In communication systems, the transmitted data is corrupted by channel perturbations, such as noise and fading, which affect the reliability of the received data. Error correction codes are employed to mitigate channel perturbations. However, design and implementation of good and efficient error correction codes remains an open problem. In this paper, Low Density Parity Check (LDPC) codes are considered as they provide a reasonable trade-off between computational complexity and reliability. Good LDPC codes should ideally provide low complexity, close to capacity acheivable transmission rate, high coding threshold, and high decoding stability. In this paper, we investigate a joint LDPC code optimization algorithm using Genetic Algorithm (GA) and Linear Programming (LP) to determine the variable nodes and check nodes degrees distributions. EXIT chart analysis and Frame Error Rate (FER) performance are used to validate the proposed method.
In communication systems, the transmitted data is corrupted by channel perturbations, such as noise and fading, which affect the reliability of the received data. Error correction codes are employed to mitigate channel perturbations. However, design and implementation of good and efficient error correction codes remains an open problem. In this paper, Low Density Parity Check (LDPC) codes are considered as they provide a reasonable trade-off between computational complexity and reliability. Good LDPC codes should ideally provide low complexity, close to capacity acheivable transmission rate, high coding threshold, and high decoding stability. In this paper, we investigate a joint LDPC code optimization algorithm using Genetic Algorithm (GA) and Linear Programming (LP) to determine the variable nodes and check nodes degrees distributions. EXIT chart analysis and Frame Error Rate (FER) performance are used to validate the proposed method.
Low-density parity check (LDPC) codes, are a family of error-correcting codes, their performances close to the Shannon limit make them very attractive solutions for digital communication systems. There are several algorithms for decoding LDPC codes that show great diversity in terms of performance related to error correction. Also, very recently, many research papers involved the genetic algorithm (GA) in coding theory, in particular, in the decoding linear block codes case, which has heavily contributed to reducing the bit error rate (BER). In this paper, an efficient method based on the GA is proposed and it is used to improve the power of correction in terms of BER and the frame error rate (FER) of LDPC codes. Subsequently, the proposed algorithm can independently decide the most suitable moment to stop the decoding process, moreover, it does not require channel information (CSI) making it adaptable for all types of channels with different noise or intensity. The simulations show that the proposed algorithm is more efficient in terms of BER compared to other LDPC code decoders.
LDPC code design tools typically rely on asymptotic code behavior and are affected by an unavoidable performance degradation due to model imperfections in the short length regime. We propose an LDPC code design scheme based on an evolutionary algorithm, the Genetic Algorithm (GenAlg), implementing a “decoder-in-the-loop” concept. It inherently takes into consideration the channel, code length and the number of iterations while optimizing the error-rate of the actual decoder hardware architecture. We construct short length LDPC codes (i.e., the parity-check matrix) with error-rate performance comparable to, or even outperforming that of well-designed standardized short length LDPC codes over both AWGN and Rayleigh fading channels. Our proposed algorithm can be used to design LDPC codes with special graph structures (e.g., accumulator-based codes) to facilitate the encoding step, or to satisfy any other practical requirement. Moreover, GenAlg can be used to design LDPC codes with the aim of reducing decoding latency and complexity, leading to coding gains of up to 0.325 dB and 0.8 dB at BLER of 10-5for both AWGN and Rayleigh fading channels, respectively, when compared to state-of-the-art short LDPC codes. Also, we analyze what can be learned from the resulting codes and, as such, the GenAlg particularly highlights design paradigms of short length LDPC codes (e.g., codes with degree-1 variable nodes obtain very good results).
Error correction plays a crucial role when transmitting data from the source to the destination through a noisy channel. It has found many applications in television broadcasting services, data transmission in radiation harsh environment (e. g. space probes or physical experiments) or memory storages influenced by Single Event Effects (SEE). Low Density Parity Check (LDPC) codes provide an important technique to correct these errors. The parameters of error correction depend both on the decoding algorithm and on the LDPC code given by the parity-check matrix. Therefore, a particular design of the paritycheck matrix is necessary. Moreover, with the development of high performance computing, the application of genetic optimization algorithms to design the parity-check matrices has been enabled. In this article, we present the application of the genetic optimization algorithm to produce error correcting codes with special properties, especially the burst types of errors. The results show the bounds of correction capabilities for various code lengths and various redundancies of LDPC codes. This is particularly useful when designing systems under the influence of noise combined with the application of the error correction codes.
Low-density parity-check (LDPC) codes had a renaissance when they were rediscovered in the 1990’s. Since then LDPC codes have been an important part of the field of error-correcting codes, and have been shown to be able to approach the Shannon capacity, the limit at which we can reliably transmit information over noisy channels. Following this, many modern communications standards have adopted LDPC codes. Error-correction is equally important in protecting data from corruption on a hard-drive as it is in deep-space communications. It is most commonly used for example for reliable wireless transmission of data to mobile devices. For practical purposes, both encoding and decoding need to be of low complexity to achieve high throughput and low power consumption. This thesis provides a literature review of the current state-of-the-art in encoding and decoding of LDPC codes. Message- passing decoders are still capable of achieving the best error-correcting performance, while more recently considered bit-flipping decoders are providing a low-complexity alternative, albeit with some loss in error-correcting performance. An implementation of a low-complexity stochastic bit-flipping decoder is also presented. It is implemented for Graphics Processing Units (GPUs) in a parallel fashion, providing a peak throughput of 1.2 Gb/s, which is significantly higher than previous decoder implementations on GPUs. The error-correcting performance of a range of decoders has also been tested, showing that the stochastic bit-flipping decoder provides relatively good error-correcting performance with low complexity. Finally, a brief comparison of encoding complexities for two code ensembles is also presented.
Four-edge type low-density parity-check (FET-LDPC) codes, as an important subclass of multi-edge type LDPC codes, offer greater design flexibility and performance potential due to their heterogeneous edge type structure. However, their multi-dimensional degree distribution significantly increases the complexity of optimization. This paper proposes a joint optimization framework for FET-LDPC codes leveraging the symmetric decoding structure inherent in their dual-branch architecture. The main contributions are as follows. First, an improved decoding model is established to analyze the mutual information transmission among the four edge types during iterative decoding, where the symmetry between the accumulator (ACC) and single parity-check (SPC) branches facilitates balanced information exchange. Second, a full-dimensional extrinsic information transfer (FEXIT) chart suitable for FET-LDPC codes is constructed, capturing the mutual information flow across branches. Third, a collaborative optimization model is designed by integrating the FEXIT chart with multi-constraint linear programming (LP) to perform asymmetric optimization for different edge types. The simulation results show that the proposed method achieves significant performance improvement over unoptimized codes in additive white Gaussian noise (AWGN) channels, particularly at a bit error rate (BER) of 10−6.
Low-density parity-check (LDPC) codes can approach the Shannon limit performance closely, and are becoming one of the most promising channel codes in the Error Control Coding area.The performance of an LDPC code with given length is mainly affected by the sizes of some combinatorial characteristics of its corresponding bipartite graph and the distribution of variable degrees and check node degrees.With the help of the density evolution algorithm, randomly designed LDPC codes, with carefully chosen degree distribution pairs, have been shown to achieve better Shannon capacity performance than their regular counterparts when decoded using the iterative belief propagation (BP) decoding algorithm.However, regular LDPC codes outperform their irregular counterparts in term of their error floors.Therefore, construction of LDPC codes which have both attractive error rate performance and low error floor performance has become an attractive topic.Currently, optimization of variable node degree distribution and check node degree distribution for an LDPC code with given length, which could help the code to achieve good Shannon limit performance, has been extensively studied.In this dissertation, we demonstrate some approaches of improving the error floor performance for a given LDPC code with desired degree distribution pair.The contribution mainly includes three parts.In the first part, the relationship between cycles and unfavorable combinatorial