Degree distribution based HARQ for irregular LDPC

Low Density Parity Check (LDPC) codes have capacity-approaching performance over several channels of interest. In practice, for good block-error rate performance, the girth of the Tanner graph of an LDPC code needs to be as high as possible. In theory, to show that block-error rate approaches zero for increasing block-lengths, the girth of the Tanner graph sequence needs to tend to infinity with block-length. To meet these requirements, we construct sequences of large-girth irregular LDPC codes for a given degree-distribution pair (DDP) by applying a general node splitting algorithm on large girth graphs. The obtained Tanner graph meets the required DDP up to a suitable approximation. By optimizing the node-splitting method and using suitable large-girth graphs, we show code constructions with smaller block length for the same girth, when compared to previous constructions. Similar gains in block length are observed in the construction of sequences of large-girth protograph LDPC codes. Simulations, over a binary erasure channel, confirm the gains in block-error rate obtained by the large girth construction.

In previous works, density evolution schemes have been used to design an irregular low-density parity-check (LDPC) code for the multi-input multi-output (MIMO) systems. However the code design based on the density evolution can be used only for simple code structure like LDPC codes and repeat-accumulate (RA) codes. Recently simple and accurate irregular LDPC code design method based on the extrinsic information transfer (EXIT) chart was introduced for an AWGN channel. This code design scheme is much flexible, therefore it can be used for any kind of code structure like turbo codes. In this paper we design an irregular LDPC code for a MIMO system using the EXIT chart based scheme. The EXIT charts are used to obtain the optimal edge degree distribution of the irregular LDPC code combined with the MMSE-SIC MIMO detector. This scheme can be generalized for designing the optimal iterative MIMO detector combined with any kind of channel codes including turbo codes.

In mobile communications, the quality of signal is deteriorated by fading. The spatial diversity technique is used to reduce the degradation of the signal by fading. There are several techniques to realize the spatial diversity gain, such as Single- Input Multiple-Output (SIMO), Space-Time Block Code (STBC), and so on. The SIMO system realizes the receive diversity. The error correcting code can be combined with spatial diversity gain. Low-Density Parity Check (LDPC) codes can achieve good performance approaching Shannon limit. In particular, an irregular LDPC code with optimum degree distribution achieves better performance than a regular LDPC code. The optimum degree distribution of the irregular LDPC code depends both on the channel and the system. In this paper, we derive the Eb/No thresholds of a regular LDPC codes and the irregular LDPC codes for SIMO systems with several diversity orders. The Eb/No threshold is the smallest Eb/No that the decoder can achieve the error free. We also derive the optimum degree distributions of the irregular LDPC codes for SIMO systems with several diversity orders. We show that with low diversity order, the optimum degree distributions of the irregular LDPC code depends on the diversity order largely, while with high diversity order, the optimum degree distribution depends both on the diversity order and the combining scheme largely. We also show that comparing the optimum degree distributions for MRC and STBC, when the diversity orders are the same, the optimum degree distributions are also the same.

In order to improve the security level of the physical layer, a new encryption scheme based on the irregular low-density parity-check (LDPC) codes is proposed in this paper. The degree distribution property of the irregular LDPC codes and a large random number are applied to encrypt the plaintext. Analyses show that the proposed scheme can provide an acceptable security level for the communication systems. The secret key size of this scheme is much smaller than those of the previous symmetric-key McEliece-like schemes. Moreover, there is no trade-off between the error correction performance and the security level in the proposed scheme.

Incremental Redundancy Hybrid ARQ (IR-HARQ) based on rate-compatible punctured low-density parity-check (LDPC) codes can achieve high throughput over a wide range of SNRs. One drawback of such IR-HARQ schemes is high computational complexity of decoding for early transmission at high rates. In order to overcome this problem, a HARQ scheme based on rate-compatible LDPC codes by shortening and extending is presented in this paper. In the HARQ scheme, a high-rate mother code is transmitted at first, and parity-bits of a shortened code are transmitted for early retransmission requests. With a low-complexity decoder of the high-rate mother code, this shortened-code approach would result in low computational complexity of decoding, but it causes smaller length and larger number of shortened codes to be decoded as retransmission repeats. To prevent the resultant degradation of performance and complexity, extending is efficiently applied to the shortened codes after predetermined retransmission-times. A multi-edge type code-design is employed to construct irregular LDPC codes that meet the requirement of the HARQ scheme. Simulation results show that the HARQ scheme can achieve lower computational complexity of decoding than a conventional IR-HARQ scheme with good throughput over a wide range of SNRs.

In comparison to Ultra-Reliable Low-Latency Communications (URLLC) in 5G mobile communication systems, the next generation URLLC (xURLLC) requires even lower latency and higher reliability. To address these requirements, we propose a novel redundancy version (RV)-adaptive hybrid automatic repeat request (HARQ) scheme. Our approach builds upon the existing 5G HARQ framework and 5G low-density parity-check (LDPC) codes, introducing an adaptive selection of the RV for the subsequent transmission based on the current decoding states. To determine the optimal RV, we use a modified version of the reciprocal channel approximation (RCA) algorithm to compare the decoding thresholds of all available RVs and select the one with the lowest threshold to maximize the likelihood of successful decoding. To further reduce processing delay, we apply a deep neural network (DNN) to predict the optimal RV for the next transmission. This prediction is made prior to the decoding process, ensuring that no additional delay is introduced. Since the selection is made before the decoding starts, our proposed method can seamlessly integrate with other adaptive-HARQ and fast HARQ schemes.

A new hybrid automatic repeat request (HARQ) scheme is proposed for multiple-input multiple-output (MIMO) systems when the acknowledgment (ACK) bundling is applied for packet retransmissions. In the proposed HARQ scheme, both Chase combining (CC) and incremental redundancy (IR) are utilised for a retransmission request, and the proposed HARQ scheme is called a multiple retransmission strategy-based HARQ (MRS-HARQ). During the reception process of the MRS-HARQ, IR packets obtain signal-to-noise ratio gains using the extended detection with CC packets and the improved IR packets are utilised to eliminate the interference from the CC packets. This sequential reliability improvement allows the MRS-HARQ to decrease the occurrence of the deficient transmissions, and the proposed MRS-HARQ can achieve an improved error performance and throughput over the conventional CC-based and IR-based HARQ schemes with the ACK bundling.

In this paper, we propose a data-driven joint modulator and demodulator based on meta-learning for hybrid automatic repeat request (HARQ) schemes, which include Type-I HARQ, HARQ with chase combining (HARQ-CC), and HARQ with incremental redundancy (HARQ-IR). Data-driven deep learning (DL) techniques have proven particularly effective for enabling wireless systems to adapt to complex scenarios with unknown or imperfect channel conditions that are difficult to characterize analytically. Most existing DL approaches to realize data-driven communication frameworks are based on joint source-channel coding (JSCC). However, the difficulty in detecting transmission errors makes JSCC unsuitable for HARQ systems. To address this limitation, we propose a novel architecture that combines classical channel coding with DLbased modulation and demodulation. Specifically, we employ an autoencoder to implement both the modulator and demodulator. To quickly adapt to time-varying fading channels, the ModelAgnostic Meta-Learning (MAML) algorithm is leveraged to accelerate the convergence of the model as well as enhance the reliability of HARQ. The MAML framework is divided into two phases, including the pre-training phase to acquire shared initialization parameters across various channel conditions and the fine-tuning phase to rapidly adapt to specific channel states. Simulation results demonstrate that the proposed architecture offers dramatic improvements in convergence speed and generalization capabilities, and meanwhile boosts the reliability of HARQ schemes.

An improved hybrid ARQ (HARQ) scheme for irregular LDPC codes based on degree distributions is introduced in this paper. In traditional degree distribution based HARQ (DDB-HARQ), the source selectively retransmits the nodes with large degrees and this scheme brings a significant gain to the irregular LDPC coded system. However, the selecting method of the traditional scheme is thought to be not accurate enough. In this paper, an improved method in which the source retransmits the nodes in different degrees at specific proportions each time has been proposed. According to the analysis with Gaussian approximation (GA) the improved scheme could be more efficient since the retransmission proportions are more accurate which has also been proved by the simulation results

In this letter, we obtain lower and upper bounds on the minimum distance $d_{\min }$ of low-density parity-check (LDPC) codes. The bounds are derived by categorizing the non-zero code words of an LDPC code into two categories of elementary and non-elementary. The first category contains code words whose induced subgraph has only degree-2 check nodes. We propose an efficient search algorithm that can find the elementary code words of an LDPC code with weight less than a certain value $a_{\max }$ , exhaustively. We also derive a lower bound $L_{ne}$ on the weight of non-elementary code words. By performing the search with $a_{\max } = L_{ne}$ , we either obtain an elementary code word with the smallest weight $d_{\min }$ , or establish the lower bound of $L_{ne}$ on $d_{\min }$ . For the upper bound, we modify our search algorithm to reach elementary codewords of larger weights at the cost of being non-exhaustive. Once such a codeword is found, its weight acts as an upper bound on $d_{\min }$ . We examine a large number of regular and irregular LDPC codes, and demonstrate the efficiency and versatility of our technique in finding lower and upper bounds on, and in many cases the exact value of, $d_{\min }$ . Finding $d_{\min }$ , or establishing search-based lower or upper bounds, for many of the examined codes are out of the reach of any existing algorithm.

This paper is concerned with density evolution for iterative decoding of low-density parity-check (LDPC) codes. We first study the problem of density evolution computation for regular LDPC codes. For this, we propose a simple computational algorithm based on the ergodicity theory. This method is shown to match very well with explicit calculations of density functions. The second problem we study is about the approach of Gaussian approximation to density evolution. We point out that it is inappropriate to use the mean of the density only to model the iterative decoding process. Instead, both the mean and variance are needed for Gaussian approximation. Finally, we consider the problem of density evolution for irregular LDPC codes. For this, we extend the density evolution algorithm for regular LDPC codes to irregular LDPC codes. We then illustrate that Gaussian approximation is also valid provided that the degree distributions are not wide. A dynamic model is also presented based on Gaussian approximation.

Hybrid automatic repeat request (HARQ) can make efficient and reliable transmission possible for radio communications. However, in the HARQ scheme, packet control information (PCI), such as HARQ block identifiers (HARQ block ids) in selective repeat ARQ (SR-ARQ), are required and the reduction of PCI overhead is an issue. In particular, type-II HARQ handles a large amount of PCI because it includes the HARQ block ids and sub-block ids. The sub-block id identifies the set of parity bits in the HARQ block of the corresponding sub-block, and is used to combine the sub-blocks. This report proposes a method of PCI reduction suitable for type-II HARQ with SR-ARQ. The method can inform the HARQ block id and sub-block id of each HARQ block by sending only the information on how many HARQ blocks are contained in each 1st, 2nd, 3rd, and 4th transmission group. The estimated size of reduced PCI and simulation results of our TDD communication system confirms that the proposed method greatly reduces PCI and improves data throughput compared to a conventional method.

This paper presents a design approach for low-density parity-check (LDPC) coding system hardware implementation by jointly conceiving irregular LDPC code construction and VLSI implementations of encoder and decoder. The key idea is to construct good irregular LDPC codes subject to two constraints that ensure the effective LDPC encoder and decoder hardware implementations. We propose a heuristic algorithm to construct such implementation-aware irregular LDPC codes that can achieve very good error correction performance. The encoder and decoder hardware architectures are correspondingly presented.

In order to solve high encoding complexities of irregular low-density parity-check (LDPC) codes, a deterministic construction of irregular LDPC codes with low encoding complexities was proposed. And the encoding algorithms were designed, whose complexities are linear equations of code length. The construction and encoding algorithms were derived from the effectively encoding characteristics of repeat-accumulate (RA) codes and masking technique. Firstly, the new construction modified parity-check matrices of RA codes to eliminate error floors of RA codes. Secondly, the new constructed parity-check matrices were based on Vandermonde matrices, this deterministic algebraic structure was easy for hardware implementation. Theoretic analysis and experimental results show that, at a bit-error rate of 10×10−4, the new codes with lower encoding complexities outperform Mackay’s random LDPC codes by 0.4–0.6 dB over an additive white Gauss noise (AWGN) channel.

Turbo codes are attractive compared with Low Density Parity Check (LDPC) codes for Forward Error Correction (FEC) applications mainly due to their superior performance, especially at low Signal-to-Noise Ratio (SNR) such as are common in Powerline channels. For example, IEEE 1901-FFT PHY used the Turbo coding scheme defined in the HomePlug AV standards. However, patent fees are usually required for each turbo-code enabled manufactured device. The objective of this paper is to examine whether unlicensed LDPC codes, with optimized choices of block lengths, could be a viable alternative for future Powerline Communications (PLC) applications. The paper shows that the performance of the LDPC codes can approximate that of the Turbo codes with higher block lengths, on channels with typical and realistic PLC characteristics. The paper also shows that the additional complexity associated with this increase in block length can be mitigated by the use of Quasi-Cyclic LDPC (QC-LDPC) codes.