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

Performance Analysis of NOMA Multicast Systems Based on Rateless Codes with Delay Constraints

To achieve an efficient and reliable data transmission in time-varying conditions, a novel non-orthogonal multiple access (NOMA) transmission scheme based on rateless codes (NOMA-RC) is proposed in the multicast system in this paper. Using rateless codes at the packet level, the system can generate enough encoded data packets according to users’ requirements to cope with adverse environments. The performance of the NOMA-RC multicast system with delay constraints is analyzed over Rayleigh fading channels. The closed-form expressions for the frame error ratio and the average transmission time are derived for two cases which are a broadcast communication scenario (Scenario 1) and a relay communication scenario (Scenario 2). Under the condition that the quality of service for the edge user is satisfied, an optimization model of power allocation is established to maximize the sum rate. Simulation results show that Scenario 2 can provide better block error ratio performance and exhibit less transmission time than Scenario 1. When compared with orthogonal multiple access (OMA) with rateless codes system, the proposed system can save on the transmission time and improve the system throughput

Efficient incremental raptor decoding over BEC for 3GPP MBMS and DVB IP-datacast services

The application layer forward error correction (FEC) schemes of the 3rd Generation Partnership Project (3GPP) Multimedia Broadcast/Multicast Service (MBMS) standard and IP Datacast over Digital Video Broadcasting (DVB) services employ systematic Raptor codes. Additionally, the 3GPP MBMS standard suggests the use of efficient enhanced Gaussian elimination (EGE) matrix inversion algorithm for the Raptor decoder. In this letter we propose a new incremental EGE (IEGE) algorithm, based on the specification of the EGE. We perform a detailed performance and complexity comparison with EGE, for various decoding scenarios. We show that IEGE performs up to 15.8 times better. Additionally, we investigate the choice of the decoding scheme, based on the symbol arrival rate. © 2011 IEEE