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

Near-capacity fixed-rate and rateless channel code constructions

Fixed-rate and rateless channel code constructions are designed for satisfying conflicting design tradeoffs, leading to codes that benefit from practical implementations, whilst offering a good bit error ratio (BER) and block error ratio (BLER) performance. More explicitly, two novel low-density parity-check code (LDPC) constructions are proposed; the first construction constitutes a family of quasi-cyclic protograph LDPC codes, which has a Vandermonde-like parity-check matrix (PCM). The second construction constitutes a specific class of protograph LDPC codes, which are termed as multilevel structured (MLS) LDPC codes. These codes possess a PCM construction that allows the coexistence of both pseudo-randomness as well as a structure requiring a reduced memory. More importantly, it is also demonstrated that these benefits accrue without any compromise in the attainable BER/BLER performance. We also present the novel concept of separating multiple users by means of user-specific channel codes, which is referred to as channel code division multiple access (CCDMA), and provide an example based on MLS LDPC codes. In particular, we circumvent the difficulty of having potentially high memory requirements, while ensuring that each user’s bits in the CCDMA system are equally protected. With regards to rateless channel coding, we propose a novel family of codes, which we refer to as reconfigurable rateless codes, that are capable of not only varying their code-rate but also to adaptively modify their encoding/decoding strategy according to the near-instantaneous channel conditions. We demonstrate that the proposed reconfigurable rateless codes are capable of shaping their own degree distribution according to the nearinstantaneous requirements imposed by the channel, but without any explicit channel knowledge at the transmitter. Additionally, a generalised transmit preprocessing aided closed-loop downlink multiple-input multiple-output (MIMO) system is presented, in which both the channel coding components as well as the linear transmit precoder exploit the knowledge of the channel state information (CSI). More explicitly, we embed a rateless code in a MIMO transmit preprocessing scheme, in order to attain near-capacity performance across a wide range of channel signal-to-ratios (SNRs), rather than only at a specific SNR. The performance of our scheme is further enhanced with the aid of a technique, referred to as pilot symbol assisted rateless (PSAR) coding, whereby a predetermined fraction of pilot bits is appropriately interspersed with the original information bits at the channel coding stage, instead of multiplexing pilots at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). We subsequently demonstrate that the PSAR code-aided transmit preprocessing scheme succeeds in gleaning more information from the inserted pilots than the classic PSAM technique, because the pilot bits are not only useful for sounding the channel at the receiver but also beneficial for significantly reducing the computational complexity of the rateless channel decoder

Comparative study of a time diversity scheme applied to G3 systems for narrowband power-line communications

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Masters of Science in Engineering (Electrical). Johannesburg, 2016Power-line communications can be used for the transfer of data across electrical net- works in applications such as automatic meter reading in smart grid technology. As the power-line channel is harsh and plagued with non-Gaussian noise, robust forward error correction schemes are required. This research is a comparative study where a Luby transform code is concatenated with power-line communication systems provided by an up-to-date standard published by electricit e R eseau Distribution France named G3 PLC. Both decoding using Gaussian elimination and belief propagation are imple- mented to investigate and characterise their behaviour through computer simulations in MATLAB. Results show that a bit error rate performance improvement is achiev- able under non worst-case channel conditions using a Gaussian elimination decoder. An adaptive system is thus recommended which decodes using Gaussian elimination and which has the appropriate data rate. The added complexity can be well tolerated especially on the receiver side in automatic meter reading systems due to the network structure being built around a centralised agent which possesses more resources.MT201

Improving the Bandwidth Efficiency of Multiple Access Channels using Network Coding and Successive Decoding

In this thesis, different approaches for improving the bandwidth efficiency of Multiple Access Channels (MAC) have been proposed. Such improvements can be achieved with methods that use network coding, or with methods that implement successive decoding. Both of these two methods have been discussed here. Under the first method, two novel schemes for using network coding in cooperative networks have been proposed. In the first scheme, network coding generates some redundancy in addition to the redundancy that is generated by the channel code. These redundancies are used in an iterative decoding system at the destination. In the second scheme, the output of the channel encoder in each source node is shortened and transmitted. The relay, by use of the network code, sends a compressed version of the parts missing from the original transmission. This facilitates the decoding procedure at the destination. Simulation based optimizations have been developed. The results indicate that in the case of sources with non-identical power levels, both scenarios outperform the non-relay case. The second method, involves a scheme to increase the channel capacity of an existing channel. This increase is made possible by the introduction of a new Raptor coded interfering channel to an existing channel. Through successive decoding at the destination, the data of both main and interfering sources is decoded. We will demonstrate that when some power difference exists, there is a tradeoff between achieved rate and power efficiency. We will also find the optimum power allocation scenario for this tradeoff. Ultimately we propose a power adaptation scheme that allocates the optimal power to the interfering channel based on an estimation of the main channel's condition. Finally, we generalize our work to allow the possibility of decoding either the secondary source data or the main source data first. We will investigate the performance and delay for each decoding scheme. Since the channels are non-orthogonal, it is possible that for some power allocation scenarios, constellation points get erased. To address this problem we use constellation rotation. The constellation map of the secondary source is rotated to increase the average distance between the points in the constellation (resulting from the superposition of the main and interfering sources constellation.) We will also determine the optimum constellation rotation angle for the interfering source analytically and confirm it with simulations

Source and channel coding using Fountain codes

The invention of Fountain codes is a major advance in the field of error correcting codes. The goal of this work is to study and develop algorithms for source and channel coding using a family of Fountain codes known as Raptor codes. From an asymptotic point of view, the best currently known sum-product decoding algorithm for non binary alphabets has a high complexity that limits its use in practice. For binary channels, sum-product decoding algorithms have been extensively studied and are known to perform well. In the first part of this work, we develop a decoding algorithm for binary codes on non-binary channels based on a combination of sum-product and maximum-likelihood decoding. We apply this algorithm to Raptor codes on both symmetric and non-symmetric channels. Our algorithm shows the best performance in terms of complexity and error rate per symbol for blocks of finite length for symmetric channels. Then, we examine the performance of Raptor codes under sum-product decoding when the transmission is taking place on piecewise stationary memoryless channels and on channels with memory corrupted by noise. We develop algorithms for joint estimation and detection while simultaneously employing expectation maximization to estimate the noise, and sum-product algorithm to correct errors. We also develop a hard decision algorithm for Raptor codes on piecewise stationary memoryless channels. Finally, we generalize our joint LT estimation-decoding algorithms for Markov-modulated channels. In the third part of this work, we develop compression algorithms using Raptor codes. More specifically we introduce a lossless text compression algorithm, obtaining in this way competitive results compared to the existing classical approaches. Moreover, we propose distributed source coding algorithms based on the paradigm proposed by Slepian and Wolf