Statistical physics of irregular low-density parity-check codes

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Weight vs magnetization enumerator for Gallager codes

We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (¸M), rather than on the weight enumerator (¸W) presented recently 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. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Critical noise levels for LDPC decoding

We determine the critical noise level for decoding low density parity check error correcting codes based on the magnetization enumerator , rather than on the weight enumerator 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 via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Magnetization enumerator for LDPC codes - a statistical physics approach

We propose a method based on the magnetization enumerator to determine the critical noise level for Gallager type low density parity check error correcting codes (LDPC). Our method provides an appealingly simple interpretation to the relation between different decoding schemes, and provides more optimistic critical noise levels than those reported in the information theory literature.

Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

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.

On Multiple Deletion Codes

In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion codes for t = 2;3;4;5 with lengths n ≤ 30. Some of these codes improve on earlier results by Hirschberg-Fereira and Swart-Fereira. Finally, we prove a recursive upper bound on L2(n;t) which is asymptotically worse than the best known bounds, but gives better estimates for small values of n.

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.