LDPC Research Articles

An Approach to Constructing Convolutional Codes With Moderate Density and Quasi-Cyclic Structure

There exist in the literature two natural generalizations of low density parity check (LDPC) codes: 1) LDPC convolutional codes or sometimes also called spatially coupled LDPC codes which have shown to be able to reach Shannon capacity in a practical way. 2) Moderate density parity check (MDPC) codes which are linear codes possessing a parity check matrix whose row weight is not more than O(√n), still allowing efficient decoding with high probability. MDPC codes became a highly interesting class of block codes for the purpose of doing code-based cryptography.In this paper we study MDPC convolutional codes and some of their basic properties. At the end of the paper we explain how one can construct a new code-based cryptographic system. This new system can be seen as a convolutional version of the famous BIKE system currently evaluated for possible standardization by the National Institute for Standards and Technology (NIST).

Rate-compatible LDPC Codes based on Primitive Polynomials and Golomb Rulers

Rate-compatible LDPC Codes based on Primitive Polynomials and Golomb Rulers

Construction of Protograph-Based LDPC Codes With Chordless Short Cycles

Construction of Protograph-Based LDPC Codes With Chordless Short Cycles

Minimum-Set Min-Sum Decoding Algorithms for Non-Binary LDPC Codes

Minimum-Set Min-Sum Decoding Algorithms for Non-Binary LDPC Codes

A Low-Complexity Bit-Embedding Decoder for Non-Binary LDPC Codes in $\mathbb {F}_{2^{q}}$

A Low-Complexity Bit-Embedding Decoder for Non-Binary LDPC Codes in $\mathbb {F}_{2^{q}}$

GC-Like LDPC Code Construction and its NN-Aided Decoder Implementation

GC-Like LDPC Code Construction and its NN-Aided Decoder Implementation

Neural Self-Corrected Min-Sum Decoder for NR LDPC Codes

Neural Self-Corrected Min-Sum Decoder for NR LDPC Codes

Boosting Ordered Statistics Decoding of Short LDPC Codes with Simple Neural Network Models

Boosting Ordered Statistics Decoding of Short LDPC Codes with Simple Neural Network Models

Customized Branched Neural Network-aided Shuffled Min-Sum Decoder for Protograph LDPC Codes

Customized Branched Neural Network-aided Shuffled Min-Sum Decoder for Protograph LDPC Codes

Performance of Spatially Coupled LDPC Codes Over the Underwater Wireless Optical Channel With Strong Turbulence and Pointing Errors

Performance of Spatially Coupled LDPC Codes Over the Underwater Wireless Optical Channel With Strong Turbulence and Pointing Errors

Low-density parity-check codes: tracking non-stationary channel noise using sequential variational Bayesian estimates

We present a sequential Bayesian learning method for tracking non-stationary signal-to-noise ratios in low-density parity-check (LDPC) codes by way of probabilistic graphical models. We represent the LDPC code as a cluster graph using a general purpose cluster graph construction algorithm called the layered trees running intersection property (LTRIP) algorithm. The channel noise estimator is a global gamma cluster, which we extend to allow for Bayesian tracking of non-stationary noise variation. We evaluate our proposed model on real-world 5G drive-test data. Our results show that our model can track non-stationary channel noise accurately while adding performance benefits to the LDPC code, which outperforms an LDPC code with a fixed stationary knowledge of the actual channel noise.

Fast computation of cyclic convolutions and their applications in code-based asymmetric encryption schemes

The development of fast algorithms for key generation, encryption and decryption not only increases the efficiency of related operations. Such fast algorithms, for example, for asymmetric cryptosystems on quasi-cyclic codes, make it possible to experimentally study the dependence of decoding failure rate on code parameters for small security levels and to extrapolate these results to large values of security levels. In this article, we explore efficient cyclic convolution algorithms, specifically designed, among other things, for use in encoding and decoding algorithms for quasi-cyclic LDPC and MDPC codes. Corresponding convolutions operate on binary vectors, which can be either sparse or dense. The proposed algorithms achieve high speed by compactly storing sparse vectors, using hardware-supported XOR instructions, and replacing modulo operations with specialized loop transformations. These fast algorithms have potential applications not only in cryptography, but also in other areas where convolutions are used.

Advances and Trends in Channel Codes for Underwater Acoustic Communications

Due to the simultaneous existence of severe difficulties caused by multi-path, Doppler, and environmental noise caused by underwater acoustic channels, designing a stable and reliable underwater acoustic communication system (UWACS) is a challenging task. In addition to channel estimation and equalization, the technique of channel codes, which is capable of approaching Shannon’s capacity at a low encoding and decoding complexity, offers an efficient and reliable solution to improve the performance of the UWACS and thus draws extensive attention from the research community. By seeking a balance between communication efficiency and channel tolerance via multiple coding rate tuning, it has been recognized that the rate-compatible codes can achieve smooth rate-adaptive transmission under highly diverse underwater acoustic channel states. While there has been a substantial number of investigations on rate-compatible channel codes for the UWACS, in this paper, the research of rate-compatible channel codes has been summarized, reviewed, and compared, mainly focusing on the low-density parity-check (LDPC) and polar codes, which render flexibility in terms of code length and rate. Furthermore, typical research was evaluated and compared from the practical viewpoint of performance under real noise in a shallow water environment. Finally, problems encountered by the LDPC and polar codes for the UWACS were highlighted, and several future research issues were discussed.

BEP evaluation of 5G LDPC codes in a pre-amplified optical PPM receiver

We present results for the performance of a pre-amplified optical pulse-position modulation (PPM) receiver that utilizes the low-density parity-check (LDPC) correction codes of the 5G standard. The code construction is suitable for correcting burst errors that are introduced by PPM. Simulation results show that the LDPC codes can provide a very significant real gain, provided that the code rate is chosen appropriately. We find that the code rates that minimize the bit-error-probabilities (BEPs) of the system range between 2/3 and 22/26, with higher code rates being required in receivers that operate under increased optical noise. It is also shown that a comparable real gain is obtained for both the sum–product and min-sum decoders, while the power penalty of the latter one is only limited to 0.2 dB, when the aforementioned code rates are utilized.

Partial Spatial Coupling of LDPC Codes: Reducing the Gap to Capacity by Improving the Rate

Partial Spatial Coupling of LDPC Codes: Reducing the Gap to Capacity by Improving the Rate

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.

Two-Round Selection-Based Bit Flipping Decoding Algorithm for LDPC Codes

This paper presents a novel iterative reliability-based bit flipping (BF) algorithm for decoding low-density parity-check codes. The new decoder is a single BF algorithm called two-round selection -based bit flipping. It introduces the idea of a two-round selection of the flipped bit, based successively on hard and soft received channel values. In the first stage, a set of unreliable bits is identified, and then a second selection is used, to pick out among them the bit to flip. In the second round of selection, the initial belief about received signals, contributes efficiently to selecting the best candidate bit. We demonstrate through simulations over the binary-input additive white Gaussian noise channel and the Rayleigh fading channel that the proposed algorithm exhibits better decoding performance when compared with some well-known soft decision BF algorithms. A complexity analysis of the proposal and a comparison to other BF decoders are also presented.

Super-Simple (v, 5, 2) Directed Designs and Their Smallest Defining Sets with Application in LDPC Codes

Super-Simple (v, 5, 2) Directed Designs and Their Smallest Defining Sets with Application in LDPC Codes

Parity Check Codes for Second Order Diversity

Short block length “block” codes are typically not used in wireless standards as soft decision decoding is computationally intensive and hard decision decoding results in performance loss. However, short block lengths are of interest to massive machine-type communications (mMTC) and ultra-reliable low-latency communications (URLLC). In this paper, we propose a diversity preserving enhanced hard-decision decoding scheme for parity check codes (PCC) over Rayleigh fading channels. The proposed flip decoding scheme has linear complexity in the block length. Theoretical analysis and simulation results verify the correctness of the proposed detection scheme.

Partial IDS decoding based on the base graph of protograph LDPC codes

AbstractThe residual belief propagation (RBP) algorithm, which is the most classic informed dynamic scheduling strategy, achieves outstanding performance in error correction and can drastically accelerate convergence speed. However, the greedy algorithmic property of this iterative decoding will inevitably cause loss of decoding performance. To address this, a novel algorithm called the partial average bundle residual belief propagation (PABRBP) is proposed in this paper. According to the construction characteristics of a base matrix of protograph‐LDPC codes, informed dynamic scheduling (IDS) strategies are applied to an edge bundle of base matrices for the first time. This edge bundle of the base matrix can be applied to a corresponding cyclic permutation matrix. Furthermore, the update level of each bundle is determined by the value of the Partially Average Bundle Residual (PABR). Therefore, the edge message with the maximum residual in each bundle is updated in order, and the process of iterative decoding is less likely to become trapped in a local optimum. Additionally, the generation of silent nodes is reduced as much as possible. To further improve the PABRBP decoding performance for medium and long codes over the fading channel, the adjusted compensation term is periodically introduced. Analysis and simulation results show that PABRBP demonstrates a notable convergence quality and decoding performance improvement over the fading channels compared to existing state‐of‐art IDS algorithms.