First-Passage Time and Large-Deviation Analysis for Erasure Channels with Memory

This article considers the performance of digital communication systems transmitting messages over finite-state erasure channels with memory. Information bits are protected from channel erasures using error-correcting codes; successful receptions of codewords are acknowledged at the source through instantaneous feedback. The primary focus of this research is on delay-sensitive applications, codes with finite block lengths and, necessarily, non-vanishing probabilities of decoding failure. The contribution of this article is twofold. A methodology to compute the distribution of the time required to empty a buffer is introduced. Based on this distribution, the mean hitting time to an empty queue and delay-violation probabilities for specific thresholds can be computed explicitly. The proposed techniques apply to situations where the transmit buffer contains a predetermined number of information bits at the onset of the data transfer. Furthermore, as additional performance criteria, large deviation principles are obtained for the empirical mean service time and the average packet-transmission time associated with the communication process. This rigorous framework yields a pragmatic methodology to select code rate and block length for the communication unit as functions of the service requirements. Examples motivated by practical systems are provided to further illustrate the applicability of these techniques.Comment: To appear in IEEE Transactions on Information Theor

Error models for digital channels and applications to wireless communication systems

Digital wireless channels are extremely prone to errors that appear in bursts or clusters. Error models characterise the statistical behaviour of bursty profiles derived from digital wireless channels. Generative error models also utilise those bursty profiles in order to create alternatives, which are more efficient for experimental purposes. Error models have a tremendous value for wireless systems. They are useful for the design and performance evaluation of error control schemes, in addition to higher layer protocols in which the statistical properties of the bursty profiles are greatly functional. Furthermore, underlying wireless digital channels can be substituted by generated error profiles. Consequently, computational load and simulation time can be significantly reduced when executing experiments and performing evaluation simulations for higher layer communications protocols and error control strategies. The burst error statistics are the characterisation metrics of error models. These statistics include: error-free run distribution; error-free burst distribution; error burst distribution; error cluster distribution; gap distribution; block error probability distribution; block burst probability distribution; bit error correlation function; normalised covariance function; gap correlation function; and multigap distribution. These burst error statistics scrutinise the error models and differentiate between them, with regards to accuracy. Moreover, some of them are advantageous for the design of digital components in wireless communication systems. This PhD thesis aims to develop accurate and efficient error models and to find applications for them. A thorough investigation has been conducted on the burst error statistics. A breakdown of this thesis is presented as follows. Firstly, an understanding of the different types of generative error models, namely, Markovian based generative models, context-free grammars based generative models, chaotic models, and deterministic process based generative models, has been presented. The most widely used models amongst the generative models have been compared with each other consulting the majority of burst error statistics. In order to study generative error models, error burst profiles were obtained mainly from the Enhanced General Packet Radio Service (EGPRS) system and also the Long Term Evolution (LTE) system. Secondly, more accurate and efficient generative error models have been proposed. Double embedded processes based hidden Markov model and three-layered processes based hidden Markov model have been developed. The two types of error profiles, particularly the bit-level and packet-level error profiles were considered. Thirdly, the deterministic process based generative models’ parameters have been tuned or modified in order to generate packet error sequences rather than only bit error sequences. Moreover, a modification procedure has been introduced to the same models to enhance their generation process and to make them more desirable. Fourthly, adaptive generative error models have been built in order to accommodate widely used generative error models to different digital wireless channels with different channel conditions. Only a few reference error profiles have been required in order to produce additional error profiles in various conditions that are beneficial for the design and performance evaluation of error control schemes and higher layer protocols. Finally, the impact of the Hybrid Automatic Repeat reQuest (HARQ) on the burst error statistics of physical layer error profiles has been studied. Moreover, a model that can generate predicted error sequences with burst error statistics similar to those of error profiles when HARQ is included has been proposed. This model is constructive in predicting the behaviour of the HARQ in terms of a set of higher order statistics rather than only predicting a first order statistic. Moreover, the whole physical layer is replaced by adaptively generated error profiles in order to check the performance of the HARQ protocol. The developed generative error models as well as the developed adaptive generative error models are expected to benefit future research towards the testing of many digital components in the physical layer as well as the wireless protocols of the link and transport layers for many existing and emerging systems in the field of wireless communications

End-to-End Delay Distribution Analysis for Stochastic Admission Control in Multi-hop Wireless Networks

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