9 research outputs found

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

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    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

    Bounds on the Error Probability of Raptor Codes under Maximum Likelihood Decoding

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    In this paper upper and lower bounds on the probability of decoding failure under maximum likelihood decoding are derived for different (nonbinary) Raptor code constructions. In particular four different constructions are considered; (i) the standard Raptor code construction, (ii) a multi-edge type construction, (iii) a construction where the Raptor code is nonbinary but the generator matrix of the LT code has only binary entries, (iv) a combination of (ii) and (iii). The latter construction resembles the one employed by RaptorQ codes, which at the time of writing this article represents the state of the art in fountain codes. The bounds are shown to be tight, and provide an important aid for the design of Raptor codes.Comment: Submitted for revie

    Fountain Codes under Maximum Likelihood Decoding

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    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

    Throughput Enhancement and Power Optimization in NOMA-based Multiuser Multicast Systems

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    In recent years, Non-Orthogonal Multiple Access (NOMA) has emerged as a promising technique for enhancing the capacity and throughput of wireless communication systems. This thesis investigates the potential of NOMA in improving the performance of multiuser multicast systems, focusing on multibeam satellite communication systems in the forward link, throughput enhancement, and power optimization. We propose a novel framework that combines a NOMA scheme with multibeam architecture and frequency reuse in multicast transmission. The proposed framework enhances system throughput by optimizing power allocation. First, we present a comprehensive review of the principles and techniques related to NOMA and multibeam multicast systems, highlighting their unique challenges and potential benefits. Next, we introduce our proposed framework in 4-color frequency reuse satellite systems. In 4-color frequency reuse, each user receives signals from other co-channel beams. However, the level of isolation is such that the interbeam interference can be treated as background noise without significant performance degradation. This means that there is no collaboration between beams, and each beam can be isolated from the rest. Therefore, NOMA is considered in single-beam multicast satellite communication systems. The optimum power allocation to maximize the minimum fairness rate and sum-rate is derived for a given user clustering in a single beam. Moreover, an optimum user clustering is derived, which improves the system throughput. Next, we investigate our proposed framework in full frequency reuse satellite systems under perfect channel state information at the transmitter (CSIT). The proposed framework integrates the NOMA scheme in multicast multibeam architecture. Linear precoding techniques, such as zero-forcing (ZF) and minimum mean square error (MMSE), are used to cancel interbeam interference while NOMA is applied on a beam basis. NOMA and linear precoding are adopted for the proposed framework in multicast transmission. A low-complexity user scheduling is proposed to deal with the trade-offs between optimum user scheduling for linear precoding and the NOMA scheme. Moreover, a low-complexity linear precoding in multicast transmission is proposed based on unicast linear precoding methods and a mapper which deals with the lack of spatial degrees of freedom. To improve the performance of linear precoding, we present three mappers, where the proposed singular-value-decomposition (SVD) mapper demonstrates the best performance. To improve system throughput, power allocation should be optimized. In this thesis, we consider two objective functions: max-min fairness rate (MMF) and sum-rate. This thesis introduces a technique for addressing the non-convex MMF optimization issue in the proposed framework by employing auxiliary variables to convert it into a semi-definite programming problem, which can then be resolved using linear programming solvers. This thesis also suggests an approach to tackle the non-convex sum-rate maximization goal function in MB-MC-NOMA systems by constructing Lagrangian multipliers concerning the constraints. By employing quadratic transformations on the sum-of-ratios, the problem is restructured within an iterative sum-rate power optimization algorithm. This thesis considers a realistic scenario with imperfect CSIT. To combat the effect of imperfect CSIT in multibeam multicast satellite communication systems, a rate-splitting approach is proposed. An averaging rate (AR) framework for MMF rate and sum-rate optimization considering ICST is proposed. To render the formulated MMF and sum-rate problems convex, we utilize the Weighted Minimum Mean Square Error (WMMSE) method. We first derive a rate-WMMSE relationship and then, using this relationship along with a low-complexity solution based on Alternating Optimization (AO), we transform the problems into equivalent convex ones. To validate the effectiveness of our proposed frameworks, we conduct extensive simulations and comparisons with state-of-the-art schemes. The results demonstrate significant improvements in throughput and power efficiency, confirming the potential of NOMA-based multiuser multicast systems for future wireless communication networks. Finally, we discuss potential future research directions, including the integration of the proposed frameworks in the cellular networks, calculating the transmitter and receiver complexity of the proposed techniques, considering higher layers of RS. This thesis contributes to the ongoing development of next-generation wireless communication systems, paving the way for more efficient and reliable data transmission in multiuser multicast environments

    Distance Spectrum of Fixed-Rate Raptor Codes With Linear Random Precoders

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    Distance Spectrum of Fixed-Rate Raptor Codes with Linear Random Precoders

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    Raptor code ensembles with linear random outer codes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight distribution. The asymptotic growth rate analysis is then exploited to develop a necessary and sufficient condition under which the fixed-rate Raptor code ensemble exhibits a strictly positive typical minimum distance. The condition involves the rate of the outer code, the rate of the inner fixed-rate Luby Transform (LT) code and the LT code degree distribution. Additionally, it is shown that for ensembles fulfilling this condition, the minimum distance of a code randomly drawn from the ensemble has a linear growth with the block length. The analytical results can be used to make accurate predictions of the performance of finite length Raptor codes. These results are particularly useful for fixed-rate Raptor codes under maximum likelihood erasure decoding, whose performance is driven by their weight distribution
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