The development of computationally-efficient algorithms is crucial to support the extremely-low latency and ultra-high reliability requirements of the next-generation radio communication systems. Error-correction codes (ECC) are used in communication systems to maintain the reliability of data transmissions. In this paper, several commonly used artificial intelligence (AI) methods are used to design algorithms for bitwise decoding of (ECC). The AI-based decoding algorithms are analysed and compared using their error-correction performance, training time and computational intensity. The efficacy is assessed using the benchmark codes: extended binary Golay and the Hamming code for varying Signal-to-Noise Ratios (SNR) over the Additive White Gaussian Noise (AWGN) channel and the decoding performance is evaluated using the block error rate (BLER). It is envisaged that the results from this comparative study would help to identify AI models most suitable for developing computationally efficient and practically-implementable algorithms for decoding longer ECC.
The development of computationally-efficient algorithms is crucial to support the extremely-low latency and ultra-high reliability requirements of the next-generation radio communication systems. Error-correction codes (ECC) are used in communication systems to maintain the reliability of data transmissions. In this paper, several commonly used artificial intelligence (AI) methods are used to design algorithms for bitwise decoding of (ECC). The AI-based decoding algorithms are analysed and compared using their error-correction performance, training time and computational intensity. The efficacy is assessed using the benchmark codes: extended binary Golay and the Hamming code for varying Signal-to-Noise Ratios (SNR) over the Additive White Gaussian Noise (AWGN) channel and the decoding performance is evaluated using the block error rate (BLER). It is envisaged that the results from this comparative study would help to identify AI models most suitable for developing computationally efficient and practically-implementable algorithms for decoding longer ECC.
The article presents a comparative study of LDPC decoding algorithms in an additive white Gaussian noise (AWGN) channel. The aim is to identify the most efficient algorithms for reliable data transmission. Simulations were carried out using the AFF3CT tool with BPSK modulation. Several decoders were analyzed, including GALA, GALB, GALE, PPBF, WBF and MWBF. Performance was evaluated by bit error rate (BER) and frame error rate (FER). The results show that the GalE decoder achieves the best error-correction performance for long codewords (length 20480), with BER values reaching 10-5 and 10-10. For shorter code lengths, MWBF and GalE algorithms also demonstrate good results, with MWBF reaching BER ≈ 10-3 at SNR = 7 dB. In resource-limited conditions, simplified bit-flipping algorithms can provide reasonable efficiency
With the development of communication technology, modern communication networks need to achieve ultra-high reliability to meet practical demands. Forward error correction coding has been widely used in real-world communication systems for providing reliable data transmission over noisy channels. In this thesis, we investigate the efficient performance evaluation methods for block codes over memoryless channels. Performance bounds are powerful tools to provide insights on the error performance of the coded systems. In many practical scenarios where performance bounds are not applicable (e.g., due to the unavailability of the relevant coding parameters under a given decoder), the Monte Carlo simulation is still popular despite its inefficiency, especially in the low error probability regime. As a variance-reduction technique, importance sampling (IS) can significantly reduce the sample size needed for reliable estimation. We firstly examine the problem of efficient performance evaluation of linear block codes over binary symmetric channels (BSCs). Contrary to the conventional wisdom, we prove that for BSCs, all bounds based on Gallager’s first bounding technique, including the famous union bound, are not asymptotically tight for all possible choices of the Gallager region. By proposing the so-called input demodulated-output weight enumerating function (IDWEF) of a code, asymptotically tight maximum-likelihood decoding upper and lower bounds for BSCs are derived. For the cases that coding parameters are absent or suboptimal decoders are applied, we propose an efficient IS estimator by deriving the optimal IS distribution of the Hamming weight of the error vector. In addition, the asymptotic percentage saving of the proposed IS estimator over the state-of-the-art IS estimator is characterized in terms of the sample size. Its accuracy in predicting the efficiency of the proposed IS estimator is verified by extensive computer simulation. We further examine the IS estimator design and efficiency analysis problems for the additive white generalized Gaussian noise (AWGGN) channel. The generalized Gaussian distribution is an effective model to describe real-world systems with impulsive noise. It can be specialized to the Laplace and Gaussian distributions depending on the choices of the decay rates of the heavy tail. By deriving the optimal IS distribution on the one-dimensional space mapped from the observation space, we present a general framework for designing IS estimators for linear block codes over a memoryless continuous channel. We apply the framework to the AWGGN channel and propose a noise-magnitude-domain IS (NM-IS) estimator. As an efficiency measure, the asymptotic IS gain of the proposed estimator is derived in a multiple integral as the signal-to-noise ratio (SNR) tends to infinity. Specifically, we reduce the gains of both Laplace and Gaussian noise cases to a one-dimensional integral. In addition, by limiting the use of the union bound to an L1-norm sphere with an optimized radius, we derive the sphere bound for the additive white Laplace noise channel. Simulation results show the efficiency of the proposed IS estimator in terms of the sample size and verify the accuracy of the prediction of the derived IS gain. Besides, we specialize the proposed framework to further improve the efficiency of the IS simulation based on the side information of the modulation. For the AWGGN channel with binary phase-shift keying (BPSK) modulation, we propose an enhanced NM-IS estimator, which outperforms the NM-IS estimator in efficiency. For the additive white Gaussian noise channel with M-PSK modulation, we propose an angular domain IS estimator and provide its efficiency analysis in terms of the asymptotic IS gain. Furthermore, in the performance evaluation of communication systems, it is often seen that researchers are more interested in the required SNR at a target error probability Pe than the other way around. The conventional solution to this Pe-targeted SNR estimation problem involves interpolation of simulated error probabilities at multiple handpicked SNRs for estimating the required SNR at the target error probability. We propose a Pe-targeted iterative IS estimator that solves the problem algorithmically. The proposed method can achieve the same efficiency (in terms of sample size) as estimating the error probability at the required SNR and allow the confidence interval of the SNR estimate to be obtained.
Error correctiong codes (ECC) are widly used in applications to correct errors in data transmission over unreliable or noisy communication channels. Recently, two kinds of promising codes attracted lots of research interest because they provide excellent error correction performance. One is non-binary LDPC codes, and the other is polar codes. This dissertation focuses on efficient decoding algorithms and decoder design for thesetwo types of codes.Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic decoding algorithms are attractive for non-binary LDPC codes, since they involve only finite field additions and multiplications as well as integer operations and hence have significantly lower complexity than other algorithms. We propose two improvements to the majority-logic decoding algorithms. Instead of the accumulation of reliability information in the ex-isting majority-logic decoding algorithms, our first improvement is a new reliability information update. The new update not only results in better error performance and fewer iterations on average, but also further reduces computational complexity. Since existing majority-logic decoding algorithms tend to have a high error floor for codes whose parity check matrices have low column weights, our second improvement is a re-selection scheme, which leads to much lower error floors, at the expense of more finite field operations and integer operations, by identifying periodic points, re-selectingintermediate hard decisions, and changing reliability information.Polar codes are of great interests because they provably achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes an explicit construction. Most existing decoding algorithms of polar codes are based on bit-wise hard or soft decisions. We propose symbol-decision successive cancellation (SC) and successive cancellation list (SCL) decoders for polar codes, which use symbol-wise hard or soft decisions for higher throughput or better error performance. Then wepropose to use a recursive channel combination to calculate symbol-wise channel transition probabilities, which lead to symbol decisions. Our proposed recursive channel combination has lower complexity than simply combining bit-wise channel transition probabilities. The similarity between our proposed method and Arıkan's channel transformations also helps to share hardware resources between calculating bit- and symbol-wise channel transition probabilities. To reduce the complexity of the list pruning, atwo-stage list pruning network is proposed to provide a trade-off between the error performance and the complexity of the symbol-decision SCL decoder. Since memory is a significant part of SCL decoders, we also propose a pre-computation memory-saving technique to reduce memory requirement of an SCL decoder.To reduce the complexity of the recursive channel combination further, we propose an approximate ML (AML) decoding unit for SCL decoders. In particular, we investigate the distribution of frozen bits of polar codes designed for both the binary erasure and additive white Gaussian noise channels, and take advantage of the distribution to reduce the complexity of the AML decoding unit, improving the throughput-area efficiency of SCL decoders.Furthermore, to adapt to variable throughput or latency requirements which exist widely in current communication applications, a multi-mode SCL decoder with variable list sizes and parallelism is proposed. If high throughput or small latency is required, the decoder decodes multiple received words in parallel with a small list size. However, if error performance is of higher priority, the multi-mode decoder switches to a serialmode with a bigger list size. Therefore, the multi-mode SCL decoder provides a flexible tradeoff between latency, throughput and error performance at the expense of small overhead.
Abstract This paper presents an intelligent decoding methodology for low-density parity-check (LDPC) and Polar codes (P-C) based on deep reinforcement learning (DRL+Soft) for modern 5G and emerging 6G communication systems. The proposed decoder adapts its decoding strategy in real-time, optimizing bit error rate (BER) performance under varying channel conditions. Evaluation is formulated through performance metrics including BER convergence, reward dynamics, computational complexity (FLOPs), and inference latency. Simulation results show that the DRL+Soft decoder achieves up to a 2.5-fold reduction in computational cost and decreases inference time from 4.8 ms (BP) to 1.6 ms per data block, while maintaining superior BER compared to classical belief propagation (BP) and cyclic redundancy check-aided successive cancellation list (CA-SCL) decoders. The decoder exhibits improved robustness against unpredictable interference and channel impairments, making it suitable for dense device deployments and ultra-reliable low-latency communication (URLLC) scenarios. The methodology also supports reprogramming or retraining of DRL agents without hardware changes, ensuring long-term adaptability for evolving 6G networks. These results demonstrate both theoretical novelty and practical value, providing a scalable and energy-efficient solution for future wireless communication systems.
Two new algorithms for decoding the (23, 12) binary Golay code are developed with channel measurement information. For a white gaussian noise channel, each of the two algorithms achieves about 0·8 dB of decoding performance over a conventional hard-decision decoding. Furthermore, one of the algorithms requires a very small amount of computation for decoding a received block, and the other is very suitable for hardware implementation owing to its simple and regular operation. The hardware decoder, based on the latter algorithm, is designed with a pipeline such that it decodes one bit of a received block in a single system clock cycle
Low-density parity-check (LDPC) codes have been one of the most popular error correction candidates in modern communication and data storage systems for the past three decades due to their capacity-approaching error correction capability under the Belief Propagation (BP) decoding algorithms. In this dissertation, we investigate three topics related to efficient and effective decoding algorithms and the code design of LDPC codes. In the first part of this dissertation, we propose a methodology with the help of artificial intelligence to design Finite Alphabet Iterative Decoders (FAID) for LDPC codes, which are not only of great theoretical but also practical importance. This model-driven neural network (NN) framework unfolds the decoding iterations, introduces quantized neural networks (QNN) to model the FAIDs, and proposes a new cost function, namely, bit error rate (BER), to address the inefficiency in discrete-output channel scenarios. The low precision activations in the QNN and quantization in the cost functions cause a critical issue that their gradients vanish almost everywhere, making it difficult to use classical backward propagation. We design and leverage straight-through estimators as surrogate gradients to tackle this issue and provide a joint training scheme. These QNN-aided FAIDs, are capable of surpassing the floating-point BP algorithms, with much lower complexity and faster convergence. The QNN-aided approach is general, as it can be applied to both continuous and discrete-output channels. In the second part of this dissertation, we propose a new code construction of LDPC codes based on the conventional parity-check matrices of Reed-Solomon (RS) codes. We investigate the girth and cycle structure and introduce an efficient searching algorithm to reduce short cycles in their Tanner graphs and to construct LDPC codes with a girth of at least eight. We use masking to further reduce the number of short cycles and to adjust the column and row weights of the parity-check matrices of the constructed codes for performance improvement. Our designs are systematic and flexible, which balance the requirements of good waterfall performance and low error-floor while maintaining a structure that facilitates implementation. In the third part of this dissertation, we investigate binary quasi-cyclic (QC) LDPC codes and their capability to correct phased bursts of erasures. We prove that the peeling algorithm when applied to such parity-check matrices of column weight two can correct all erasures that can be corrected by a maximum likelihood (ML) decoder. We show that by modifying the parity-check matrices of column weight two and globally coupling them, the erasure correcting capability can be further enhanced. For the Additive White Gaussian Noise (AWGN) channel, we design QC LDPC codes with parity-check matrices of column weight three or more that can correct phased bursts of erasures and perform well over the AWGN channel. Our analysis of QC-LDPC codes with parity-check matrices of column weight two is rather comprehensive as we determine, for all such codes, their dimensions, minimum Hamming distances, and their capabilities to correct phased bursts.