Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Evaluating and improving the performance of video content distribution in lossy networks

The contributions in this research are split in to three distinct, but related, areas. The focus of the work is based on improving the efficiency of video content distribution in the networks that are liable to packet loss, such as the Internet. Initially, the benefits and limitations of content distribution using Forward Error Correction (FEC) in conjunction with the Transmission Control Protocol (TCP) is presented. Since added FEC can be used to reduce the number of retransmissions, the requirement for TCP to deal with any losses is greatly reduced. When real-time applications are needed, delay must be kept to a minimum, and retransmissions not desirable. A balance, therefore, between additional bandwidth and delays due to retransmissions must be struck. This is followed by the proposal of a hybrid transport, specifically for H.264 encoded video, as a compromise between the delay-prone TCP and the loss-prone UDP. It is argued that the playback quality at the receiver often need not be 100% perfect, providing a certain level is assured. Reliable TCP is used to transmit and guarantee delivery of the most important packets. The delay associated with the proposal is measured, and the potential for use as an alternative to the conventional methods of transporting video by either TCP or UDP alone is demonstrated. Finally, a new objective measurement is investigated for assessing the playback quality of video transported using TCP. A new metric is defined to characterise the quality of playback in terms of its continuity. Using packet traces generated from real TCP connections in a lossy environment, simulating the playback of a video is possible, whilst monitoring buffer behaviour to calculate pause intensity values. Subjective tests are conducted to verify the effectiveness of the metric introduced and show that the results of objective and subjective scores made are closely correlated.

H264 data partitioned video streaming

Motivated by the increasing demand and challenges of video streaming in this thesis, we investigate methods by which the quality of the video can be improved. We utilise overlay networks that have been created by implemented relay nodes to produce path diversity, and show through analytical and simulation models for which environments path diversity can improve the packet loss probability. We take the simulation and analytical models further by implementing a real overlay network on top of Planetlab, and show that when the network conditions remain constant the video quality received by the client can be improved. In addition, we show that in the environments where path diversity improves the video quality forward error correction can be used to further enhance the quality. We then investigate the effect of IEEE 802.11e Wireless LAN standard with quality of service enabled on the video quality received by a wireless client. We find that assigning all the video to a single class outperforms a cross class assignment scheme proposed by other researchers. The issue of virtual contention at the access point is also examined. We increase the intelligence of our relay nodes and enable them to cache video, in order to maximise the usefulness of these caches. For this purpose, we introduce a measure, called the PSNR profit, and present an optimal caching method for achieving the maximum PSNR profit at the relay nodes where partitioned video contents are stored and provide an enhanced quality for the client. We also show that the optimised cache the degradation in the video quality received by the client becomes more graceful than the non-optimised system when the network experiences packet loss or is congested.

Investigation of different techniques to upgrade legacy WDM communication systems

This thesis presents experimental investigation of different effects/techniques that can be used to upgrade legacy WDM communication systems. The main issue in upgrading legacy systems is that the fundamental setup, including components settings such as EDFA gains, does not need to be altered thus the improvement must be carried out at the network terminal. A general introduction to optical fibre communications is given at the beginning, including optical communication components and system impairments. Experimental techniques for performing laboratory optical transmission experiments are presented before the experimental work of this thesis. These techniques include optical transmitter and receiver designs as well as the design and operation of the recirculating loop. The main experimental work includes three different studies. The first study involves a development of line monitoring equipment that can be reliably used to monitor the performance of optically amplified long-haul undersea systems. This equipment can provide instant finding of the fault locations along the legacy communication link which in tum enables rapid repair execution to be performed hence upgrading the legacy system. The second study investigates the effect of changing the number of transmitted 1s and Os on the performance of WDM system. This effect can, in reality, be seen in some coding systems, e.g. forward-error correction (FEC) technique, where the proportion of the 1s and Os are changed at the transmitter by adding extra bits to the original bit sequence. The final study presents transmission results after all-optical format conversion from NRZ to CSRZ and from RZ to CSRZ using semiconductor optical amplifier in nonlinear optical loop mirror (SOA-NOLM). This study is mainly based on the fact that the use of all-optical processing, including format conversion, has become attractive for the future data networks that are proposed to be all-optical. The feasibility of the SOA-NOLM device for converting single and WDM signals is described. The optical conversion bandwidth and its limitations for WDM conversion are also investigated. All studies of this thesis employ 10Gbit/s single or WDM signals being transmitted over dispersion managed fibre span in the recirculating loop. The fibre span is composed of single-mode fibres (SMF) whose losses and dispersion are compensated using erbium-doped fibre amplifiers (EDFAs) and dispersion compensating fibres (DCFs), respectively. Different configurations of the fibre span are presented in different parts.

Impact of Raman amplification on a 2 Tb/s coherent WDM system

The impact of hybrid erbium-doped fiber amplifier (EDFA)/Raman amplification on a spectrally efficient coherent-wavelength-division-multiplexed (CoWDM) optical communication system is experimentally studied and modeled. Simulations suggested that 23-dB Raman gain over an unrepeatered span of 124 km single-mode fiber would allow a decrease of the mean input power of ~6 dB for a fixed bit-error rate (BER). Experimentally we demonstrated 1.2-dB Q-factor improvement for a 2-Tb/s seven-band CoWDM with backward Raman amplification. The system delivered an optical signal-to-noise ratio of 35 dB at the output of the receiver preamplifier providing a worst-case BER of 2 × 10 -6 over 49 subcarriers at 42.8 Gbaud, leaving a system margin (in terms of Q -factor) of ~4 dB from the forward-error correction threshold.

A 20-Mb/s VLC link with a polymer LED and a multilayer perceptron equalizer

This letter experimentally demonstrates a visible light communication system using a 350-kHz polymer lightemitting diode operating at a total bit rate of 19 Mb/s with a bit error rate (BER) of 10-6and 20 Mb/s at the forward error correction limit for the first time. This represents a remarkable net data rate gain of ~55 times. The modulation format adopted is ON-OFF keying in conjunction with an artificial neural network classifier implemented as an equalizer. The number of neurons used in the experiment is varied from the set N = {5, 10, 20, 30, 40} with 40 neurons offering the best performance at 19 Mb/s and the BER of 10-6.

Critical noise levels for low-density parity check decoding

We determine the critical noise level for decoding low-density parity check error-correcting codes based on the magnetization enumerator (M), rather than on the weight enumerator (W) employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived using the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

A 10 Mb/s visible light communication system using a low bandwidth polymer light-emitting diode

In this paper we experimentally demonstrate a 10 Mb/s error free visible light communications (VLC) system using polymer light-emitting diodes (PLEDs) for the first time. The PLED under test is a blue emitter with ∼600 kHz bandwidth. Having such a low bandwidth means the introduction of an intersymbol interference (ISI) induced penalty at higher transmission speeds and thus the requirement for an equalizer. In this work we improve on previous literature by implementing a decision feedback equalizer, rather than a linear equalizer. Considering 7% and 20% forward error correction codes, transmission speeds up to ∼12 Mb/s can be supported.

Dimensioning BCH codes for coherent DQPSK systems with laser phase noise and cycle slips

Forward error correction (FEC) plays a vital role in coherent optical systems employing multi-level modulation. However, much of coding theory assumes that additive white Gaussian noise (AWGN) is dominant, whereas coherent optical systems have significant phase noise (PN) in addition to AWGN. This changes the error statistics and impacts FEC performance. In this paper, we propose a novel semianalytical method for dimensioning binary Bose-Chaudhuri-Hocquenghem (BCH) codes for systems with PN. Our method involves extracting statistics from pre-FEC bit error rate (BER) simulations. We use these statistics to parameterize a bivariate binomial model that describes the distribution of bit errors. In this way, we relate pre-FEC statistics to post-FEC BER and BCH codes. Our method is applicable to pre-FEC BER around 10-3 and any post-FEC BER. Using numerical simulations, we evaluate the accuracy of our approach for a target post-FEC BER of 10-5. Codes dimensioned with our bivariate binomial model meet the target within 0.2-dB signal-to-noise ratio.

Upgrading legacy long-haul WDM systems through unbalancing the proportion of 1s and 0s in the transmitted data

We present experimental results for wavelength-division multiplexed (WDM) transmission performance using unbalanced proportions of 1s and 0s in pseudo-random bit sequence (PRBS) data. This investigation simulates the effect of local, in time, data unbalancing which occurs in some coding systems such as forward error correction when extra bits are added to the WDM data stream. We show that such local unbalancing, which would practically give a time-dependent error-rate, can be employed to improve the legacy long-haul WDM system performance if the system is allowed to operate in the nonlinear power region. We use a recirculating loop to simulate a long-haul fibre system.

WDM orthogonal subcarrier multiplexing

Electro-optical transceivers can be implemented employing all-analog signal processing in order to achieve low values of power consumption and latency. This paper shows that the spectral efficiency of such solutions can be increased by combining orthogonal multicarrier techniques and off-the-shelf microwave components. A real-time 108-Gbit/s experiment was performed emulating a wavelength division multiplexing (WDM) system composed of five optical channels. The optical carriers were provided by an externally injected gain switched optical frequency comb. Each optical channel transmitted a 21.6-Gbit/s orthogonal subcarrier multiplexing (SCM) signal that was modulated and demodulated in the electrical domain without the requirement for digital signal processing. The net data rate remained higher than 100 Gbit/s after taking into account forward error correction overheads. The use of orthogonally overlapping subchannels achieves an unprecedented spectral efficiency in all-analog real-time broadband WDM/SCM links.

Low-complexity BCH codes with optimized interleavers for DQPSK systems with laser phase noise

The presence of high phase noise in addition to additive white Gaussian noise in coherent optical systems affects the performance of forward error correction (FEC) schemes. In this paper, we propose a simple scheme for such systems, using block interleavers and binary Bose–Chaudhuri–Hocquenghem (BCH) codes. The block interleavers are specifically optimized for differential quadrature phase shift keying modulation. We propose a method for selecting BCH codes that, together with the interleavers, achieve a target post-FEC bit error rate (BER). This combination of interleavers and BCH codes has very low implementation complexity. In addition, our approach is straightforward, requiring only short pre-FEC simulations to parameterize a model, based on which we select codes analytically. We aim to correct a pre-FEC BER of around (Formula presented.). We evaluate the accuracy of our approach using numerical simulations. For a target post-FEC BER of (Formula presented.), codes selected using our method result in BERs around 3(Formula presented.) target and achieve the target with around 0.2 dB extra signal-to-noise ratio.

Effective video content distribution by combining TCP with adaptive FEC coding

This paper will look at the benefits and limitations of content distribution using Forward Error Correction (FEC) in conjunction with the Transmission Control Protocol (TCP). FEC can be used to reduce the number of retransmissions which would usually result from a lost packet. The requirement for TCP to deal with any losses is then greatly reduced. There are however side-effects to using FEC as a countermeasure to packet loss: an additional requirement for bandwidth. When applications such as real-time video conferencing are needed, delay must be kept to a minimum, and retransmissions are certainly not desirable. A balance, therefore, between additional bandwidth and delay due to retransmissions must be struck. Our results show that the throughput of data can be significantly improved when packet loss occurs using a combination of FEC and TCP, compared to relying solely on TCP for retransmissions. Furthermore, a case study applies the result to demonstrate the achievable improvements in the quality of streaming video perceived by end users.

Robust H.264/AVC video transmission using data partitioning and unequal loss protection

In this work, we present an adaptive unequal loss protection (ULP) scheme for H264/AVC video transmission over lossy networks. This scheme combines erasure coding, H.264/AVC error resilience techniques and importance measures in video coding. The unequal importance of the video packets is identified in the group of pictures (GOP) and the H.264/AVC data partitioning levels. The presented method can adaptively assign unequal amount of forward error correction (FEC) parity across the video packets according to the network conditions, such as the available network bandwidth, packet loss rate and average packet burst loss length. A near optimal algorithm is developed to deal with the FEC assignment for optimization. The simulation results show that our scheme can effectively utilize network resources such as bandwidth, while improving the quality of the video transmission. In addition, the proposed ULP strategy ensures graceful degradation of the received video quality as the packet loss rate increases. © 2010 IEEE.

Bounds on end-to-end performance of networks employing erasure control coding

Erasure control coding has been exploited in communication networks with an aim to improve the end-to-end performance of data delivery across the network. To address the concerns over the strengths and constraints of erasure coding schemes in this application, we examine the performance limits of two erasure control coding strategies, forward erasure recovery and adaptive erasure recovery. Our investigation shows that the throughput of a network using an (n, k) forward erasure control code is capped by r =k/n when the packet loss rate p ≤ (te/n) and by k(l-p)/(n-te) when p > (t e/n), where te is the erasure control capability of the code. It also shows that the lower bound of the residual loss rate of such a network is (np-te)/(n-te) for (te/n) < p ≤ 1. Especially, if the code used is maximum distance separable, the Shannon capacity of the erasure channel, i.e. 1-p, can be achieved and the residual loss rate is lower bounded by (p+r-1)/r, for (1-r) < p ≤ 1. To address the requirements in real-time applications, we also investigate the service completion time of different schemes. It is revealed that the latency of the forward erasure recovery scheme is fractionally higher than that of the scheme without erasure control coding or retransmission mechanisms (using UDP), but much lower than that of the adaptive erasure scheme when the packet loss rate is high. Results on comparisons between the two erasure control schemes exhibit their advantages as well as disadvantages in the role of delivering end-to-end services. To show the impact of the bounds derived on the end-to-end performance of a TCP/IP network, a case study is provided to demonstrate how erasure control coding could be used to maximize the performance of practical systems. © 2010 IEEE.