Searcharxiv⌕ Search

arXiv subjects

Gianluigi Liva

Publications and source records attributed to Gianluigi Liva.

At least 55 records · Page 3Linked to original sources
arXiv2019

Symbol Message Passing Decoding of Nonbinary Low-Density Parity-Check Codes

We present a novel decoding algorithm for q-ary low-density parity-check codes, termed symbol message passing. The proposed algorithm can be seen as a generalization of Gallager B and the binary message passing algorithm by Lechner et al. to q-ary codes. We derive density evolution equations for the q-ary symmetric channel, compute thresholds for a number of regular low-density parity-check code ensembles, and verify those by Monte Carlo simulations of long channel codes. The proposed algorithm shows performance advantages with respect to an algorithm of comparable complexity from the literature.

cs.IT↗
arXiv2019

Binary Message Passing Decoding of Product-like Codes

We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to $0.29$ dB and $0.31$ dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.

cs.IT↗
arXiv2019

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

The performance and the decoding complexity of a novel coding scheme based on the concatenation of maximum distance separable (MDS) codes and linear random fountain codes are investigated. Differently from Raptor codes (which are based on a serial concatenation of a high-rate outer block code and an inner Luby-transform code), the proposed coding scheme can be seen as a parallel concatenation of a MDS code and a linear random fountain code, both operating on the same finite field. Upper and lower bounds on the decoding failure probability under maximum-likelihood (ML) decoding are developed. It is shown how, for example, the concatenation of a $(15,10)$ Reed-Solomon (RS) code and a linear random fountain code over a finite field of order $16$, $\mathbb {F}_{16}$, brings to a decoding failure probability $4$ orders of magnitude lower than the one of a linear random fountain code for the same receiver overhead in a channel with a erasure probability of $ε=5\cdot10^{-2}$. It is illustrated how the performance of the novel scheme approaches that of an idealized fountain code for higher-order fields and moderate erasure probabilities. An efficient decoding algorithm is developed for the case of a (generalized) RS code.

cs.IT↗
arXiv2019

Successive Cancellation List Decoding of Product Codes with Reed-Muller Component Codes

This letter proposes successive cancellation list (SCL) decoding of product codes with Reed--Muller (RM) component codes. SCL decoding relies on a product code description based on the $2\times 2$ Hadamard kernel, which enables interpreting the code as an RM subcode. The focus is on a class of product codes considered in wireless communication systems, based on single parity-check and extended Hamming component codes. For short product codes, it is shown that SCL decoding with a moderate list size performs as well as (and, sometimes, outperforms) belief propagation (BP) decoding. Furthermore, by concatenating a short product code with a high-rate outer code, SCL decoding outperforms BP decoding by up to $1.4$ dB.

cs.IT↗
arXiv2019

Short Non-Binary Low-Density Parity-Check Codes for Phase Noise Channels

This work considers the design of short non-binary low-density parity-check (LDPC) codes over finite fields of order m, for channels with phase noise. In particular, m-ary differential phase-shift keying (DPSK) modulated code symbols are transmitted over an additive white Gaussian noise (AWGN) channel with Wiener phase noise. At the receiver side, non-coherent detection takes place, with the help of a multi-symbol detection algorithm, followed by a non-binary decoding step. Both the detector and decoder operate on a joint factor graph. As a benchmark, finite length bounds and information rate expressions are computed and compared with the codeword error rate (CER) performance, as well as the iterative threshold of the obtained codes. As a result, performance within 1:2 dB from finite-length bounds is obtained, down to a CER of 1e-3.

cs.IT↗
arXiv2019

Efficient Error-Correcting Codes in the Short Blocklength Regime

The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we review some of the most promising code constructions targeting the short block regime, and we compare them with both finite-length performance bounds and classical error-correction coding schemes. The work addresses the use of both binary and high-order modulations over the additive white Gaussian noise channel. We will illustrate how to effectively approach the theoretical bounds with various performance versus decoding complexity tradeoffs.

cs.IT↗
arXiv2019

Multiple-Relay Slotted ALOHA: Performance Analysis and Bounds

Wireless random access protocols are attracting a revived research interest as a simple yet effective solution for machine-type communications. In the quest to improve reliability and spectral efficiency of such schemes, the use of multiple receivers has recently emerged as a promising option. We study the potential of this approach considering a population of users that transmit data packets following a simple slotted ALOHA policy to a set of non-cooperative receivers or relays (uplink phase). These, in turn, independently forward - part of - what decoded towards a collecting sink (downlink phase). For an on-off fading channel model, we provide exact expressions for uplink throughput and packet loss rate for an arbitrary number of relays, characterising the benefits of multi-receiver schemes. Moreover, a lower bound on the minimum amount of downlink resources needed to deliver all information collected on the uplink is provided. The bound is proven to be achievable via random linear coding when no constraints in terms of latency are set. We complement our study discussing a family of simple forwarding policies that require no packet-level coding, and optimising their performance based on the amount of available downlink resources. The behaviour of both random linear coding and simplified policies is also characterised when receivers are equipped with finite buffers, revealing non-trivial tradeoffs.

cs.IT↗
arXiv2019

From 5G to 6G: Has the Time for Modern Random Access Come?

This short paper proposes the use of modern random access for IoT applications in 6G. A short overview of recent advances in uncoordinated medium access is provided, highlighting the gains that can be achieved by leveraging smart protocol design intertwined with advanced signal processing techniques at the receiver. The authors' vision on the benefits such schemes can yield for beyond-5G systems is presented, with the aim to trigger further discussion.

eess.SP↗
arXiv2019

Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding

We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric. The proposed algorithm closes half of the gap between conventional iterative bounded distance decoding (iBDD) and turbo product decoding based on the Chase--Pyndiah algorithm, at the expense of some increase in complexity. Furthermore, the proposed algorithm entails only a limited increase in data flow compared to iBDD.

cs.IT↗
arXiv2019

A Lower Bound on the Error Exponent of Linear Block Codes over the Erasure Channel

A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities, when the ensemble weight spectral shape function tends to a negative value as the fractional codeword weight tends to zero. For these ensembles we can therefore lower bound the block-wise ML decoding threshold. Two examples are presented, namely, linear random parity-check codes and fixed-rate Raptor codes with linear random precoders. While for the former a full analytical solution is possible, for the latter we can lower bound the ML decoding threshold on the erasure channel by simply solving a 2 x 2 system of nonlinear equations.

cs.IT↗
arXiv2019

Low-Complexity Joint Channel Estimation and List Decoding of Short Codes

A pilot-assisted transmission (PAT) scheme is proposed for short blocklengths, where the pilots are used only to derive an initial channel estimate for the list construction step. The final decision of the message is obtained by applying a non-coherent decoding metric to the codewords composing the list. This allows one to use very few pilots, thus reducing the channel estimation overhead. The method is applied to an ordered statistics decoder for communication over a Rayleigh block-fading channel. Gains of up to $1.2$ dB as compared to traditional PAT schemes are demonstrated for short codes with QPSK signaling. The approach can be generalized to other list decoders, e.g., to list decoding of polar codes.

cs.IT↗
arXiv2018

Energy-Efficient Soft-Assisted Product Decoders

We implement a 1-Tb/s 0.63-pJ/bit soft-assisted product decoder in a 28-nm technology. The decoder uses one bit of soft information to improve its net coding gain by 0.2 dB, reaching 10.3-10.4 dB, which is similar to that of more complex hard-decision staircase decoders.

cs.IT↗
arXiv2018

Caching at the Edge with LT codes

We study the performance of caching schemes based on LT under peeling (iterative) decoding algorithm. We assume that users ask for downloading content to multiple cache-aided transmitters. Transmitters are connected through a backhaul link to a master node while no direct link exists between users and the master node. Each content is fragmented and coded with LT code. Cache placement at each transmitter is optimized such that transmissions over the backhaul link is minimized. We derive a closed form expression for the calculation of the backhaul transmission rate. We compare the performance of a caching scheme based on LT with respect to a caching scheme based on maximum distance separable codes. Finally, we show that caching with \acl{LT} codes behave as good as caching with maximum distance separable codes.

cs.IT↗
arXiv2018

Protograph-Based LDPC Code Design for Ternary Message Passing Decoding

A ternary message passing (TMP) decoding algorithm for low-density parity-check codes is developed. All messages exchanged between variable and check nodes have a ternary alphabet, and the variable nodes exploit soft information from the channel. A density evolution analysis is developed for unstructured and protograph-based ensembles. For unstructured ensembles the stability condition is derived. Optimized ensembles for TMP decoding show asymptotic gains of up to 0.6 dB with respect to ensembles optimized for binary message passing decoding. Finite length simulations of codes from TMP-optimized ensembles show gains of up to 0.5 dB under TMP compared to protograph-based codes designed for unquantized belief propagation decoding.

cs.IT↗
arXiv2018

A Droplet Approach Based on Raptor Codes for Distributed Computing With Straggling Servers

We propose a coded distributed computing scheme based on Raptor codes to address the straggler problem. In particular, we consider a scheme where each server computes intermediate values, referred to as droplets, that are either stored locally or sent over the network. Once enough droplets are collected, the computation can be completed. Compared to previous schemes in the literature, our proposed scheme achieves lower computational delay when the decoding time is taken into account.

cs.IT↗
arXiv2018

Bit-Metric Decoding of Non-Binary LDPC Codes with Probabilistic Amplitude Shaping

A new approach for combining non-binary low-density parity-check (NB-LDPC) codes with higher-order modulation and probabilistic amplitude shaping (PAS) is presented. Instead of symbol-metric decoding (SMD), a bit-metric decoder (BMD) is used so that matching the field order of the non-binary code to the constellation size is not needed, which increases the flexibility of the coding scheme. Information rates, density evolution thresholds and finite-length simulations show that the flexibility comes at no loss of performance if PAS is used.

cs.IT↗