Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design

In this paper we analyze LT and Raptor codes under inactivation decoding. A first order analysis is introduced, which provides the expected number of inactivations for an LT code, as a function of the output distribution, the number of input symbols and the decoding overhead. The analysis is then extended to the calculation of the distribution of the number of inactivations. In both cases, random inactivation is assumed. The developed analytical tools are then exploited to design LT and Raptor codes, enabling a tight control on the decoding complexity vs. failure probability trade-off. The accuracy of the approach is confirmed by numerical simulations.Comment: Accepted for publication in IEEE Transactions on Communication

Fountain Codes under Maximum Likelihood Decoding

This dissertation focuses on fountain codes under maximum likelihood (ML) decoding. First LT codes are considered under a practical and widely used ML decoding algorithm known as inactivation decoding. Different analysis techniques are presented to characterize the decoding complexity. Next an upper bound to the probability of decoding failure of Raptor codes under ML decoding is provided. Then, the distance properties of an ensemble of fixed-rate Raptor codes with linear random outer codes are analyzed. Finally, a novel class of fountain codes is presented, which consists of a parallel concatenation of a block code with a linear random fountain code.Comment: PhD Thesi

Band Codes for Energy-Efficient Network Coding with Application to P2P Mobile Streaming

A key problem in random network coding (NC) lies in the complexity and energy consumption associated with the packet decoding processes, which hinder its application in mobile environments. Controlling and hence limiting such factors has always been an important but elusive research goal, since the packet degree distribution, which is the main factor driving the complexity, is altered in a non-deterministic way by the random recombinations at the network nodes. In this paper we tackle this problem proposing Band Codes (BC), a novel class of network codes specifically designed to preserve the packet degree distribution during packet encoding, ecombination and decoding. BC are random codes over GF(2) that exhibit low decoding complexity, feature limited and controlled degree distribution by construction, and hence allow to effectively apply NC even in energy-constrained scenarios. In particular, in this paper we motivate and describe our new design and provide a thorough analysis of its performance. We provide numerical simulations of the performance of BC in order to validate the analysis and assess the overhead of BC with respect to a onventional NC scheme. Moreover, peer-to-peer media streaming experiments with a random-push protocol show that BC reduce the decoding complexity by a factor of two, to a point where NC-based mobile streaming to mobile devices becomes practically feasible.Comment: To be published in IEEE Transacions on Multimedi

Finite Length Analysis of Rateless Codes and Their Application in Wireless Networks

Mobile communication systems are undergoing revolutionary developments as a result of the rapidly growing demands for high data rates and reliable communication connections. The key features of the next-generation mobile communication systems are provision of high-speed and robust communication links. However, wireless communications still need to address the same challenge–unreliable communication connections, arising from a number of causes including noise, interference, and distortion because of hardware imperfections or physical limitations. Forwarding error correction (FEC) codes are used to protect source information by adding redundancy. With FEC codes, errors among the transmitted message can be corrected by the receiver. Recent work has shown that, by applying rateless codes (a class of FEC codes), wireless transmission efficiency and reliability can be dramatically improved. Unlike traditional codes, rateless codes can adapt to different channel conditions. Rateless codes have been widely used in many multimedia broadcast/multicast applications. Among the known rate- less codes, two types of codes stand out: Luby transform (LT) codes and Raptor codes. However, our understanding of LT codes and Raptor codes is still in- complete due to the lack of complete theoretical analysis on the decoding error performance of these codes. Particularly, this thesis focuses on the decoding error performance of these codes under maximum-likelihood (ML) decoding, which provides a benchmark on the optimum system performance for gauging other decoding schemes. In this thesis, we discuss the effectiveness of rateless codes in terms of the success probability of decoding. It is defined as the probability that all source symbols can be successfully decoded with a given number of success- fully received coded symbols under ML decoding. This thesis provides a detailed mathematical analysis on the rank profile of general LT codes to evaluate the decoding success probability of LT codes under ML decoding. Furthermore, by analyzing the rank of the product of two random coefficient matrices, this thesis derived bounds on the decoding success probability of Raptor codes with a systematic low-density generator matrix (LDGM) code as the pre-code under ML decoding. Additionally, by resorting to stochastic geometry analysis, we develop a rateless codes based broadcast scheme. This scheme allows a base station (BS) to broadcast a given number of symbols to a large number of users, without user acknowledgment, while being able to pro- vide a performance guarantee on the probability of successful delivery. Further, the BS has limited statistical information about the environment including the spatial distribution of users (instead of their exact locations and number) and the wireless propagation model. Based on the analysis of finite length LT codes and Raptor codes, an upper and a lower bound on the number of transmissions required to meet the performance requirement are obtained. The technique and analysis developed in this thesis are useful for designing efficient and reliable wireless broadcast strategies. It is of interest to implement rateless codes into modern communication systems

S-RLNC based MAC Optimization for Multimedia Data Transmission over LTE/LTE-A Network

The high pace emergence in communication systems and associated demands has triggered academia-industries to achieve more efficient solution for Quality of Service (QoS) delivery for which recently introduced Long Term Evolution (LTE) or LTE-Advanced has been found as a promising solution. However, enabling QoS and Quality of Experience (QoE) delivery for multimedia data over LTE has always been a challenging task. QoS demands require reliable data transmission with minimum signalling overheads, computational complexity, minimum latency etc, for which classical Hybrid Automatic Repeat Request (HREQ) based LTE-MAC is not sufficient. To alleviate these issues, in this paper a novel and robust Multiple Generation Mixing (MGM) assisted Systematic Random Linear Network Coding (S-RLNC) model is developed to be used at the top of LTE MAC protocol stack for multimedia data transmission over LTE/LTE-A system. Our proposed model incorporated interleaving and coding approach along with MGM to ensure secure, resource efficient and reliable multiple data delivery over LTE systems. The simulation results reveal that our proposed S-RLNC-MGM based MAC can ensure QoS/QoE delivery over LTE systems for multimedia data communication

A STUDY OF ERASURE CORRECTING CODES

This work focus on erasure codes, particularly those that of high performance, and the related decoding algorithms, especially with low computational complexity. The work is composed of different pieces, but the main components are developed within the following two main themes. Ideas of message passing are applied to solve the erasures after the transmission. Efficient matrix-representation of the belief propagation (BP) decoding algorithm on the BEG is introduced as the recovery algorithm. Gallager's bit-flipping algorithm are further developed into the guess and multi-guess algorithms especially for the application to recover the unsolved erasures after the recovery algorithm. A novel maximum-likelihood decoding algorithm, the In-place algorithm, is proposed with a reduced computational complexity. A further study on the marginal number of correctable erasures by the In-place algoritinn determines a lower bound of the average number of correctable erasures. Following the spirit in search of the most likable codeword based on the received vector, we propose a new branch-evaluation- search-on-the-code-tree (BESOT) algorithm, which is powerful enough to approach the ML performance for all linear block codes. To maximise the recovery capability of the In-place algorithm in network transmissions, we propose the product packetisation structure to reconcile the computational complexity of the In-place algorithm. Combined with the proposed product packetisation structure, the computational complexity is less than the quadratic complexity bound. We then extend this to application of the Rayleigh fading channel to solve the errors and erasures. By concatenating an outer code, such as BCH codes, the product-packetised RS codes have the performance of the hard-decision In-place algorithm significantly better than that of the soft-decision iterative algorithms on optimally designed LDPC codes

Coding Theory For Security And Reliability In Wireless Networks

Wireless networks hold many applications and are an integral part of our lives. Security and reliability are extremely important in wireless networks. These networks must be reliable so that data can be conveyed from transmitters to receivers. Data sent across wireless networks must be kept confidential from unintended users and it is necessary that false packets generated by illegitimate users are rejected by the receiver. Another important task is for the network to determine which network components can be trusted and to what degree. The work presented in this dissertation addresses the security and reliability issues in wireless networks through the use of coding theory. The network is composed of numerous nodes and we consider a classical point to point communication problem. We explore the network reliability issue and develop two algorithms (exponential and polynomial time) which determine minimum redundancy and optimal symbol allocation to assure that the probability of successful decoding is greater than or equal to a specified threshold. The performance of the algorithms is compared with each other, and MDS, LT, and Raptor codes are compared using the exponential algorithm. We also consider the security problem of keeping a message confidential from an illegitimate eavesdropper in a multiple path network. Carefully crafted Raptor codes are shown to asymptotically achieve perfect secrecy and zero-error probability, and a bit allocation method across the paths is developed. Lastly, we look into the problem of determining the integrity of nodes in the network. In particular, we show how the malicious nodes can be localized in the network through the use of ReedMuller codes. The Reed-Muller codes represent the paths that are necessary in the network. For the case where a path is not realizable according to the network connectivity matrix, we conceived an algorithm to treat the non-realizable paths as erasures and decode to localize malicious nodes. The performance of the algorithm is compared to several techniques

A Tutorial on Coding Methods for DNA-based Molecular Communications and Storage

Exponential increase of data has motivated advances of data storage technologies. As a promising storage media, DeoxyriboNucleic Acid (DNA) storage provides a much higher data density and superior durability, compared with state-of-the-art media. In this paper, we provide a tutorial on DNA storage and its role in molecular communications. Firstly, we introduce fundamentals of DNA-based molecular communications and storage (MCS), discussing the basic process of performing DNA storage in MCS. Furthermore, we provide tutorials on how conventional coding schemes that are used in wireless communications can be applied to DNA-based MCS, along with numerical results. Finally, promising research directions on DNA-based data storage in molecular communications are introduced and discussed in this paper