Raptor-like Low-density Parity-check Research Articles

High-speed information reconciliation with syndrome-based early termination for continuous-variable quantum key distribution.

Information reconciliation (IR) is an indispensable component in the post-processing stage of continuous-variable quantum key distribution (CV-QKD), which adopts error-correcting codes to address the asymmetry of secret keys. Currently, low-density parity-check (LDPC) decoding in IR is a post-processing bottleneck in high-speed CV-QKD systems since the upper bound on secret key rate is higher than the information throughput delivered by decoder. In this paper, we study the relationship between the syndrome variation pattern (SVP) in iterative decoding and reconciliation frame error rate. An early termination scheme based on SVP is proposed and applied to multidimensional reconciliation, which can increase information throughput by adaptively adjusting the iteration number of iterative decoding to real-time decoding status. Furthermore, we show that only the resulting syndrome of the highest-rate code part in Raptor-like LDPC codes needs to be calculated to verify whether the reconciliation is successful by studying the convergency of resulting syndrome, which can save a large fraction of computational resources for syndrome calculation. Simulation results show that information throughput of the proposed scheme can be improved by 617.1% compared to the existing scheme when the IR efficiency reaches 97.09%. The proposed scheme points out a new direction for breaking the post-processing bottleneck in high-speed CV-QKD systems.

Block Markov superposition transmission of LDPC codes

In this paper, based on the block Markov superposition transmission (BMST) technique, we present a new class of coupled low-density parity-check (LDPC) codes for the transport block (TB)-based transmission to improve the error-correcting performance. For encoding, the previous LDPC codewords corresponding to a TB (at prior time slot) are interleaved and superimposed onto the current LDPC codewords, resulting in the transmitted codewords. For decoding, the sliding window decoding algorithm with sum-product or min-sum implementations can be employed, inheriting a relatively low-latency decoding. A distinguished advantage of the proposed coded transmission over spatially coupled LDPC (SC-LDPC) codes is that the encoder/decoder of the proposed codes can be designed by reusing the encoder/decoder architecture of component block LDPC codes. To analyze the waterfall performance of BMST-LDPC code ensembles, we present the protograph-based EXIT chart analysis, which can efficiently predict the error-correcting performance in waterfall region. To analyze the error-floor performance of BMST-LDPC codes, we employ the genie-aided (GA) lower bound, which can efficiently predict the error-correcting performance in error-floor region. For ease of implementation, the BMST-LDPC codes are constructed by taking the (2, 4)-raptor-like LDPC codes or the 5G LDPC codes as the basic components. The numerical results reveal that the proposed codes can have capacity-approaching performance, exhibiting a gap of 0.007 ​dB away from the corresponding Shannon limit. They also reveal that, by using the proposed BMST construction, the error-correcting performance of the original 5G block LDPC codes can be significantly improved, achieving coding gains up to one dB over the AWGN channels and two dB over the fast fading channels.

Neural Network Aided Impulsive Perturbation Decoding for Short Raptor-Like LDPC Codes

As short packet communications become more important, multi-round belief propagation decoding with impulsive perturbation (MBPD-IP) was proposed to improve the decoding of short low-density parity-check (LDPC) codes. To operate the MBPD-IP effectively, it is crucial to select proper symbols to be perturbed in as few trials as possible. Unfortunately, existing perturbation symbol selection criteria are heuristic and not effective for special codes such as raptor-like (RL) LDPC codes. In this letter, a neural network (NN) based perturbation symbol selection scheme for MBPD-IP is proposed where the symbols to be perturbed are selected from a pre-trained NN. It is shown that the proposed scheme performs significantly better than existing schemes for the RL LDPC code of 5G new radio and still works well for plain code structures.

A Low Complexity Decoding Scheme for Raptor-Like LDPC Codes

Recently, a new structure of low density parity check (LDPC) code named raptor-like LDPC code has attracted much attention. It has better performance at low code rate. In this paper, a novel decoding scheme for raptor-like LDPC code is proposed. First, the Gaussian approximation density evolution (GADE) algorithm is used to track and analyze the message transmission during the decoding process. It is found that certain log likelihood ratio (LLR) messages can be approximated by “zero” setting in the early iteration of raptor-like LDPC decoding. In other words, some column and row operations could be eliminated without compromise the performance. Next, we propose a new decoding scheme, which can skip unnecessary column and row operations. In comparison with the traditional belief propagation (BP)-based LDPC decoding scheme, the proposed scheme can reduce the decoding complexity. Additionally, a new algorithm is developed to facilitate the selection of the early iteration number. With this novel design, the proposed decoding scheme performs almost the same as the traditional BP-based scheme. To proof the concept, the raptor-like LDPC codes in the ATSC3.0 digital TV system are used to evaluate the proposed scheme, in comparison with the traditional BP-based schemes, i.e., sum-product algorithm (SPA), offset min-sum algorithm (OMSA), and normalized min-sum algorithm (NMSA). The simulation results confirm that the proposed scheme can reduce the decoding complexity without sacrifice in performance for all SPA, OMSA, and NMSA methods. About 10% complexity reduction can be achieved. This will reduce the buttery consumption for Internet of Things (IoT) and handheld devices.

Density Evolution Based on Two-Type Degree Distribution Framework of Raptor-Like LDPC

The traditional degree distribution framework is a useful tool to analyze irregular low density parity check (LDPC) code. However, it cannot be used to analyze raptor-like LDPC code as it cannot describe the most important structural feature of raptor-like LDPC code, which is that any check node is connected to at most one degree-one variable node. In this paper, we propose a two-type degree distribution framework for raptor-like LDPC code. The proposed framework can describe the special structural feature of raptor-like LDPC code by dividing the check nodes into two different sets. One is the set of check nodes connected to those degree-one variable nodes, the other is the set of check nodes unconnected to those degree-one variable nodes. Furthermore, we propose a two-type discrete density evolution algorithm and a two-type Gaussian approximation density evolution algorithm based on the proposed two-type degree distribution framework to estimate the threshold of raptor-like LDPC code. During the decoding analysis, the proposed algorithms treat the check nodes belonging the two separate sets differently. Compared with the traditional multi-edge type (MET) algorithm, the proposed algorithms allow us to calculate the threshold more quickly without much sacrifice in accuracy. For some raptor-like LDPC codes adopted by the Advanced Television Systems Committee 3.0 (ATSC3.0) standard, the thresholds estimated by the proposed algorithms can be very close to the thresholds estimated by the traditional MET algorithm. The deviations are less than 0.07 dB. Meanwhile, the proposed algorithms can tremendously reduce the computation complexity because of the two-type degree distribution framework and the Gaussian approximation.