Efficient soft decoding techniques for reed-solomon codes

The main focus of this thesis is on finding efficient decoding methods for Reed-Solomon (RS) codes, i.e., algorithms with acceptable performance and affordable complexity. Three classes of decoders are considered including sphere decoding, belief propagation decoding and interpolation-based decoding. Originally proposed for finding the exact solution of least-squares problems, sphere decoding (SD) is used along with the most reliable basis (MRB) to design an efficient soft decoding algorithm for RS codes. For an (N, K ) RS code, given the received vector and the lattice of all possible transmitted vectors, we propose to look for only those lattice points that fall within a sphere centered at the received vector and also are valid codewords. To achieve this goal, we use the fact that RS codes are maximum distance separable (MDS). Therefore, we use sphere decoding in order to find tentative solutions consisting of the K most reliable code symbols that fall inside the sphere. The acceptable values for each of these symbols are selected from an ordered set of most probable transmitted symbols. Based on the MDS property, K code symbols of each tentative solution can he used to find the rest of codeword symbols. If the resulting codeword is within the search radius, it is saved as a candidate transmitted codeword. Since we first find the most reliable code symbols and for each of them we use an ordered set of most probable transmitted symbols, candidate codewords are found quickly resulting in reduced complexity. Considerable coding gains are achieved over the traditional hard decision decoders with moderate increase in complexity. Due to their simplicity and good performance when used for decoding low density parity check (LDPC) codes, iterative decoders based on belief propagation (BP) have also been considered for RS codes. However, the parity check matrix of RS codes is very dense resulting in lots of short cycles in the factor graph and consequently preventing the reliability updates (using BP) from converging to a codeword. In this thesis, we propose two BP based decoding methods. In both of them, a low density extended parity check matrix is used because of its lower number of short cycles. In the first method, the cyclic structure of RS codes is taken into account and BP algorithm is applied on different cyclically shifted versions of received reliabilities, capable of detecting different error patterns. This way, some deterministic errors can be avoided. The second method is based on information correction in BP decoding where all possible values are tested for selected bits with low reliabilities. This way, the chance of BP iterations to converge to a codeword is improved significantly. Compared to the existing iterative methods for RS codes, our proposed methods provide a very good trade-off between the performance and the complexity. We also consider interpolation based decoding of RS codes. We specifically focus on Guruswami-Sudan (GS) interpolation decoding algorithm. Using the algebraic structure of RS codes and bivariate interpolation, the GS method has shown improved error correction capability compared to the traditional hard decision decoders. Based on the GS method, a multivariate interpolation decoding method is proposed for decoding interleaved RS (IRS) codes. Using this method all the RS codewords of the interleaved scheme are decoded simultaneously. In the presence of burst errors, the proposed method has improved correction capability compared to the GS method. This method is applied for decoding IRS codes when used as outer codes in concatenated code

Improving Bandwidth Utilization in a 1 Tbps Airborne MIMO Communications Downlink

FEC techniques are compared for different MIMO configurations of a high altitude, extremely wide bandwidth radio frequency downlink. Monte Carlo simulations are completed in MATLAB® with the aim of isolating the impacts of turbo codes and LDPC codes on system throughput and error performance. The system is modeled as a transmit-only static array at an altitude of 60,000 feet, with no interferers in the channel. Transmissions are received by a static receiver array. Simulations attempt to determine what modulation types should be considered for practical implementation, and what FEC codes enable these modulation schemes. The antenna configurations used in this study are [44:352], [62:248], and [80:160] transmitters to receivers. Effects from waveform generation, mixing, down-conversion, and amplification are not considered. Criteria of interest were BER and throughput, with the maximum allowable value of the former set at 1 x 10-5, and the latter set at a 1 terabits per second (Tbps) transfer rate for a successful configuration. Results show that the best performing system configuration was unable to meet both criteria, but was capable of improving over Brueggen\u27s 2012 research, which used Reed-Solomon codes and a MIMO configuration of [80:160], by 18.6%. The best-case configuration produced a throughput rate of 0.83 Tbps at a BER of less than 1 x 10-8, by implementing a rate 2/3 LDPC code with QAM constellation of 16 symbols

Channel Coding in Molecular Communication

This dissertation establishes and analyzes a complete molecular transmission system from a communication engineering perspective. Its focus is on diffusion-based molecular communication in an unbounded three-dimensional fluid medium. As a basis for the investigation of transmission algorithms, an equivalent discrete-time channel model (EDTCM) is developed and the characterization of the channel is described by an analytical derivation, a random walk based simulation, a trained artificial neural network (ANN), and a proof of concept testbed setup. The investigated transmission algorithms cover modulation schemes at the transmitter side, as well as channel equalizers and detectors at the receiver side. In addition to the evaluation of state-of-the-art techniques and the introduction of orthogonal frequency-division multiplexing (OFDM), the novel variable concentration shift keying (VCSK) modulation adapted to the diffusion-based transmission channel, the lowcomplex adaptive threshold detector (ATD) working without explicit channel knowledge, the low-complex soft-output piecewise linear detector (PLD), and the optimal a posteriori probability (APP) detector are of particular importance and treated. To improve the error-prone information transmission, block codes, convolutional codes, line codes, spreading codes and spatial codes are investigated. The analysis is carried out under various approaches of normalization and gains or losses compared to the uncoded transmission are highlighted. In addition to state-of-the-art forward error correction (FEC) codes, novel line codes adapted to the error statistics of the diffusion-based channel are proposed. Moreover, the turbo principle is introduced into the field of molecular communication, where extrinsic information is exchanged iteratively between detector and decoder. By means of an extrinsic information transfer (EXIT) chart analysis, the potential of the iterative processing is shown and the communication channel capacity is computed, which represents the theoretical performance limit for the system under investigation. In addition, the construction of an irregular convolutional code (IRCC) using the EXIT chart is presented and its performance capability is demonstrated. For the evaluation of all considered transmission algorithms the bit error rate (BER) performance is chosen. The BER is determined by means of Monte Carlo simulations and for some algorithms by theoretical derivation

Scalable Video Streaming with Prioritised Network Coding on End-System Overlays

PhDDistribution over the internet is destined to become a standard approach for live broadcasting of TV or events of nation-wide interest. The demand for high-quality live video with personal requirements is destined to grow exponentially over the next few years. Endsystem multicast is a desirable option for relieving the content server from bandwidth bottlenecks and computational load by allowing decentralised allocation of resources to the users and distributed service management. Network coding provides innovative solutions for a multitude of issues related to multi-user content distribution, such as the coupon-collection problem, allocation and scheduling procedure. This thesis tackles the problem of streaming scalable video on end-system multicast overlays with prioritised push-based streaming. We analyse the characteristic arising from a random coding process as a linear channel operator, and present a novel error detection and correction system for error-resilient decoding, providing one of the first practical frameworks for Joint Source-Channel-Network coding. Our system outperforms both network error correction and traditional FEC coding when performed separately. We then present a content distribution system based on endsystem multicast. Our data exchange protocol makes use of network coding as a way to collaboratively deliver data to several peers. Prioritised streaming is performed by means of hierarchical network coding and a dynamic chunk selection for optimised rate allocation based on goodput statistics at application layer. We prove, by simulated experiments, the efficient allocation of resources for adaptive video delivery. Finally we describe the implementation of our coding system. We highlighting the use rateless coding properties, discuss the application in collaborative and distributed coding systems, and provide an optimised implementation of the decoding algorithm with advanced CPU instructions. We analyse computational load and packet loss protection via lab tests and simulations, complementing the overall analysis of the video streaming system in all its components

Network coding: from theory to media streaming

Network coding has recently emerged as an alternative to traditional routing algorithms in communication systems. In network coding, the network nodes can combine the packets they receive before forwarding them to the neighbouring nodes. Intensive research efforts have demonstrated that such a processing in the network nodes can provide advantages in terms of throughput or robustness. These potentials, combined with the advent of ad hoc and wireless delivery architectures have triggered the interest of research community about the application of the network coding principles to streaming applications. This paper describes the potentials of network coding in emerging delivery architectures such as overlay or peer-to-peer networks. It overviews the principles of practical network coding algorithms and outlines the challenges posed by multimedia streaming applications. Finally, it provides a survey of the recent work on the application of network coding to media streaming applications, both in wireless or wired communication scenarios. Promising results have been demonstrated where network coding is able to bring benefits in media streaming applications. However, delay and complexity constraints are often posed as the main challenging issues that still prevent the wide-scale deployment of network coding algorithms in multimedia communication

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