LT Code Design for Inactivation Decoding

We present a simple model of inactivation decoding for LT codes which can be used to estimate the decoding complexity as a function of the LT code degree distribution. The model is shown to be accurate in variety of settings of practical importance. The proposed method allows to perform a numerical optimization on the degree distribution of a LT code aiming at minimizing the number of inactivations required for decoding.Comment: 6 pages, 7 figure

Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design

In this paper we analyze LT and Raptor codes under inactivation decoding. A first order analysis is introduced, which provides the expected number of inactivations for an LT code, as a function of the output distribution, the number of input symbols and the decoding overhead. The analysis is then extended to the calculation of the distribution of the number of inactivations. In both cases, random inactivation is assumed. The developed analytical tools are then exploited to design LT and Raptor codes, enabling a tight control on the decoding complexity vs. failure probability trade-off. The accuracy of the approach is confirmed by numerical simulations.Comment: Accepted for publication in IEEE Transactions on Communication

Doped Fountain Coding for Minimum Delay Data Collection in Circular Networks

This paper studies decentralized, Fountain and network-coding based strategies for facilitating data collection in circular wireless sensor networks, which rely on the stochastic diversity of data storage. The goal is to allow for a reduced delay collection by a data collector who accesses the network at a random position and random time. Data dissemination is performed by a set of relays which form a circular route to exchange source packets. The storage nodes within the transmission range of the route's relays linearly combine and store overheard relay transmissions using random decentralized strategies. An intelligent data collector first collects a minimum set of coded packets from a subset of storage nodes in its proximity, which might be sufficient for recovering the original packets and, by using a message-passing decoder, attempts recovering all original source packets from this set. Whenever the decoder stalls, the source packet which restarts decoding is polled/doped from its original source node. The random-walk-based analysis of the decoding/doping process furnishes the collection delay analysis with a prediction on the number of required doped packets. The number of doped packets can be surprisingly small when employed with an Ideal Soliton code degree distribution and, hence, the doping strategy may have the least collection delay when the density of source nodes is sufficiently large. Furthermore, we demonstrate that network coding makes dissemination more efficient at the expense of a larger collection delay. Not surprisingly, a circular network allows for a significantly more (analytically and otherwise) tractable strategies relative to a network whose model is a random geometric graph

Fountain Codes under Maximum Likelihood Decoding

This dissertation focuses on fountain codes under maximum likelihood (ML) decoding. First LT codes are considered under a practical and widely used ML decoding algorithm known as inactivation decoding. Different analysis techniques are presented to characterize the decoding complexity. Next an upper bound to the probability of decoding failure of Raptor codes under ML decoding is provided. Then, the distance properties of an ensemble of fixed-rate Raptor codes with linear random outer codes are analyzed. Finally, a novel class of fountain codes is presented, which consists of a parallel concatenation of a block code with a linear random fountain code.Comment: PhD Thesi

Outage Capacity and Code Design for Dying Channels

In wireless networks, communication links may be subject to random fatal impacts: for example, sensor networks under sudden power losses or cognitive radio networks with unpredictable primary user spectrum occupancy. Under such circumstances, it is critical to quantify how fast and reliably the information can be collected over attacked links. For a single point-to-point channel subject to a random attack, named as a dying channel, we model it as a block-fading (BF) channel with a finite and random channel length. First, we study the outage probability when the coding length K is fixed and uniform power allocation is assumed. Furthermore, we discuss the optimization over K and the power allocation vector PK to minimize the outage probability. In addition, we extend the single point to-point dying channel case to the parallel multi-channel case where each sub-channel is a dying channel, and investigate the corresponding asymptotic behavior of the overall outage probability with two different attack models: the independent-attack case and the m-dependent-attack case. It can be shown that the overall outage probability diminishes to zero for both cases as the number of sub-channels increases if the rate per unit cost is less than a certain threshold. The outage exponents are also studied to reveal how fast the outage probability improves over the number of sub-channels. Besides the information-theoretical results, we also study a practical coding scheme for the dying binary erasure channel (DBEC), which is a binary erasure channel (BEC) subject to a random fatal failure. We consider the rateless codes and optimize the degree distribution to maximize the average recovery probability. In particular, we first study the upper bound of the average recovery probability, based on which we define the objective function as the gap between the upper bound and the average recovery probability achieved by a particular degree distribution. We then seek the optimal degree distribution by minimizing the objective function. A simple and heuristic approach is also proposed to provide a suboptimal but good degree distribution

Error resilient stereoscopic video streaming using model-based fountain codes

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 2009.Thesis (Ph.D.) -- Bilkent University, 2009.Includes bibliographical references leaves 101-110.Error resilient digital video streaming has been a challenging problem since the introduction and deployment of early packet switched networks. One of the most recent advances in video coding is observed on multi-view video coding which suggests methods for the compression of correlated multiple image sequences. The existing multi-view compression techniques increase the loss sensitivity and necessitate the use of efficient loss recovery schemes. Forward Error Correction (FEC) is an efficient, powerful and practical tool for the recovery of lost data. A novel class of FEC codes is Fountain codes which are suitable to be used with recent video codecs, such as H.264/AVC, and LT and Raptor codes are practical examples of this class. Although there are many studies on monoscopic video, transmission of multi-view video through lossy channels with FEC have not been explored yet. Aiming at this deficiency, an H.264-based multi-view video codec and a model-based Fountain code are combined to generate an effi- cient error resilient stereoscopic streaming system. Three layers of stereoscopic video with unequal importance are defined in order to exploit the benefits of Unequal Error Protection (UEP) with FEC. Simply, these layers correspond to intra frames of left view, predicted frames of left view and predicted frames of right view. The Rate-Distortion (RD) characteristics of these dependent layers are de- fined by extending the RD characteristics of monoscopic video. The parameters of the models are obtained with curve fitting using the RD samples of the video, and satisfactory results are achieved where the average difference between the analytical models and RD samples is between 1.00% and 9.19%. An heuristic analytical model of the performance of Raptor codes is used to obtain the residual number of lost packets for given channel bit rate, loss rate, and protection rate. This residual number is multiplied with the estimated average distortion of the loss of a single Network Abstraction Layer (NAL) unit to obtain the total transmission distortion. All these models are combined to minimize the end-toend distortion and obtain optimal encoder bit rates and UEP rates. When the proposed system is used, the simulation results demonstrate up to 2dB increase in quality compared to equal error protection and only left view error protection. Furthermore, Fountain codes are analyzed in the finite length region, and iterative performance models are derived without any assumptions or asymptotical approximations. The performance model of the belief-propagation (BP) decoder approximates either the behavior of a single simulation results or their average depending on the parameters of the LT code. The performance model of the maximum likelihood decoder approximates the average of simulation results more accurately compared to the model of the BP decoder. Raptor codes are modeled heuristically based on the exponential decay observed on the simulation results, and the model parameters are obtained by line of best fit. The analytical models of systematic and non-systematic Raptor codes accurately approximate the experimental average performance.Tan, A SerdarPh.D

Enhanced Rateless Coding and Compressive Sensing for Efficient Data/multimedia Transmission and Storage in Ad-hoc and Sensor Networks

In this dissertation, we investigate the theory and applications of the novel class of FEC codes called rateless or fountain codes in video transmission and wireless sensor networks (WSN). First, we investigate the rateless codes in intermediate region where the number of received encoded symbols is less that minimum required for full datablock decoding. We devise techniques to improve the input symbol recovery rate when the erasure rate is unknown, and also for the case where an estimate of the channel erasure rate is available. Further, we design unequal error protection (UEP) rateless codes for distributed data collection of data blocks of unequal lengths, where two encoders send their rateless coded output symbols to a destination through a common relay. We design such distributed rateless codes, and jointly optimize rateless coding parameters at each nodes and relaying parameters. Moreover, we investigate the performance of rateless codes with finite block length in the presence of feedback channel. We propose a smart feedback generation technique that greatly improves the performance of rateless codes when data block is finite. Moreover, we investigate the applications of UEP-rateless codes in video transmission systems. Next, we study the optimal cross-layer design of a video transmission system with rateless coding at application layer and fixed-rate coding (RCPC coding) at physical layer. Finally, we review the emerging compressive sensing (CS) techniques that have close connections to FEC coding theory, and designed an efficient data storage algorithm for WSNs employing CS referred to by CStorage. First, we propose to employ probabilistic broadcasting (PB) to form one CS measurement at each node and design CStorage- P. Later, we can query any arbitrary small subset of nodes and recover all sensors reading. Next, we design a novel parameterless and more efficient data dissemination algorithm that uses two-hop neighbor information referred to alternating branches (AB).We replace PB with AB and design CStorage-B, which results in a lower number of transmissions compared to CStorage-P.Electrical Engineerin