Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes

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.Comment: 16 pages, 22 figures, 2 table

An improvement and a fast DSP implementation of the bit flipping algorithms for low density parity check decoder

For low density parity check (LDPC) decoding, hard-decision algorithms are sometimes more suitable than the soft-decision ones. Particularly in the high throughput and high speed applications. However, there exists a considerable gap in performances between these two classes of algorithms in favor of soft-decision algorithms.  In order to reduce this gap, in this work we introduce two new improved versions of the hard-decision algorithms, the adaptative gradient descent bit-flipping (AGDBF) and adaptative reliability ratio weighted GDBF (ARRWGDBF).  An adaptative weighting and correction factor is introduced in each case to improve the performances of the two algorithms allowing an important gain of bit error rate. As a second contribution of this work a real time implementation of the proposed solutions on a digital signal processors (DSP) is performed in order to optimize and improve the performance of these new approchs. The results of numerical simulations and DSP implementation reveal a faster convergence with a low processing time and a reduction in consumed memory resources when compared to soft-decision algorithms. For the irregular LDPC code, our approachs achieves gains of 0.25 and 0.15 dB respectively for the AGDBF and ARRWGDBF algorithms

New low-density-parity-check decoding approach based on the hard and soft decisions algorithms

It is proved that hard decision algorithms are more appropriate than a soft decision for low-density parity-check (LDPC) decoding since they are less complex at the decoding level. On the other hand, it is notable that the soft decision algorithm outperforms the hard decision one in terms of the bit error rate (BER) gap. In order to minimize the BER and the gap between these two families of LDPC codes, a new LDPC decoding algorithm is suggested in this paper, which is based on both the normalized min-sum (NMS) and modified-weighted bit-flipping (MWBF). The proposed algorithm is named normalized min sum- modified weighted bit flipping (NMSMWBF). The MWBF is executed after the NMS algorithm. The simulations show that our algorithm outperforms the NMS in terms of BER at 10-8 over the additive white gaussian noise (AWGN) channel by 0.25 dB. Furthermore, the proposed NMSMWBF and the NMS are both at the same level of decoding difficulty

High performance binary LDPC-coded OFDM systems over indoor PLC channels

Power line communication (PLC) technology is actually among the most renowned technologies for home environments due to their low-cost installation opportunities. In this study, the bit error rate (BER) performances of binary low-density parity check (LDPC) coded orthogonal frequency-division multiplexing (OFDM) systems have been considered over indoor PLC channels. Performances comparison of diverse soft and hard decision LDPC decoder schemes such as Min-Sum (MS), weighted bit flipping (WBF), gradient descent bit-flip (GDBF), noisy gradient descent bit-flip (NGDBF) and its few variants including the single-bit NGDBF (S-NGDBF), multi-bit NGDBF (M-NGDBF) and smoothed-multi-bit NGDBF (SM-NGDBF) decoders were examined in the modeled network. To evaluate the BER performance analyses three different PLC channel scenarios were generated by using new and more realistic PLC channel model proposal were also employed. All of the simulations performed in Canete’s PLC channel model showed that remarkable performance improvement can be achieved by using short-length LDPC codes. Especially, the improvements are striking when the MS or SM-NGDBF decoding algorithms are employed on the receiver side