Augmented LDPC Graph for Distributed Video Coding with Multiple Side Information

The advances made in channel-capacity codes, such as turbo codes and low-density parity-check (LDPC) codes, have played a major role in the emerging distributed source coding paradigm. LDPC codes can be easily adapted to new source coding strategies due to their natural representation as bipartite graphs and the use of quasi-optimal decoding algorithms, such as belief propagation. This paper tackles a relevant scenario in distributedvideo coding: lossy source coding when multiple side information (SI) hypotheses are available at the decoder, each one correlated with the source according to different correlation noise channels. Thus, it is proposed to exploit multiple SI hypotheses through an efficient joint decoding technique withmultiple LDPC syndrome decoders that exchange information to obtain coding efficiency improvements. At the decoder side, the multiple SI hypotheses are created with motion compensated frame interpolation and fused together in a novel iterative LDPC based Slepian-Wolf decoding algorithm. With the creation of multiple SI hypotheses and the proposed decoding algorithm, bitrate savings up to 8.0% are obtained for similar decoded quality.

Implementação de códigos LDPC em OFDM e SC-FDE

Os desenvolvimentos dos sistemas de comunicação sem fios apontam para transmissões de alta velocidade e alta qualidade de serviço com um uso eficiente de energia. Eficiência espectral pode ser obtida por modulações multinível, enquanto que melhorias na eficiência de potência podem ser proporcionadas pelo uso de códigos corretores de erros. Os códigos Low-Density Parity-Check (LDPC), devido ao seu desempenho próximo do limite de Shannon e baixa complexidade na implementação e descodificação são apropriados para futuros sistemas de comunicações sem fios. Por outro lado, o uso de modulações multinível acarreta limitações na amplificação. Contudo, uma amplificação eficiente pode ser assegurada por estruturas de transmissão onde as modulações multinível são decompostas em submodulações com envolvente constante que podem ser amplificadas por amplificadores não lineares a operar na zona de saturação. Neste tipo de estruturas surgem desvios de fase e ganho, produzindo distorções na constelação resultante da soma de todos os sinais amplificados. O trabalho foca-se no uso dos códigos LDPC em esquemas multiportadora e monoportadora, com especial ênfase na performance de uma equalização iterativa implementada no domínio da frequência por um Iterative Block-Decision Feedback Equalizer (IB-DFE). São analisados aspectos como o impacto do número de iterações no processo de descodificação dentro das iterações do processo de equalização. Os códigos LDPC também serão utilizados para compensar os desvios de fase em recetores iterativos para sistemas baseados em transmissores com vários ramos de amplificação. É feito um estudo sobre o modo como estes códigos podem aumentar a tolerância a erros de fase que incluí uma análise da complexidade e um algoritmo para estimação dos desequilíbrios de fase.

Outage thresholds of LDPC codes over nonergodic block-fading channels

This paper derives approximations allowing the estimation of outage probability for standard irregular LDPC codes and full-diversity Root-LDPC codes used over nonergodic block-fading channels. Two separate approaches are discussed: a numerical approximation, obtained by curve fitting, for both code ensembles, and an analytical approximation for Root-LDPC codes, obtained under the assumption that the slope of the iterative threshold curve of a given code ensemble matches the slope of the outage capacity curve in the high-SNR regime.

On iterative performance of LDPC and Root-LDPC codes over block-fading channels

This paper presents our investigation on iterativedecoding performances of some sparse-graph codes on block-fading Rayleigh channels. The considered code ensembles are standard LDPC codes and Root-LDPC codes, first proposed in and shown to be able to attain the full transmission diversity. We study the iterative threshold performance of those codes as a function of fading gains of the transmission channel and propose a numerical approximation of the iterative threshold versus fading gains, both both LDPC and Root-LDPC codes.Also, we show analytically that, in the case of 2 fading blocks,the iterative threshold root of Root-LDPC codes is proportional to (α1 α2)1, where α1 and α2 are corresponding fading gains.From this result, the full diversity property of Root-LDPC codes immediately follows.

Progetto e implementazione di un decodificatore ldpc su architettura gpu

In accordo con la filosofia della Software Defined Radio è stato progettato un decoder LDPC software che utilizza una GPU per ottenere prestazioni migliori. Il lavoro, che comprende anche l'encoder e un simulatore di canale AWGN, può essere utilizzato sia per eseguire simulazioni che per elaborare dati in real time. Come caso di studio si sono considerati i codici LDPC dello standard DVB-S2.

Rate-Adaptive LDPC-based key reconciliation for high performance quantum key distribution

The postprocessing or secret-key distillation process in quantum key distribution (QKD) mainly involves two well-known procedures: information reconciliation and privacy amplification. Information or key reconciliation has been customarily studied in terms of efficiency. During this, some information needs to be disclosed for reconciling discrepancies in the exchanged keys. The leakage of information is lower bounded by a theoretical limit, and is usually parameterized by the reconciliation efficiency (or inefficiency), i.e. the ratio of additional information disclosed over the Shannon limit. Most techniques for reconciling errors in QKD try to optimize this parameter. For instance, the well-known Cascade (probably the most widely used procedure for reconciling errors in QKD) was recently shown to have an average efficiency of 1.05 at the cost of a high interactivity (number of exchanged messages). Modern coding techniques, such as rate-adaptive low-density parity-check (LDPC) codes were also shown to achieve similar efficiency values exchanging only one message, or even better values with few interactivity and shorter block-length codes.

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.

A statistical-mechanical analysis of coded CDMA with regular LDPC codes

We analyze, using the replica method of statistical mechanics, the theoretical performance of coded code-division multiple-access (CDMA) systems in which regular low-density parity-check (LDPC) codes are used for channel coding.

Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases. © 2007 IOP Publishing Ltd.

Design and performance of a novel low-density parity-check code for distributed video coding

Low-density parity-check (LDPC) codes are nowadays one of the hottest topics in coding theory, notably due to their advantages in terms of bit error rate performance and low complexity. In order to exploit the potential of the Wyner-Ziv coding paradigm, practical distributed video coding (DVC) schemes should use powerful error correcting codes with near-capacity performance. In this paper, new ways to design LDPC codes for the DVC paradigm are proposed and studied. The new LDPC solutions rely on merging parity-check nodes, which corresponds to reduce the number of rows in the parity-check matrix. This allows to change gracefully the compression ratio of the source (DCT coefficient bitplane) according to the correlation between the original and the side information. The proposed LDPC codes reach a good performance for a wide range of source correlations and achieve a better RD performance when compared to the popular turbo codes.

Codificación a nivel de paquete para comunicaciones móviles por satélite

Una de les opcions que es contemplen per transmetre continguts multimèdia i proporcionar accés a Internet a grups de usuaris mòbils és fer servir satèl·lits. Les condiciones de propagació del canal mòbil impliquen que d'una manera o altra haurem de garantir la qualitat de servei. Això té fins i tot més importància si tenim en compte que, en el cas d'accés a Internet, no es té la capacitat d'assumir cert percentatge de pèrdua de dades que tenim, per exemple, en la transmissió de so o vídeo (rebaixant la qualitat). Entre les principals alternatives per a aquesta classe d’entorns es troba la inclusió de codificacions a nivell de paquet. El funcionament d'aquesta tècnica es basa en incloure a la transmissió paquets redundants, obtinguts mitjançant un determinat algoritme. El receptor podrà recuperar la informació original que es volia enviar, sempre que hagi rebut una certa quantitat de paquets, similar a la quantitat de paquets originals. A aquest mecanisme se'l coneix com Forward Error Correction (FEC) a nivell de paquet. En aquesta memòria es valoren breument les alternatives existents i s'expliquen algunes de les codificacions per a FEC més importants. A continuació es realitza un estudi compartiu d’algunes d'elles: les variants de LDPC (Low Density Parity Check) conegudes com LDGM (Low Density Generator Matrix), i la codificació Raptor

Low-density parity-check codes for nonergodic block-fading channels

We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not performwell under iterative decoding, we introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.

Virheenkorjausalgoritmit

Virheenkorjausalgoritmit mahdollistavat kommunikaation häiriöisen kanavan välityksellä. Esimerkiksi reaaliaikaisessa kommunikaatiossa on suotavaa, ettei virheenkorjausta toteuteta uudelleenlähetyksin, vaan häiriöiden sietämiseksi viestiin lisätään redundanssia eli päällekkäisyyttä. Tätä kutsutaan kanavakoodaukseksi. Virheenkorjausalgoritmien suorituskykyä voidaan vertailla ainakin niiden etäisyydellä, hyvyydellä suhteessa kanavan kapasiteettiin sekä koodausvahvistuksella. Koodausvahvistus on näistä konkreettisin, joskaan se ei huomioi algoritmien informaatiosuhdetta. Tällä hetkellä suorituskykyisimpiä algoritmeja ovat konvoluutiokoodeihin kuuluvat turbokoodit, lohkokoodeihin kuuluvat LDPC-koodit sekä ketjukoodit, joissa käytetään ulompana koodina pitkän lohkokoon lohkokoodia ja sisempänä jotakin modernia konvoluutiokoodia.

Packet Level Coding for Mobile Broadcasting

The thesis deals with channel coding theory applied to upper layers in the protocol stack of a communication link and it is the outcome of four year research activity. A specific aspect of this activity has been the continuous interaction between the natural curiosity related to the academic blue-sky research and the system oriented design deriving from the collaboration with European industry in the framework of European funded research projects. In this dissertation, the classical channel coding techniques, that are traditionally applied at physical layer, find their application at upper layers where the encoding units (symbols) are packets of bits and not just single bits, thus explaining why such upper layer coding techniques are usually referred to as packet layer coding. The rationale behind the adoption of packet layer techniques is in that physical layer channel coding is a suitable countermeasure to cope with small-scale fading, while it is less efficient against large-scale fading. This is mainly due to the limitation of the time diversity inherent in the necessity of adopting a physical layer interleaver of a reasonable size so as to avoid increasing the modem complexity and the latency of all services. Packet layer techniques, thanks to the longer codeword duration (each codeword is composed of several packets of bits), have an intrinsic longer protection against long fading events. Furthermore, being they are implemented at upper layer, Packet layer techniques have the indisputable advantages of simpler implementations (very close to software implementation) and of a selective applicability to different services, thus enabling a better matching with the service requirements (e.g. latency constraints). Packet coding technique improvement has been largely recognized in the recent communication standards as a viable and efficient coding solution: Digital Video Broadcasting standards, like DVB-H, DVB-SH, and DVB-RCS mobile, and 3GPP standards (MBMS) employ packet coding techniques working at layers higher than the physical one. In this framework, the aim of the research work has been the study of the state-of-the-art coding techniques working at upper layer, the performance evaluation of these techniques in realistic propagation scenario, and the design of new coding schemes for upper layer applications. After a review of the most important packet layer codes, i.e. Reed Solomon, LDPC and Fountain codes, in the thesis focus our attention on the performance evaluation of ideal codes (i.e. Maximum Distance Separable codes) working at UL. In particular, we analyze the performance of UL-FEC techniques in Land Mobile Satellite channels. We derive an analytical framework which is a useful tool for system design allowing to foresee the performance of the upper layer decoder. We also analyze a system in which upper layer and physical layer codes work together, and we derive the optimal splitting of redundancy when a frequency non-selective slowly varying fading channel is taken into account. The whole analysis is supported and validated through computer simulation. In the last part of the dissertation, we propose LDPC Convolutional Codes (LDPCCC) as possible coding scheme for future UL-FEC application. Since one of the main drawbacks related to the adoption of packet layer codes is the large decoding latency, we introduce a latency-constrained decoder for LDPCCC (called windowed erasure decoder). We analyze the performance of the state-of-the-art LDPCCC when our decoder is adopted. Finally, we propose a design rule which allows to trade-off performance and latency.