A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported GDBF variant, and comes within 0.5 dB of the belief propagation algorithm for several tested codes. Unlike other previous GDBF algorithms that provide an escape from local maxima, the proposed algorithm uses only local, fully parallelizable operations and does not require computing a global objective function or a sort over symbol metrics, making it highly efficient in comparison. The proposed NGDBF algorithm requires channel state information which must be obtained from a signal to noise ratio (SNR) estimator. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.
Several researchers proposed alternative GDBF algorithms in order to obtain fully parallel bit-flipping and improved performance. proposed an Adaptive Threshold GDBF (AT-GDBF) algorithm that achieves good performance without the use of mode-switching, allowing for fully-parallel operation @cite_23 . The same authors also introduced an early-stopping condition (ES-AT-GDBF) that significantly reduces the average decoding iterations at lower Signal to Noise Ratio (SNR). Phromsa- proposed a more complex Reliability-Ratio Weighted GDBF algorithm (RRWGDBF) that uses a weighted summation over syndrome components with an adaptive threshold to obtain reduced latency @cite_25 . The RRWGDBF method has the drawback of increased arithmetic complexity because it performs a summation of weighted syndrome components, similar to previous WBF algorithms. proposed an improved multi-bit GDBF algorithm (IGDBF) that performs very close to the H-GDBF algorithm, but requires a global sort operation to determine which bits to flip @cite_11 .
@cite_25 @cite_23 @cite_11
2061867767 2082688301 1493432783
For LDPC decoding, a class of weighted bit-flipping algorithms is much simpler than a belief propagation algorithm. This work proposes a modified Gradient Descent Bit-Flipping algorithm based on Reliability Ratio with an adaptive threshold to address trade-off between performance and latency. From numerical results, the proposed algorithm achieves lower latency without an expense of performance. It yields average iteration reduction of 15–27 over SNR range from 2.5 dB to 4.5 dB. In addition, it provides better decoding performance gains, i.e. 0.05–0.25 dB over low-to-medium SNR range between 1.5 dB and 4 dB comparing to previous schemes. Wireless sensor networks are used in many diverse application scenarios that require the network designer to trade off different factors. Two such factors of importance in many wireless sensor networks are communication reliability and battery life. This paper describes an efficient, low complexity, high throughput channel decoder suited to decoding low-density parity-check (LDPC) codes. LDPC codes have demonstrated excellent error-correcting ability such that a number of recent wireless standards have opted for their inclusion. Hardware realisation of practical LDPC decoders is a challenging area especially when power efficient solutions are needed. Implementation details are given for an LDPC decoding algorithm, termed adaptive threshold bit flipping (ATBF), designed for low complexity and low power operation. The ATBF decoder was implemented in 90 nm CMOS at 0.9 V using a standard cell design flow and was shown to operate at 250 MHz achieving a throughput of 252 Gb s iteration. The decoder area was 0.72 mm2 with a power consumption of 33.14 mW and a very small energy decoded bit figure of 1.3 pJ. Gradient Descent Bit Flipping (GDBF) decoding has one of the best decoding performances of the bit flip type decoding algorithms for low density parity check code. Multi-bit type GDBF decoding, however, achieves good error performance only with suitable thresholds. In this paper, we propose multi-bit type GDBF decoding without using thresholds. The proposed method estimates the number of bits to flip from the received soft sequence using the characteristic of the probability density distribution of the additive white Gaussian noise channel. The error performance of the proposed method is almost equal to that of the conventional method despite not using thresholds.