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Alexandre Graell i Amat

Publications and source records attributed to Alexandre Graell i Amat.

At least 127 records · Page 7Linked to original sources
arXiv2017

Private Information Retrieval in Distributed Storage Systems Using an Arbitrary Linear Code

We propose an information-theoretic private information retrieval (PIR) scheme for distributed storage systems where data is stored using a linear systematic code of rate $R > 1/2$. The proposed scheme generalizes the PIR scheme for data stored using maximum distance separable codes recently proposed by Tajeddine and El Rouayheb for the scenario of a single spy node. We further propose an algorithm to optimize the communication price of privacy (cPoP) using the structure of the underlying linear code. As an example, we apply the proposed algorithm to several distributed storage codes, showing that the cPoP can be significantly reduced by exploiting the structure of the distributed storage code.

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arXiv2017

A Unified Ensemble of Concatenated Convolutional Codes

We introduce a unified ensemble for turbo-like codes (TCs) that contains the four main classes of TCs: parallel concatenated codes, serially concatenated codes, hybrid concatenated codes, and braided convolutional codes. We show that for each of the original classes of TCs, it is possible to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. We also derive the density evolution (DE) equations for this ensemble over the binary erasure channel. The thresholds obtained from the DE indicate that the TC ensembles from the unified ensemble have similar asymptotic behavior to the original TC ensembles.

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arXiv2017

Density Evolution for Deterministic Generalized Product Codes on the Binary Erasure Channel at High Rates

Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed to randomized code ensembles) and analyze the asymptotic performance over the binary erasure channel under iterative decoding. Our code construction encompasses several classes of GPCs previously proposed in the literature, such as irregular PCs, block-wise braided codes, and staircase codes. It is assumed that the component codes can correct a fixed number of erasures and that the length of each component code tends to infinity. We show that this setup is equivalent to studying the behavior of a peeling algorithm applied to a sparse inhomogeneous random graph. Using a convergence result for these graphs, we derive the density evolution equations that characterize the asymptotic decoding performance. As an application, we discuss the design of irregular GPCs employing a mixture of component codes with different erasure-correcting capabilities.

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arXiv2017

MDS-Coded Distributed Caching for Low Delay Wireless Content Delivery

We investigate the use of maximum distance separable (MDS) codes to cache popular content to reduce the download delay of wireless content delivery. In particular, we consider a cellular system where devices roam in an out of a cell according to a Poisson random process. Popular content is cached in a limited number of the mobile devices using an MDS code and can be downloaded from the mobile devices using device-to-device communication. We derive an analytical expression for the delay incurred in downloading content from the wireless network and show that distributed caching using MDS codes can dramatically reduce the download delay with respect to the scenario where content is always downloaded from the base station and to the case of uncoded distributed caching.

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arXiv2016

On Frame Asynchronous Coded Slotted ALOHA: Asymptotic, Finite Length, and Delay Analysis

We consider a frame asynchronous coded slotted ALOHA (FA-CSA) system for uncoordinated multiple access, where users join the system on a slot-by-slot basis according to a Poisson random process and, in contrast to standard frame synchronous CSA (FS-CSA), users are not frame-synchronized. We analyze the performance of FA-CSA in terms of packet loss rate and delay. In particular, we derive the (approximate) density evolution that characterizes the asymptotic performance of FA-CSA when the frame length goes to infinity. We show that, if the receiver can monitor the system before anyone starts transmitting, a boundary effect similar to that of spatially-coupled codes occurs, which greatly improves the iterative decoding threshold. Furthermore, we derive tight approximations of the error floor (EF) for the finite frame length regime, based on the probability of occurrence of the most frequent stopping sets. We show that, in general, FA-CSA provides better performance in both the EF and waterfall regions as compared to FS-CSA. Moreover, FA-CSA exhibits better delay properties than FS-CSA.

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arXiv2016

Distributed Storage in Mobile Wireless Networks with Device-to-Device Communication

We consider the use of distributed storage (DS) to reduce the communication cost of content delivery in wireless networks. Content is stored (cached) in a number of mobile devices using an erasure correcting code. Users retrieve content from other devices using device-to-device communication or from the base station (BS), at the expense of higher communication cost. We address the repair problem when a device storing data leaves the cell. We introduce a repair scheduling where repair is performed periodically and derive analytical expressions for the overall communication cost of content download and data repair as a function of the repair interval. The derived expressions are then used to evaluate the communication cost entailed by DS using several erasure correcting codes. Our results show that DS can reduce the communication cost with respect to the case where content is downloaded only from the BS, provided that repairs are performed frequently enough. If devices storing content arrive to the cell, the communication cost using DS is further reduced and, for large enough arrival rate, it is always beneficial. Interestingly, we show that MDS codes, which do not perform well for classical DS, can yield a low overall communication cost in wireless DS.

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arXiv2016

Unequal Error Protection in Coded Slotted ALOHA

We analyze the performance of coded slotted ALOHA systems for a scenario where users have different error protection requirements and correspondingly can be divided into user classes. The main goal is to design the system so that the requirements for each class are satisfied. To that end, we derive analytical error floor approximations of the packet loss rate for each class in the finite frame length regime, as well as the density evolution in the asymptotic case. Based on this analysis, we propose a heuristic approach for the optimization of the degree distributions to provide the required unequal error protection. In addition, we analyze the decoding delay for users in different classes and show that better protected users experience a smaller average decoding delay.

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arXiv2016

MDS-Coded Distributed Storage for Low Delay Wireless Content Delivery

We address the use of maximum distance separable (MDS) codes for distributed storage (DS) to enable efficient content delivery in wireless networks. Content is stored in a number of the mobile devices and can be retrieved from them using device-to-device communication or, alternatively, from the base station (BS). We derive an analytical expression for the download delay in the hypothesis that the reliability state of the network is periodically restored. Our analysis shows that MDS-coded DS can dramatically reduce the download time with respect to the reference scenario where content is always downloaded from the BS.

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arXiv2016

Finite Length Weight Enumerator Analysis of Braided Convolutional Codes

Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes (SC-TCs) with excellent belief propagation (BP) thresholds. In this paper, we analyze the performance of BCCs in the finite block-length regime. We derive the average weight enumerator function (WEF) and compute the union bound on the performance for the uncoupled BCC ensemble. Our results suggest that the union bound is affected by poor distance properties of a small fraction of codes. By computing the union bound for the expurgated ensemble, we show that the floor improves substantially and very low error rates can be achieved for moderate permutation sizes. Based on the WEF, we also obtain a bound on the minimum distance which indicates that it grows linearly with the permutation size. Finally, we show that the estimated error floor for the uncoupled BCC ensemble is also valid for the coupled ensemble by proving that the minimum distance of the coupled ensemble is lower bounded by the minimum distance of the uncoupled ensemble.

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arXiv2016

Density Evolution for Deterministic Generalized Product Codes with Higher-Order Modulation

Generalized product codes (GPCs) are extensions of product codes (PCs) where coded bits are protected by two component codes but not necessarily arranged in a rectangular array. It has recently been shown that there exists a large class of deterministic GPCs (including, e.g., irregular PCs, half-product codes, staircase codes, and certain braided codes) for which the asymptotic performance under iterative bounded-distance decoding over the binary erasure channel (BEC) can be rigorously characterized in terms of a density evolution analysis. In this paper, the analysis is extended to the case where transmission takes place over parallel BECs with different erasure probabilities. We use this model to predict the code performance in a coded modulation setup with higher-order signal constellations. We also discuss the design of the bit mapper that determines the allocation of the coded bits to the modulation bits of the signal constellation.

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arXiv2016

Asymptotic and Finite Frame Length Analysis of Frame Asynchronous Coded Slotted ALOHA

We consider a frame-asynchronous coded slotted ALOHA (FA-CSA) system where users become active according to a Poisson random process. In contrast to standard frame-synchronous CSA (FS-CSA), users transmit a first replica of their message in the slot following their activation and other replicas uniformly at random in a number of subsequent slots. We derive the (approximate) density evolution that characterizes the asymptotic performance of FA-CSA when the frame length goes to infinity. We show that, if users can monitor the system before they start transmitting, a boundary-effect similar to that of spatially-coupled codes occurs, which greatly improves the decoding threshold as compared to FS-CSA. We also derive analytical approximations of the error floor (EF) in the finite frame length regime. We show that FA-CSA yields in general lower EF, better performance in the waterfall region, and lower average delay, as compared to FS-CSA.

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arXiv2016

Secure Repairable Fountain Codes

In this letter, we provide the construction of repairable fountain codes (RFCs) for distributed storage systems that are information-theoretically secure against an eavesdropper that has access to the data stored in a subset of the storage nodes and the data downloaded to repair an additional subset of storage nodes. The security is achieved by adding random symbols to the message, which is then encoded by the concatenation of a Gabidulin code and an RFC. We compare the achievable code rates of the proposed codes with those of secure minimum storage regenerating codes and secure locally repairable codes.

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arXiv2016

Broadcast Coded Slotted ALOHA: A Finite Frame Length Analysis

We propose an uncoordinated medium access control (MAC) protocol, called all-to-all broadcast coded slotted ALOHA (B-CSA) for reliable all-to-all broadcast with strict latency constraints. In B-CSA, each user acts as both transmitter and receiver in a half-duplex mode. The half-duplex mode gives rise to a double unequal error protection (DUEP) phenomenon: the more a user repeats its packet, the higher the probability that this packet is decoded by other users, but the lower the probability for this user to decode packets from others. We analyze the performance of B-CSA over the packet erasure channel for a finite frame length. In particular, we provide a general analysis of stopping sets for B-CSA and derive an analytical approximation of the performance in the error floor (EF) region, which captures the DUEP feature of B-CSA. Simulation results reveal that the proposed approximation predicts very well the performance of B-CSA in the EF region. Finally, we consider the application of B-CSA to vehicular communications and compare its performance with that of carrier sense multiple access (CSMA), the current MAC protocol in vehicular networks. The results show that B-CSA is able to support a much larger number of users than CSMA with the same reliability.

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arXiv2016

Deterministic and Ensemble-Based Spatially-Coupled Product Codes

Several authors have proposed spatially-coupled (or convolutional-like) variants of product codes (PCs). In this paper, we focus on a parametrized family of generalized PCs that recovers some of these codes (e.g., staircase and block-wise braided codes) as special cases and study the iterative decoding performance over the binary erasure channel. Even though our code construction is deterministic (and not based on a randomized ensemble), we show that it is still possible to rigorously derive the density evolution (DE) equations that govern the asymptotic performance. The obtained DE equations are then compared to those for a related spatially-coupled PC ensemble. In particular, we show that there exists a family of (deterministic) braided codes that follows the same DE equation as the ensemble, for any spatial length and coupling width.

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arXiv2016

Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel

We analyze the asymptotic performance of nonbinary spatially-coupled low-density parity-check (SC-LDPC) code ensembles defined over the general linear group on the binary erasure channel. In particular, we prove threshold saturation of belief propagation decoding to the so called potential threshold, using the proof technique based on potential functions introduced by Yedla \textit{et al.}, assuming that the potential function exists. We rewrite the density evolution of nonbinary SC-LDPC codes in an equivalent vector recursion form which is suited for the use of the potential function. We then discuss the existence of the potential function for the general case of vector recursions defined by multivariate polynomials, and give a method to construct it. We define a potential function in a slightly more general form than one by Yedla \textit{et al.}, in order to make the technique based on potential functions applicable to the case of nonbinary LDPC codes. We show that the potential function exists if a solution to a carefully designed system of linear equations exists. Furthermore, we show numerically the existence of a solution to the system of linear equations for a large number of nonbinary LDPC code ensembles, which allows us to define their potential function and thus prove threshold saturation.

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arXiv2016

On the Information Loss of the Max-Log Approximation in BICM Systems

We present a comprehensive study of the information rate loss of the max-log approximation for $M$-ary pulse-amplitude modulation (PAM) in a bit-interleaved coded modulation (BICM) system. It is widely assumed that the calculation of L-values using the max-log approximation leads to an information loss. We prove that this assumption is correct for all $M$-PAM constellations and labelings with the exception of a symmetric 4-PAM constellation labeled with a Gray code. We also show that for max-log L-values, the BICM generalized mutual information (GMI), which is an achievable rate for a standard BICM decoder, is too pessimistic. In particular, it is proved that the so-called "harmonized" GMI, which can be seen as the sum of bit-level GMIs, is achievable without any modifications to the decoder. We then study how bit-level channel symmetrization and mixing affect the mutual information (MI) and the GMI for max-log L-values. Our results show that these operations, which are often used when analyzing BICM systems, preserve the GMI. However, this is not necessarily the case when the MI is considered. Necessary and sufficient conditions under which these operations preserve the MI are provided.

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arXiv2015

A Family of Erasure Correcting Codes with Low Repair Bandwidth and Low Repair Complexity

We present the construction of a new family of erasure correcting codes for distributed storage that yield low repair bandwidth and low repair complexity. The construction is based on two classes of parity symbols. The primary goal of the first class of symbols is to provide good erasure correcting capability, while the second class facilitates node repair, reducing the repair bandwidth and the repair complexity. We compare the proposed codes with other codes proposed in the literature.

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