Luby Transform Research Articles

Joint network and fountain codes design for relay-assisted multi-user system

In relay-assisted multi-user system, relay coding is important to enhance the robustness and reliability of cooperative transmission. For better adaptability and efficiency, two joint network and fountain coding (JNFC) schemes are proposed. When the condition of all direct channels is worse, JNFC scheme based on distributed LT(DLT) codes is used. Otherwise, JNFC scheme based on multi-dimensional LT(MD-LT) codes is suited. For both two above-mentioned schemes, the united degree distribution design method for short-length fountain codes is proposed. For the latter scheme, MD-LT codes are proposed for equal error protection (EEP) of each user. Simulation results and analysis show that the united degree distribution need less decoding overhead compared with other degree distribution for short-length fountain codes. And then, all users are protected equally in despite of asymmetric uplinks.

A New Cross-Level Decoding Scheme for LT Codes

In this letter, we propose a new cross-level decoding method for LT codes, where the results of packet-level decoding are fed back to bit-level decoding to improve the overall decoding performance. Another advantage of our method is that it keeps the original LT decoder structure and does not require extra real field computation. We provide the revised And-Or Tree analysis for the proposed method and validate it with numerical simulations.

Adapting Distributed LT codes to Y-Networks: An Abstraction of Collection Tree in Sensor Networks

The conventional approach for collecting data in sensor networks is the combination of automatic repeat-request techniques with a collection tree scheme in which all routes end up in the sink node. A high number of acknowledgments and retransmissions is the main drawback of this scheme. Erasure-correcting codes, in particular Fountain codes, can be employed to reduce the number of retransmissions. In the collection tree scheme, it is common for multiple routes to share a bottleneck. In such scenarios, to reach the optimal network throughput, it is necessary to combine the Fountain codes and Network Coding (NC) technique. Y-networks can be considered as an abstraction to this scenario. This article proposes a new algorithm, namely, Adaptive Distributed LT code (ADLT), for combining LT codes with NC in Y-networks. The ADLT algorithm enables belief propagation decoding by employing a novel technique called degree distribution updating, to preserve Robust Soliton degree distribution at destination. Unlike previously proposed algorithms in the literature, the ADLT algorithm has the flexibility to handle any number of sources with different block sizes and transmission rates, where sources perform standard LT coding. Simulation results confirm that the performance of the ADLT algorithm is close to that of standard LT code.

Improved finite‐length Luby‐transform codes in the binary erasure channel

Fountain codes were introduced to provide high reliability and scalability and low complexities for networks such as the Internet. Luby-transform (LT) codes, which are the first realisation of Fountain codes, achieve the capacity of the binary erasure channel (BEC) asymptotically and universally. Most previous work on single-layer Fountain coding targets the design via the right degree distribution. The left degree distribution of an LT code is left as a Poisson to protect the universality. For finite lengths, this is no longer an issue; thus, the author's focus is on designing better codes for the BEC at practical lengths. Their left degree shaping provides codes outperforming LT codes and all other competing schemes in the literature. At a bit error rate of 10−7 and packet length k = 256, their scheme provides a realised rate of 0.6 which is 23.5% higher than that of Sorensen et al.’s decreasing-ripple-size scheme.

Generation of Luby Transform Codes with Low Redundancy

Given the same number of encoded symbols, a Luby Transform (LT) decoder is more likely to decode successfully when there is little redundancy among the symbols. With the use of a Tanner graph, we describe two kinds of redundancy appearing in LT codes in this paper. We further propose an encoding algorithm called Low Redundancy (LR) algorithm used in the formation of the encoded symbols. The algorithm aims to reduce the redundancy of LT codes and to improve the decoder performance under the same complexity. Simulation results show various LT codes improve in terms of average overhead factor and probability of successful decoding when the codes are encoded using the proposed LR algorithm. Moreover, the encoding complexity remains unchanged.

Fountain Code Design for the Y-Network

This paper describes a novel approach for designing distributed fountain codes based on polynomial factorization. The proposed approach is used for the well known Y-network configuration. The suggested factorization approach is applicable to LT codes and Raptor codes or any other fountain code describable with a degree distribution. Simulation results verify the success of this technique.

A Distributed LT Code Design for Multiple-Access Relay Networks Subject to Erasures

This letter proposes a new distributed Luby transform (LT) code which is particularly suitable for the multiple-access relay network with erasure channels. We analyze the asymptotic performance of our distributed coding scheme by virtue of AND-OR tree analysis and present the simulation results of finite length comparing with existing methodologies. The proposed coding scheme is shown to be superior to conventional strategies in presence of both source-relay and relay-sink erasures.

Counteracting an Active Attack within MANET by Exploiting Luby Transform Codes

Counteracting an Active Attack within MANET by Exploiting Luby Transform Codes

LT-based Multi-source Transmission Strategy for Information-centric Networking

Information-centric Networking (ICN) is a promising network architecture that has attracted much attention in the area of future network. ICN supports multi-source communications innately because of the content-based routing mechanism. In this paper, we explore an LT-based (Luby Transform) multi- source transmission strategy applied to Named Data Networking which is a widely-researched ICN paradigm. Each content stored in difierent provider is encoded into a stream of symbols by LT codes to be delivered to a consumer. A decoding algorithm difierent from belief propagation is presented and simulation results show that our algorithm is better at the aspect of decoding success rate. Furthermore, some necessary modiflcation on forwarding process is conducted to make the process better compatible with our strategy. simulation results demonstrate that our LT based multi-source transmission strategy has a signiflcant efiect when the number of providers is increasing.

Performance Analysis of Joint Degree Distribution (JDD) in Luby Transform Codes

Luby Transform (LT) codes, the first realization of rateless codes are widely used in wireless communication mainly for its adaptability to varying channel conditions and its capacity approaching performance. In spite of the above advantages and its simplicity in implementation, LT codes suffer from a bottle neck of premature termination due to the poor design of degree distribution. In this study, a novel degree distribution called Joint Degree Distribution (JDD) is proposed for the successful completion of LT encoder/decoder processes. The efficient utilization of the bandwidth is tried to be achieved by using only 'k' encoded symbols for 'k' source symbols, unlike in traditional systems. JDD is carefully designed to ensure that the encoding/decoding delay does not exceed that which is existent in the traditional systems. The performance of JDD for throughput and bit error rate, experimented over Additive White Gaussian Noise (AWGN) channel compared to conventional degree distribution was observed to be much better.

Distributed Luby transform coding for three‐source single‐relay networks based on the deconvolution of robust soliton distribution

The distributed Luby transform (LT) coding is investigated for the multisource networks, especially with three sources. Based on the three-source single-relay network model, the authors propose a threefold deconvolution method of the robust soliton distribution (RSD). The deconvolved distribution is used at each source, and a simple and feasible combining algorithm is developed for re-encoding at the relay. Such a modified LT code with three sources (MLT-3) is constructed. Simulation results verify that the overall degree distribution of the proposed MLT-3 codes agrees well with the RSD. The performance of MLT-3 codes is evaluated and compared with other coding schemes. Simulations reveal that MLT-3 codes have similar behaviour with the two-source or four-source distributed LT codes and the benefits are observed in comparison with the separate LT codes. Simulations also show that MLT-3 codes exhibit good performance on various erasure channels.

Erasure Floor Analysis of Distributed LT Codes

We investigate the erasure floor performance of distributed Luby transform (DLT) codes for transmission within a multi-source, single-relay, and single-destination erasure-link network. In general, Luby transform (LT) codes exhibit a high erasure floor due to poor minimum-distance properties, which can be improved by maximizing the minimum variable-node degree. The same behavior is observed for DLT codes, and therefore a new combining scheme at the relay is proposed to maximize the minimum variable-node degree in the decoding graph. Furthermore, the encoding process at the sources and the combining scheme at the relay are coordinated to improve the transmission overhead. To characterize the asymptotic performance of the proposed DLT codes, we derive closed-form density-evolution expressions, considering both lossless and lossy source-relay channels, respectively. To support the asymptotic analysis, we evaluate the performance of the proposed DLT codes by numerical examples and demonstrate that the numerical results correspond closely to the analysis. Significant improvements in both the erasure floor and transmission overhead are obtained for the proposed DLT codes, as compared to conventional DLT codes.

Enhanced unequal error protection coding scheme of Luby transform codes

A Luby transform (LT) coding scheme providing unequal error protection (UEP) is proposed. As an enhanced method, the proposed UEP-LT coding scheme can be easily applied to the existing UEP rateless codes to achieve further bit error rate (BER) performance improvement. In the proposed UEP-LT encoder, a number of the so-called fixed symbols are added to the original source symbols. The level of importance of them can be assigned as that of any subset of the original source symbols. When the encoded symbols are generated, the proposed encoder only XOR the original source symbols. Therefore the efficiency of the UEP-LT codes remains unchanged. It is found that this can benefit the belief propagation decoding. Using the And–Or tree analysis technique, the asymptotic BER performance of the proposed method is analysed in detail. Compared with some existing UEP rateless codes, the asymptotic BERs of the proposed UEP-LT codes are much lower when the parameters are properly chosen. Besides, the proposed method needs less decoding iterations to converge, which means the source symbols can be recovered earlier. Simulation results show that the BER performances are improved when the proposed scheme is applied to the existing UEP rateless codes.

Message propagation decoder with error correction code based on rateless code under partial information

The receiver with message propagation (MP) decoder algorithm realises the decoding of traditional Luby transform (LT) encoded packages when there is only one unknown packet adjacent to the encoded package. Error packets can be recovered by decoding with jointing product code composed of shifted Luby transform (SLT)-encoded package and error packets. In this study, error correction scheme based on single feedback of SLT-encoded package was adopted for the recovery of received partial error packets over the erasure channel. The scheme of an MP decoder with an error correction code was proposed, and expand shifted robust soliton distribution (ESRSD) appropriate for the scheme feature was designed. Experimental results indicate that the scheme effectively improves the efficiency of the decoder. Compared with the traditional shifted robust soliton distribution, the ESRSD has better decoding performance for the LT code.

Ideal Forward Error Correction Codes for High-Speed Rail Multimedia Communications

In recent years, application-layer forward error correction (AL-FEC), particularly rateless AL-FEC, has received much attention due to its superior performance in both transmissional and computational efficiency. Rateless AL-FEC (e.g., Raptor code or Luby transform (LT) code) can protect a large data block with an overhead somewhat close to ideal codes. In the meantime, its data processing rates of both encoding and decoding are quite efficient even in software implementations. However, we found that conventional rateless AL-FEC schemes may not be the best candidates when considering streaming over Worldwide Interoperability for Microwave Access (WiMAX) networks for high-speed rail reception in Taiwan. In this paper, we propose a new ideal AL-FEC scheme based on the Chinese remainder theorem (CRT) to facilitate streaming service delivery for high-speed rail reception. The proposed scheme can support the rateless property, but it requires less transmission overhead than conventional rateless codes. Although it requires higher computational cost than conventional rateless codes, the cost is affordable for commodity laptops. In addition to measuring the FEC computation, storage, and decoder overhead, we also evaluate its performance in an emulation environment for simulating high-speed rail reception over WiMAX networks. The emulation result shows that the proposed scheme can achieve the same error protection as Raptor codes, but it requires less transmission overhead, which is suitable for protecting data transmission over bandwidth-limited high-mobility erasure channels.

Buffer-Based Distributed LT Codes

We focus on the design of distributed Luby transform (DLT) codes for erasure networks with multiple sources and multiple relays, communicating to a single destination. The erasure-floor performance of DLT codes improves with the maximum degree of the relay-degree distribution. However, for conventional DLT codes, the maximum degree is upper-bounded by the number of sources. An additional constraint is that the sources are required to have the same information block length. We introduce a $D$-bit buffer for each source-relay link, which allows the relay to select multiple encoded bits from the same source for the relay-encoding process; thus, the number of sources no longer limits the maximum degree at the relay. Furthermore, the introduction of buffers facilitates the use of different information block sizes across sources. Based on density evolution we develop an asymptotic analytical framework for optimization of the relay-degree distribution. We further integrate techniques for unequal erasure protection into the optimization framework. The proposed codes are considered for both lossless and lossy source-relay links. Numerical examples show that there is no loss in erasure performance for transmission over lossy source-relay links as compared to lossless links. Additional delays, however, may occur. The design framework and our contributions are demonstrated by a number of illustrative examples, showing the improvements obtained by the proposed buffer-based DLT codes.

Decomposed LT Codes for Cooperative Communications

In order to reduce computation complexity and latency in cooperative communication system based on fountain code, a decomposed LT codes (DLT) based cooperative transmission scheme was proposed. The scheme comprises of two layers of random encoding but only a single layer of decoding. A general decomposition technique for the decomposed LT codes construction is developed. The transmission latency for the proposed scheme was analyzed. Simulation results show that the total time consumed under the proposed scheme can be significantly reduced compared to direct transmission and conventional cooperative transmission based on LT codes in the medium to high packet erasure rate regimes. Moreover, With the increase of packet erasure rate, the advantage of the proposed scheme is more evident.

THROUGHPUT AND BIT ERROR RATE ANALYSIS OF LUBY TRANSFORM CODES WITH LOW AND MEDIUM NODAL DEGREE DISTRIBUTIONS

This study presents two degree distributions namely low and medium nodal degree distributions aiming to build a low overhead Luby Transform (LT) codes. The motivation is to design a fast encoder/decoder especially for real-time multimedia streaming and multicasting applications using LT codes. The key idea of this study is to restrict the average degree of the transmitted encoded symbols as minimal. The impacts of low and medium degree encoded symbols on the performance of LT codes over an Additive White Gaussian Noise channel (AWGN) have been analyzed by the means of Bit Error Rate (BER), encoder/decoder delay, ripple size, throughput, overhead and bandwidth utilization as the performance metrics. Simulation results show that the proposed nodal degree distributions for LT codes achieve better throughput and BER performance at low overhead and delay with minimal decoding iterations by having a constantly decreasing ripple in comparison with conventional Robust Soliton Distribution (RSD) based LT codes.

A Degree Distribution Optimization Algorithm in Unequal-Protected LT Code

LT code is the first practical implementation of digital fountain code. The coding behavior of LT code is mainly decided by the degree distribution which determines the relationship between source data and codeword. Since coding systems with unequal loss protection are widely applied, a degree distribution optimization algorithm is designed for unequal-protected LT code. The degree distribution that minimizes the number of un-recovered source symbols is found. By introducing the weighted cost, the optimal degree distribution can be solved by evolutionary strategy. The experimental results are quite promising. Compared with LT code with robust soliton distribution, the proposed algorithm improves the number of the recovered symbols obviously with the same overhead.

Rateless Codes Design Scheme Based on Two Stages

Current rateless codes coding schemes ignored the order recovery of packets. To cope with this problem, average delay and maximum memory consumption were proposed as performance indices to characterize the order recovery performance, then a coding scheme based on two stages coding was proposed to improve the order recovery performance. Encoding of the front k coded symbols is the first stage, which the i th coded symbol is compose of the i th packet and other d i -1 packets which are chosen from the front i-1 packets with equal probability. Encoding of the remaining infinite coded symbols is the second stage which the packets are chosen from all packets equal probably. The simulation results show that the rateless codes from the proposed scheme have better order recovery performance, meanwhile have high bandwidth efficiency and good uniformity recovery than LT codes.