Fountain Codes Research Articles

Reinforcement-Learning-Based Overhead Reduction for Online Fountain Codes With Limited Feedback

We investigate the application of reinforcement learning (RL) on online fountain codes, and propose two schemes to reduce the full-recovery overhead with limited feedback. First, we use RL in determining the optimal degree of coded symbols for a given number of feedback, and propose the RL-based degree determination (RL-DD), with the help of theoretical analysis of the relationship between recovery rate and buffer occupancy. Then we propose online fountain codes with no build-up phase using sectioned distribution (OFCNB-SD), where the encoder sends symbols whose degrees are sampled from different sections of an overall distribution, and the decoder is improved to utilize coded symbols that are not immediately decodable. We present theoretical analysis of OFCNB-SD, and introduce RL-based sectioned distribution (RL-SD) scheme where the sectioning of the overall distribution is optimized with RL. Simulation results show that our proposed schemes could achieve lower full-recovery overhead with limited feedback compared to existing schemes.

Performance statistics of broadcasting networks with receiver diversity and Fountain codes

ABSTRACT The performance of broadcasting networks employing Fountain codes with receiver diversity techniques is investigated in the present work. Particularly, we derive the closed-form expressions of the cumulative distribution function (CDF), the probability mass function (PMF), and the raw moments of the number of the needed time slots to deliver a common message to all users under two diversity schemes, namely, maximal ratio combining (MRC) and selection combining (SC). Numerical results are supplied to verify the accuracy of the considered networks and highlight the behaviours of these metrics as a function of some vital parameters such as the number of receivers, and the number of received antennae. Additionally, we also confirm the advantages of the MRC scheme compared with the SC scheme in the broadcasting networks.

Towards long double-stranded chains and robust DNA-based data storage using the random code system.

DNA has become a popular choice for next-generation storage media due to its high storage density and stability. As the storage medium of life's information, DNA has significant storage capacity and low-cost, low-power replication and transcription capabilities. However, utilizing long double-stranded DNA for storage can introduce unstable factors that make it difficult to meet the constraints of biological systems. To address this challenge, we have designed a highly robust coding scheme called the "random code system," inspired by the idea of fountain codes. The random code system includes the establishment of a random matrix, Gaussian preprocessing, and random equilibrium. Compared to Luby transform codes (LT codes), random code (RC) has better robustness and recovery ability of lost information. In biological experiments, we successfully stored 29,390 bits of data in 25,700 bp chains, achieving a storage density of 1.78 bits per nucleotide. These results demonstrate the potential for using long double-stranded DNA and the random code system for robust DNA-based data storage.

Basis-Finding Algorithm for Decoding Fountain Codes for DNA-Based Data Storage

In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in DNA-based data storage systems where the inner code decoding, which generally has undetectable errors, is performed before the outer fountain code decoding. We propose a novel and efficient decoding algorithm, namely basis-finding algorithm (BFA), followed by three implementations. The key idea of the BFA is to find a basis of the received symbols, and then use the most reliable basis elements to recover the source symbols with the inactivation decoding. Gaussian elimination is used to find the basis and to identify the most reliable basis elements. As a result, the BFA has polynomial time complexity. For random fountain codes, we are able to derive some theoretical bounds for the frame error rate (FER) of the BFA. Extensive simulations with Luby transform (LT) codes show that, the BFA has significantly lower FER than the belief propagation (BP) algorithm except for an extremely large amount of received symbols, and the FER of the BFA generally decreases as the average weight of basis elements increases.

Fountain Codes for Reliable and Deterministic Packet Transmission in Industrial Cloud Control Systems

With the thriving of digitalization in industry and the rapid development of cloud computing and Internet of Things (IoT), it has become a growing trend to integrate industrial control with the cloud platform to form industrial cloud control systems (ICCSs). However, ICCSs bring great challenges to legacy communication networks, especially, wireless networks, on reliability and determinacy. This article utilizes fountain code as application-layer coding to provide high-reliability low-latency deterministic communication for ICCSs. According to the simulation results, fountain code scheme, especially, RaptorQ code significantly improves communication reliability. The performance difference of fountain codes between time-critical use cases and nontime-critical use cases provides another perspective to analyze and evaluate fountain codes. Then, we propose a self-adaptive coding parameter selection method based on different industrial use cases, to better meet the communication requirements and reduce the coding cost.

Performance on Cognitive Broadcasting Networks Employing Fountain Codes and Maximal Ratio Transmission

Performance on Cognitive Broadcasting Networks Employing Fountain Codes and Maximal Ratio Transmission

A cost-efficient hybrid redundancy coding scheme for wireless storage systems

With distributed storage technique becoming a promising technology for storing massive data in wireless environment, how to improve the reliability of the storage systems has become the focus of researchers. As a redundancy scheme, the erasure coding has been widely used because of its high fault tolerance and low storage overhead performance. However, a large amount of repair overhead consumed to reconstruct lost data has become the most significant issue in erasure-coded storage systems. In this paper, a wireless heterogeneous storage network with two-layer is designed, where processing units and storage nodes communicate cooperatively. Furthermore, with the consideration of the access frequency skew of stored information and the performance difference of storage nodes, we propose a novel repairable fountain code scheme based on partial duplication technique (PD-RFC), which can modify the repair bandwidth and improve the availability of links between nodes without almost increasing additional storage space overhead. Furthermore, a hybrid code scheme combined by PD-RFC scheme and RFC scheme is designed for the heterogeneous two-layer storage network. The simulation results have shown that the hybrid scheme significantly outperforms other redundant schemes in energy communication cost saving.

Fountain Coded Streaming for SAGIN With Learning-Based Pause-and-Listen

Efficient adaptive bitrate streaming (ABS) over long-distance and lossy space-air-ground-integrated network (SAGIN) links is an important demand, where fountain transmission is attractive as it does not require feedback/retransmissions. However, the conventional fountain scheme may waste many packets due to the propagation delay of stop messages. This letter proposes a novel fountain coded ABS design with a pause-and-listen approach which, across segments of ABS, learns proper pause time in an on-line manner based on multi-armed bandit modeling. Evaluation using a real-life implementation shows that the scheme can avoid most packet wastes while still maintaining the key benefits of the fountain transmission.

A Simulink model for modified fountain codes

This paper introduces a Simulink model design for a modified fountain code. The code is a new version of the traditional Luby transform (LT) codes. The design constructs the blocks required for generation of the generator matrix of a limited-degree-hopping-segment Luby transform (LDHS-LT) codes. This code is especially designed for short length data files which have assigned a great interest for wireless sensor networks. It generates the degrees in a predetermined sequence but random generation and partitioned the data file in segments. The data packets selection has been made serialy according to the integer generated from both degree and segment generators. The code is tested using Monte Carlo simulation approach with the conventional code generation using robust soliton distribution (RSD) for degree generation, and the simulation results approve better performance with all testing parameter.

Application of Fountain Code to High-Rate Delay Tolerant Networks

Application of Fountain Code to High-Rate Delay Tolerant Networks

Efficient unequal error protection for online fountain codes

In this paper, an efficient unequal error protection (UEP) scheme for online fountain codes is proposed. In the buildup phase, the traversing-selection strategy is proposed to select the most important symbols (MIS). Then, in the completion phase, the weighted-selection strategy is applied to provide low overhead. The performance of the proposed scheme is analyzed and compared with the existing UEP online fountain scheme. Simulation results show that in terms of MIS and the least important symbols (LIS), when the bit error ratio is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> , the proposed scheme can achieve 85% and 31.58% overhead reduction, respectively.

Online Analog Fountain Codes

Analog fountain codes (AFC) are a class of near-capacity rateless codes which have a great potential for meeting the requirements of ultra-reliable low latency communication. In this letter, an online feedback scheme is introduced to enhance error performance and achievable rate of AFC. The retransmission messages are chosen according to Euclidean distance between AFC codewords. Our simulation results show that the proposed online AFC can improve achievable rate up to 0.49 bits/symbols at 25 dB, and reduce block error rate by more than one order of magnitude.

Triangular code: Near-optimal linear time fountain code

In this paper, we propose Triangular Code (TC), a new class of fountain code with near-zero redundancy and linear encoding and decoding computational complexities of O(Lklogk), where k is the packet batch size and L is the packet data length. Different from previous works where the optimal performance of codes has been shown under asymptotic assumption, TC enjoys near-zero redundancy even under non-asymptotic settings for small-moderate number of packets. These features make TC suitable for practical implementation in battery-constrained devices in IoT, D2D and M2M network paradigms to achieve scalable reliability, and minimize latency due to its low decoding delay. TC is a non-linear code, which is encoded using the simple shift and XOR addition operations, and decoded using the simple back-substitution algorithm. Although it is nonlinear code at the packet level, it remains linear code when atomized at the bit level. We use this property to show that the back-substitution decoder of TC is equivalent to the Belief Propagation (BP) decoder of LT code. Therefore, TC can benefit from rich prolific literature published on LT code, to design efficient code for various applications. Despite the equivalency between the decoders of TC and LT code, we show that compared to state-of-the-art optimized LT code, TC reduces the redundancy of LT code by 68%–99% for k reaching 1024.© 2022 Published by Elsevier Ltd.

Statistical Degree Distribution Design for Using Fountain Codes to Control the Peak-To-Average Power Ratio in an OFDM System.

Utilizing fountain codes to control the peak-to-average power ratio (PAPR) is a classic scheme in Orthogonal Frequency Division Multiplexing (OFDM) wireless communication systems. However, because the robust soliton distribution (RSD) produces large-degree values, the decoding performance is severely reduced. In this paper, we design statistical degree distribution (SD) under a scenario that utilizes fountain codes to control the PAPR. The probability of the PAPR produced is combined with RSD to design PRSD, which enhances the smaller degree value produced. Subsequently, a particle swarm optimization (PSO) algorithm is used to search the optimal degree value between the binary exponential distribution (BED) and PRSD distribution according to the minimum average degree principle. Simulation results demonstrate that the proposed method outperforms other relevant degree distributions in the same controlled PAPR threshold, and the average degree value and decoding efficiency are remarkably improved.

Broadcasting in Cognitive Radio Networks: A Fountain Codes Approach

The present paper addresses the performance of the broadcasting scheme in cognitive radio networks (CRNs) under a fountain codes (FC) approach. Particularly, closed-form expressions are derived for the cumulative distribution function (CDF) and the expectation of the number of FC clock cycles required for broadcasting packets to all secondary receivers. The energy efficiency (EE) of the secondary networks (SN) is also provided. Moreover, a simple transmit power scheme is proposed to enhance the performance of the SN and guarantee the quality-of-service (QoS) of the primary network (PN). The trends of the introduced closed-form performance metrics are then examined versus important network parameters allowing for the optimization of those parameters. Finally, numerical results are provided to confirm the accuracy of the derived mathematical framework and the superior performance of the introduced FC scheme over uncoded broadcasting protocols.

Performance enhancing of MIMO‐OFDM system utilizing different interleaving techniques with rate‐less fountain raptor code

Due to the importance of both rate-less digital fountain codes and Multi-Input Multi-Output (MIMO) schemes in Fifth and Sixth Generation (5G/6G) wireless networks, this paper investigates enhancing the performance of MIMO-Orthogonal Frequency Division Multiplexing (MIMO-OFDM) based system by employing the rate-less fountain codes. The rate-less codes, such as the Tornado codes and Raptor codes, have a flexible code rate that differs from the classical channel coding schemes. This paper uses Raptor code to study the MIMO system's performance with the rate-less codes over different wireless communications channels. The proposed MIMO-fountain code-based system has been tested over the various wireless communication channel conditions concerning the varied Frequency Doppler (FD). In the proposed rate-less wireless communication system, multiple interleaving techniques and equalizers are used to improve its performance. Computer-based simulation experiments are assigned to evaluate the MIMO-fountain code system using the different data transmission scenarios. Simulation results confirm the superiority of the presented wireless rate-less system compared to fixed-rate wireless systems in terms of Bit Error Rate (BER) and throughput.

Analysis and Design of Enhanced Distributed Fountain Codes in Multiple Access Networks with Cooperative Relay

Distributed fountain coding plays an important role in rateless code research. The reliability and effectiveness of these coding schemes are increasingly challenged with the growing applications. In this paper, a novel multiple-access network with cooperative relay is presented, and a novel enhanced distributed fountain coding scheme for this network is proposed. The overall degree distributions are derived, and the asymptotic decoding performance is analyzed theoretically by employing the And-Or tree method. On this basis, a design method using joint iterative optimization algorithms is proposed to optimize the degree distributions of the sources and relays. Simulation results show that the proposed enhanced distributed fountain codes outperform the existing generalized distributed fountain codes (GDFC) and have a good performance on both lossless and lossy channels. It reveals that the proposed codes can provide unequal error protection (UEP) property for different sources by introducing the extra cooperative relay. The performance improvement is not restricted to the sources connected to the cooperative relay but applies to all sources. With the additional relay, the proposed codes are able to overcome the effects of bad channel conditions caused by terrain, obstacles, and so on, to avoid communication interruptions and improve the reliability of the network.

Weighted zigzag decodable fountain codes for unequal error protection

By combining bit-shift and exclusive-or operations, a weighted zigzag decodable fountain code is proposed to achieve an unequal error protection property. In the proposed scheme, the input symbols of different importance levels are first pre-coded into variable nodes using low-density parity-check codes. Then, bit-shift operations prior to exclusive-or are performed on the non-uniformly selected variable nodes to generate encoded symbols. An analysis of the erasure probabilities based on the and-or tree is further introduced. Simulation results show that by appropriately choosing the maximum bit-shift amount, the proposed weighted zigzag decodable fountain codes can successfully recover the more important input symbols prior to the less important ones.

Secure Online Fountain Codes With Low Complexity

In this letter, a scheme that achieves strong security using online fountain codes is proposed. By combining coset precoding, we minimize the number of leaked symbols of fountain codes to achieve strong security. We analyze the security performance of fountain codes using uni-partite graphs, and propose an optimal graph structure that achieves the smallest number of leaked symbols. Based on the optimal graph structure, we proposed a coding scheme called “Chain Buildup” and analyzed its expected number of leaked symbols. Simulation results show that our proposed scheme could achieve smaller number of leaked symbols compared to other security fountain codes. The proposed scheme also has smaller decoding overhead and lower complexity compared to conventional online fountain codes.

Downsampling and Transparent Coding for Blockchain

Blockchain is considered to be able to solve the problem of trust between distributed nodes. However, it's a challenge to store the large amount of data produced by blockchain. Therefore, it is necessary to reduce node storage overhead while ensuring node independence and data recoverability. This paper proposes to downsample these data to reduce the storage overhead of nodes. These nodes keep good independence, if downsampling follows the entropy of blockchain and the block bodies are continuously stored. Moreover, it demonstrates that the entire blockchain history can be efficiently recovered through the cooperative decoding of a group of nodes like fountain codes, if reserved data over these nodes obey the soliton distribution. However, these data on nodes are transparent (stored data are uncoded and can be used directly by the node without decoding). Thus, the proposed algorithm not only keeps decentralization and security, but also has good scalability in independence and recoverability.