arXiv subjects

Gianluigi Liva

Publications and source records attributed to Gianluigi Liva.

At least 91 records · Page 5Linked to original sources

arXiv2017

On the Error Probability of Short Concatenated Polar and Cyclic Codes with Interleaving

In this paper, the analysis of the performance of the concatenation of a short polar code with an outer binary linear block code is addressed from a distance spectrum viewpoint. The analysis targets the case where an outer cyclic code is employed together with an inner systematic polar code. A concatenated code ensemble is introduced placing an interleaver at the input of the polar encoder. The introduced ensemble allows deriving bounds on the achievable error rates under maximum likelihood decoding, by applying the union bound to the (expurgated) average weight enumerators. The analysis suggests the need of careful optimization of the outer code, to attain low error floors.

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arXiv2016

Low-latency Ultra Reliable 5G Communications: Finite-Blocklength Bounds and Coding Schemes

Future autonomous systems require wireless connectivity able to support extremely stringent requirements on both latency and reliability. In this paper, we leverage recent developments in the field of finite-blocklength information theory to illustrate how to optimally design wireless systems in the presence of such stringent constraints. Focusing on a multi-antenna Rayleigh block-fading channel, we obtain bounds on the maximum number of bits that can be transmitted within given bandwidth, latency, and reliability constraints, using an orthogonal frequency-division multiplexing system similar to LTE. These bounds unveil the fundamental interplay between latency, bandwidth, rate, and reliability. Furthermore, they suggest how to optimally use the available spatial and frequency diversity. Finally, we use our bounds to benchmark the performance of an actual coding scheme involving the transmission of short packets.

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arXiv2016

Bounds on the Error Probability of Raptor Codes

In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn randomly from some ensemble of codes. The bound is shown to be tight by means of simulations. This bound provides a new insight into Raptor codes since it shows how Raptor codes can be analyzed similarly to a classical fixed-rate serial concatenation.

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arXiv2016

Code Design for Short Blocks: A Survey

The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem which is gaining relevance thanks to emerging applications in wireless communication networks. In this work, we review some of the most recent code constructions targeting the short block regime, and we compare then with both finite-length performance bounds and classical error correction coding schemes. We will see how it is possible to effectively approach the theoretical bounds, with different performance vs. decoding complexity trade-offs.

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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

Detection and Combining Techniques for Asynchronous Random Access with Time Diversity

Asynchronous random access (RA) protocols are particularly attractive for their simplicity and avoidance of tight synchronization requirements. Recent enhancements have shown that the use of successive interference cancellation (SIC) can largely boost the performance of these schemes. A further step forward in the performance can be attained when diversity combining techniques are applied. In order to enable combining, the detection and association of the packets to their transmitters has to be done prior to decoding. We present a solution to this problem, that articulates into two phases. Non-coherent soft-correlation as well as interference-aware soft-correlation are used for packet detection. We evaluate the detection capabilities of both solutions via numerical simulations. We also evaluate numerically the spectral efficiency achieved by the proposed approach, highlighting its benefits.

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arXiv2015

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

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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arXiv2015

Inactivation Decoding Analysis for LT Codes

We provide two analytical tools to model the inactivation decoding process of LT codes. First, a model is presented which derives the expected number of inactivations occurring in the decoding process of an LT code. This analysis is then extended allowing the derivation of the distribution of the number of inactivations. The accuracy of the method is verified by Monte Carlo simulations. The proposed analysis opens the door to the design of LT codes optimized for inactivation decoding.

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arXiv2015

Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access

In this paper, a random access scheme is introduced which relies on the combination of packet erasure correcting codes and successive interference cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph representation of the SIC process, resembling iterative decoding of generalized low-density parity-check codes over the erasure channel, is exploited to optimize the selection probabilities of the component erasure correcting codes via density evolution analysis. The capacity (in packets per slot) of the scheme is then analyzed in the context of the collision channel without feedback. Moreover, a capacity bound is developed and component code distributions tightly approaching the bound are derived.

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arXiv2015

On The Weight Distribution of Fixed-Rate Raptor Codes

In this paper Raptor code ensembles with linear random precodes 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.

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arXiv2015

Protograph-Based LDPC Code Design for Shaped Bit-Metric Decoding

A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels for the code design are used. The constructed codes for uniform inputs perform as good as the multi-edge type codes of Zhang and Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, codes of rates 2/3 and 5/6 with blocklength 64800 are designed, which operate within 0.63dB and 0.69dB of continuous AWGN capacity for a target frame error rate of 1e-3 at spectral efficiencies of 1.38 and 4.25 bits/channel use, respectively.

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arXiv2015

Protograph-Based LDPC Code Design for Bit-Metric Decoding

A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels are constructed and used for code design. The constructed codes perform as good as multi-edge type codes of Zhang and Kschischang (2013). For 64-ASK with probabilistic shaping, a blocklength 64800 code is constructed that operates within 0.69 dB of 0.5log(1+SNR) at a spectral efficiency of 4.2 bits/channel use and a frame error rate of 1e-3.

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arXiv2014

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.

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arXiv2014

The Throughput of Slotted Aloha with Diversity

In this paper, a simple variation of classical Slotted Aloha is introduced and analyzed. The enhancement relies on adding multiple receivers that gather different observations of the packets transmitted by a user population in one slot. For each observation, the packets transmitted in one slot are assumed to be subject to independent on-off fading, so that each of them is either completely faded, and then does not bring any power or interference at the receiver, or it arrives unfaded, and then may or may not, collide with other unfaded transmissions. With this model, a novel type of diversity is introduced to the conventional SA scheme, leading to relevant throughput gains already for moderate number of receivers. The analytical framework that we introduce allows to derive closed-form expression of both throughput and packet loss rate an arbitrary number of receivers, providing interesting hints on the key trade-offs that characterize the system. We then focus on the problem of having receivers forward the full set of collected packets to a final gateway using the minimum possible amount of resources, i.e., avoiding delivery of duplicate packets, without allowing any exchange of information among them. We derive what is the minimum amount of resources needed and propose a scheme based on random linear network coding that achieves asymptotically this bound without the need for the receivers to coordinate among them.

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arXiv2012

Spatially-Coupled Random Access on Graphs

In this paper we investigate the effect of spatial coupling applied to the recently-proposed coded slotted ALOHA (CSA) random access protocol. Thanks to the bridge between the graphical model describing the iterative interference cancelation process of CSA over the random access frame and the erasure recovery process of low-density parity-check (LDPC) codes over the binary erasure channel (BEC), we propose an access protocol which is inspired by the convolutional LDPC code construction. The proposed protocol exploits the terminations of its graphical model to achieve the spatial coupling effect, attaining performance close to the theoretical limits of CSA. As for the convolutional LDPC code case, large iterative decoding thresholds are obtained by simply increasing the density of the graph. We show that the threshold saturation effect takes place by defining a suitable counterpart of the maximum-a-posteriori decoding threshold of spatially-coupled LDPC code ensembles. In the asymptotic setting, the proposed scheme allows sustaining a traffic close to 1 [packets/slot].

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arXiv2012

Graph-Based Random Access for the Collision Channel without Feedback: Capacity Bound

A random access scheme for the collision channel without feedback is proposed. The scheme is based on erasure correcting codes for the recovery of packet segments that are lost in collisions, and on successive interference cancellation for resolving collisions. The proposed protocol achieves reliable communication in the asymptotic setting and attains capacities close to 1 [packets/slot]. A capacity bound as a function of the overall rate of the scheme is derived, and code distributions tightly approaching the bound developed.

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arXiv2011

On the Concatenation of Non-Binary Random Linear Fountain Codes with Maximum Distance Separable Codes

A novel fountain coding scheme has been introduced. The scheme consists of a parallel concatenation of a MDS block code with a LRFC code, both constructed over the same field, $F_q$. The performance of the concatenated fountain coding scheme has been analyzed through derivation of tight bounds on the probability of decoding failure as a function of the overhead. It has been shown how the concatenated scheme performs as well as LRFC codes in channels characterized by high erasure probabilities, whereas they provide failure probabilities lower by several orders of magnitude at moderate/low erasure probabilities.

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arXiv2011

On the Application of the Baum-Welch Algorithm for Modeling the Land Mobile Satellite Channel

Accurate channel models are of high importance for the design of upcoming mobile satellite systems. Nowadays most of the models for the LMSC are based on Markov chains and rely on measurement data, rather than on pure theoretical considerations. A key problem lies in the determination of the model parameters out of the observed data. In this work we face the issue of state identification of the underlying Markov model whose model parameters are a priori unknown. This can be seen as a HMM problem. For finding the ML estimates of such model parameters the BW algorithm is adapted to the context of channel modeling. Numerical results on test data sequences reveal the capabilities of the proposed algorithm. Results on real measurement data are finally presented.

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