Standard Low-density Parity-check Codes Research Articles

Enhanced symbol capacity and loss budget employing joint channel coded modulation in DMT-WDM-PON

A joint channel coded modulation scheme based on symbol division multiplexing (SDM) is proposed and experimentally demonstrated in a 100-Gb/s discrete multi-tone wavelength division multiplexing passive optical network (DMT-WDM-PON) with enhanced symbol capacity and system power loss budget. The SDM was performed through low-density parity check (LDPC) coded quadrature amplitude modulation (QAM) following the optimized many-to-one mapping rule. By time domain multiplexing all four 6-bit/symbol 64QAM symbols together onto the same complex constellation point, the produced SDM-16QAM can achieve a 50% symbol capacity gain compared to the typical 16QAM with the same symbol rate. For low-latency intention, the fifth-generation new radio standard LDPC code with ultra-short code length and flexible code rate is structured to provide high signal transmission reliability and a robust mechanism within both intra- and inter-SDM symbols, supporting the iterative SDM de-multiplexing. The SDM significantly reduces the QAM orders and widens the constellation Euclidean distance, which can optimize the signal launch fiber power and reduce the resolution requirements for optoelectronic and electronic components, thus leading to apparent enhancement of the power loss budget to serve more optical network units. The experimental results show that a 4.11-dB power loss budget gain can be achieved including 1.25-dB superior receiver power sensitivity and 2.86-dB improvement of launch fiber power in the proposed DMT-WDM-PON over 20-km fiber transmission.

Hybrid neural coded modulation: Design and training methods

We propose a hybrid coded modulation scheme which composes of inner and outer codes. The outer-code can be any standard binary linear code with efficient soft decoding capability (e.g. low-density parity-check (LDPC) codes). The inner code is designed using a deep neural network (DNN) which takes the channel coded bits and outputs modulated symbols. For training the DNN, we propose to use a loss function that is inspired by the generalized mutual information. The resulting constellations are shown to outperform the conventional quadrature amplitude modulation (QAM) based coding scheme for modulation order 16 and 64 with 5G standard LDPC codes.

On the Construction of Multitype Quasi-Cyclic Low-Density Parity-Check Codes With Different Girth and Length

Multitype quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of protograph LDPC codes lifted cyclically from protographs with multiple edges, represented by two weight and slope matrices. For a given weight-matrix, an approach is proposed to find the maximum-achievable girth $g_{\max }$ of the corresponding multitype QC-LDPC codes by some inevitable chains having less complexity than the existing methods. This advantage leads to some new patterns of the weight matrices such that the corresponding codes have some improvements in terms of the maximum-achievable girths or the minimum-distance upper-bounds. In continue, for a given weight-matrix with maximum-achievable girth $g_{\max }$ , some slope-matrices are constructed by a depth-first search algorithm for which the corresponding multitype QC-LDPC codes with even girth $g$ , $g\le g_{\max }$ , have smaller lengths, higher rates, or larger minimum-distances than the state-of-the-art achievements. Simulation results show that the constructed codes have some error-rate advantages than PEG, random-like, CCSDS, and 802.11n/ac IEEE standard LDPC codes.

LDPC-based Joint Source Channel Coding and Decoding Strategies for single relay cooperative communications

This paper investigates new cooperative communication strategies based on Low-Density Parity-Check codes (LDPC) with Joint Source-Channel (JSC) coding and decoding algorithms to efficiently deliver a correlated content to a destination node. The proposed strategies rely on double LDPC codes where the source and the channel coding are similar to standard LDPC operations, and can be mapped on Tanner graphs for message-passing decoding. Three coding strategies are proposed where different LDPC source and channel coding setups are applied at the source node and the relay node. For each transmission strategy, we propose a graph mapping the whole network, over which iterative message-passing decoding is applied, and where the probability of errors in the source–relay link are taken into account. We showed, based on computer simulations, that the proposed strategies can provide substantial improvements compared to equivalent rates point-to-point systems. Simulation results also showed that the system performance depends on the relay position, and that adapting the source and the relay channel coding rates accordingly can enhance the overall system performance for a time-varying network.

Multilevel Coding for the Full-Duplex Decode-Compress-Forward Relay Channel

The Decode-Compress-Forward (DCF) is a generalization of Decode-Forward (DF) and Compress-Forward (CF). This paper investigates conditions under which DCF offers gains over DF and CF, addresses the problem of coded modulation for DCF, and evaluates the performance of DCF coded modulation implemented via low-density parity-check (LDPC) codes and polar codes. We begin by revisiting the achievable rate of DCF in discrete memoryless channels under backward decoding. We then study coded modulation for the decode-compress-forward via multi-level coding. We show that the proposed multilevel coding approaches the known achievable rates of DCF. The proposed multilevel coding is implemented (and its performance verified) via a combination of standard DVB-S2 LDPC codes, and polar codes whose design follows the method of Blasco-Serrano.

Analysis of Saturated Belief Propagation Decoding of Low-Density Parity-Check Codes

We consider the effect of log-likelihood ratio saturation on the belief-propagation decoding of low-density parity-check codes. Saturation is commonly done in practice and is known to have a significant effect on the error-floor performance. Our focus is on threshold analysis and the stability of density evolution. We analyze the decoder for standard low-density parity-check code ensembles and show that belief-propagation decoding generally degrades gracefully with saturation. Stability of density evolution is, on the other hand, rather strongly affected by saturation, and the asymptotic qualitative effect of saturation is similar to reduction by one of variable-node degree. We also describe conditions under which the block-error threshold for saturated belief-propagation decoding equals the bit-error threshold.

Searching for Binary and Nonbinary Block and Convolutional LDPC Codes

A unified approach to search for and optimize codes determined by their sparse parity-check matrices is presented. Replacing the nonzero elements of a binary parity-check matrix (the base or parent matrix) either by circulants or by companion matrices of elements from a finite field GF $(2^{m})$ , we obtain quasi-cyclic low-density parity-check (LDPC) block codes and binary images of nonbinary LDPC block codes, respectively. By substituting monomials of a formal variable $D$ , we obtain the polynomial description of an LDPC convolutional code. A set of performance measures applicable to different classes of LDPC codes is considered, and a greedy algorithm for code performance optimization is presented. The heart of the new optimization algorithm is a fast procedure for searching for LDPC codes with large girth of their Tanner graphs. For a few classes of LDPC codes, examples of codes combining good error-correcting performance with compact representation are obtained. In particular, we present optimized convolutional LDPC codes and conclude that the LDPC block codes are still superior to their convolutional counterparts if both decoding complexity and coding delay are considered. Moreover, a specific channel model can easily be embedded into the optimization loop. Thereby, the code can be optimized for a specific channel. The efficiency of such an optimization is demonstrated via an example of faster than Nyquist (FTN) signaling using LDPC codes. The FTN strategy combined with a rate $R=1/2$ LDPC code of length 64 800 optimized for effective data rate $R=3/4$ gains more than 0.5 dB compared with the standard LDPC codes of the same rate and length. The obtained gain corresponds to transmission at the capacity of the binary input additive white Gaussian noise channel. In most numerical examples, we consider codes with bidiagonal structure of the parity-check matrix. This restriction preserves low encoding complexity and allows fair comparison with codes selected for communication standards.

Quasi-cyclic LDPC codes using overlapping matrices and their layered decoders

Quasi-cyclic (QC) low-density parity-check (LDPC) codes have the parity-check matrices consisting of circulant matrices. Since QC LDPC codes whose parity-check matrices consist of only circulant permutation matrices are difficult to support layered decoding and, at the same time, have a good degree distribution with respect to error correcting performance, adopting multi-weight circulant matrices to parity-check matrices is useful but it has not been much researched. In this paper, we propose a new code structure for QC LDPC codes with multi-weight circulant matrices by introducing overlapping matrices. This structure enables a system to operate on dual mode in an efficient manner, that is, a standard QC LDPC code is used when the channel is relatively good and an enhanced QC LDPC code adopting an overlapping matrix is used otherwise. We also propose a new dual mode parallel decoder which supports the layered decoding both for the standard QC LDPC codes and the enhanced QC LDPC codes. Simulation results show that QC LDPC codes with the proposed structure have considerably improved error correcting performance and decoding throughput.

Performance of Standard Irregular LDPC Codes under Maximum Likelihood Decoding

In this paper, we derive an upper bound for the average block error probability of a standard irregular low-density parity-check (LDPC) code ensemble under the maximum-likelihood (ML) decoding. Moreover, we show that the upper bound asymptotically decreases polynomially with the code length. Furthermore, when we consider several regular LDPC code ensembles as special cases of standard irregular ones over an additive white Gaussian noise channel, we numerically show that the signal-to-noise ratio (SNR) thresholds at which the proposed bound converges to zero as the code length tends to infinity are smaller than those for a bound provided by Miller et al. We also give an example of a standard irregular LDPC code ensemble which has a lower SNR threshold than a given regular LDPC code ensemble.

LDPC Codes in Communications and Broadcasting

SUMMARY Low-density parity-check (LDPC) codes are one of the most powerful error correcting codes and are attracting much attention these days. LDPC codes are promising for communications and broadcasting as well where the use of error correcting codes are essential. LDPC codes have been standardized in some communication standards, such as, IEEE802.16e, DVB-S2, IEEE802.3an (10BASE-T), and so on. The performance of LDPC codes largely depend on their code structure and decoding algorithm. In this paper, we present the basics of LDPC codes and their decoding algorithms. We also present some LDPC codes that have good performance and are receiving much attention particularly in communication systems. We also overview some standardized LDPC codes, the LDPC codes standardized in DVB-S2 and the IEEE802.16e standard LDPC codes. Moreover, we present some research on LDPC coded MIMO systems and HARQ using LDPC codes.

Turbo Equalization With Single-Parity Check Codes and Unequal Error Protection Codes

The performance of turbo equalization with interleaved single-parity check codes on partial-response channels is evaluated. Single-parity check codes are weak codes, but are shown to have modest performance gain. The proposed system achieves gains of 3.5, 3.4, 2.7, and 2.4 dB with code rates of 19/20,24/25,49/50, and 63/64, respectively, at a BER of 10-5. The complexity of the proposed decoder is significantly lower than that of turbo equalization using standard low-density parity-check codes. These single-parity check codes are modified to be unequal error protection codes, designed to decrease the probability that Viterbi error events span Reed-Solomon symbol boundaries, resulting in a decrease of the sector error rate. Once such code gains an additional 0.1 dB over a single-parity check code of the same code rate of 24/25

Serial concatenation of LDPC codes and differential modulations

In this paper, we consider serially concatenated schemes with outer novel and efficient low-density parity-check (LDPC) codes and inner modulations effective against channel impairments. With a pragmatic approach, we show how to design LDPC codes tailored for simple and robust modulation formats, such as differentially encoded (DE) modulations. The LDPC codes are optimized through the use of a recently proposed analysis technique based on extrinsic information transfer (EXIT) charts. In particular, we optimize, through a clever random walk in the parametric space, the degree distributions of the outer LDPC codes, obtaining significant insights on the impact of such distributions on the performance of the proposed concatenated schemes. The optimization is carried out for transmission over both the additive white Gaussian noise channel and a noncoherent channel. The performance predicted by the EXIT chart-based optimization is confirmed by results obtained via computer simulations, considering phase-shift keying and quadrature amplitude modulation at the transmitter side, and iterative demodulation/decoding at the receiver side. The significance of the proposed optimized design of LDPC-coded schemes with DE modulations is validated by the fact that standard nonoptimized LDPC codes perform poorly when used together with inner DE modulations.