDBF) decoder offers a significant improvement in decoding performance for Low-Density Parity-Check (LDPC) codes on Binary Symmetric Channel (BSC). However, this outstanding decoding performance comes along with a non-negligible extra hardware cost to realize the probabilistic behavior on top of the deterministic Gradient Descent Bit-Flipping (GDBF) decoder. This paper presents a novel solution to implement PGDBF decoder on Quasi-Cyclic LDPC codes. The proposed architecture takes advantage of the cyclic shift permutation nature of QC-LDPC and changes the message flow such that a probabilistic behavior is emulated without the cost of an actual probabilistic signal generator. It is shown that, the proposed architecture improves the PGDBF decoding performance with respect to the state-of-the-art implementation while reducing hardware complexity, even being lower than that of the deterministic GDBF. The efficiency of our proposed method is verified through the ASIC 90nm CMOS technology implementations and decoding simulations.
Conventional bit-flipping (BF) algorithms spectacularly fail to handle punctured LDPC codes as they use hard decisions and, therefore, they cannot effectively cope with zero-reliability punctured symbols. However, BF techniques lead to low-cost high-speed decoders. This paper introduces a novel method that enables the use of BF-based iterative decoders for punctured LDPC codes. An erasure preprocessor is introduced and is shown to successfully mitigate the impact of puncturing, substantially improving the coding gain achieved for punctured codes under BF decoding. The proposed technique renders BF decoding of punctured codes useful, something that was not possible so far to our knowledge. Furthermore, two hardware architectures are introduced and evaluated. Hardware sharing is shown to efficiently exploit common structures in the proposed combined erasure and BF decoder, leading to a new architecture found to be particularly efficient. The proposed architecture requires extremely low hardware resources, facilitating full-parallel architectures that sustain multi-Gbps throughput rates when implemented on Virtex-7 FPGA devices.