Recommendations for Face Coverings While Exercising During the COVID-19 Pandemic

In an effort to reduce transmission and number of infections of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2 or COVID-19) virus, governments and official bodies around the world have produced guidelines on the use of face masks and face coverings. While there is a growing body of recommendations for healthcare professionals and the wider population to use facial protection in “enclosed spaces” where minimal distancing from other individuals is not possible, there is a dearth of clear guidelines for individuals undertaking exercise and sporting activity. The present viewpoint aims to propose recommendations for face coverings while exercising during the COVID-19 pandemic that consider physical distancing, the environment, the density of active cases associated with the specific sports activity, and the practical use of face coverings in order to reduce potential viral transmission. Recommendations are provided on the basis of very limited available evidence in conjunction with the extensive collective clinical experience of the authors and acknowledging the need to consider the likelihood of the presence of the SARS-CoV-2 in the general population. We recommend that face coverings should be used in any environment considered to be of a high or moderate transmission risk, where tolerated and after individual risk assessment. In addition, as national caseloads fluctuate, individual sporting bodies should consider up to date guidance on the use of face coverings during sport and exercise, alongside other preventative measures

Analysis of serial concatenation schemes for non-binary modulations

International audienc

ML performances of serial turbo codes do not concentrate!

In this paper we investigate the typical behaviour of minimum distance and ML word error probability of a serial turbo concatenation with random interleaver, when the interleaver length N goes to infinity. Our main result shows that the word error probability P(e) goes to zero subexponentially in N with probability one. While it is known that 10glE[P(e)]/logN converges to a constant, we prove that with probability one the sequence 10g(-log(P(e)))/logN approaches an interval [α, β] C (0 ,1 ), thus showing that the expected error rate is dominated by an asymptotically negligible fraction of bad interleavers. Our analysis is based on precise estimations of the minimum distance distribution

The performance of serial turbo codes does not concentrate

Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are an- alyzed. It is shown that, for a fraction of interleavers approaching one as the block-length grows large, the minimum distance of se- rial turbo codes grows as a positive power of their block-length, while their error probability decreases exponentially fast in some positive power of their block-length, on sufficiently good memory- less channels. Such a typical code behavior contrasts the perfor- mance of the average serial turbo code, whose error probability is dominated by an asymptotically negligible fraction of poorly per- forming interleavers, and decays only as a negative power of the block-length. The analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code, whose scaling law is shown to depend both on the free distance of its outer constituent encoder, which determines the exponent of its sub-linear growth in the block-length, and on the effective free distance of its inner constituent encoder. The latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two, and appears as a linear scaling factor for the minimum distance of the typical serial turbo code. Hence, despite the lack of concentration of the maximum likeli- hood error probability around its expected value, the main de- sign parameters suggested by the average-code analysis turn out to characterize also the performance of the typical serial turbo code. By showing for the first time that the typical serial turbo code’s minimum distance scales linearly in the effective free distance of the inner constituent encoder, the presented results generalize, and improve upon, the probabilistic bounds of Kahale and Urbanke, as well as the deterministic upper bound of Bazzi, Mahdian, and Spielman, where only the dependence on the outer encoder’s free distance was proved

Staircase and other structured linear-time encodable LDPC codes: analysis and design

We consider a family of codes which can be seen both as a special kind of serial turbo codes and as LDPC codes having a parity check matrix which is partly random and partly structured. These codes are linear-time encodable, thanks to the turbo structure, and can be decoded as LDPC codes. We provide an ensemble analysis for the waterfall region, on the line of classical results for serial turbo codes, and we And some design parameters

Average ML Asymptotic Performances of Different Serial Turbo Ensembles

International audienc

The performance of serial turbo codes does not concentrate

Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are an- alyzed. It is shown that, for a fraction of interleavers approaching one as the block-length grows large, the minimum distance of se- rial turbo codes grows as a positive power of their block-length, while their error probability decreases exponentially fast in some positive power of their block-length, on sufficiently good memory- less channels. Such a typical code behavior contrasts the perfor- mance of the average serial turbo code, whose error probability is dominated by an asymptotically negligible fraction of poorly per- forming interleavers, and decays only as a negative power of the block-length. The analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code, whose scaling law is shown to depend both on the free distance of its outer constituent encoder, which determines the exponent of its sub-linear growth in the block-length, and on the effective free distance of its inner constituent encoder. The latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two, and appears as a linear scaling factor for the minimum distance of the typical serial turbo code. Hence, despite the lack of concentration of the maximum likeli- hood error probability around its expected value, the main de- sign parameters suggested by the average-code analysis turn out to characterize also the performance of the typical serial turbo code. By showing for the first time that the typical serial turbo code’s minimum distance scales linearly in the effective free distance of the inner constituent encoder, the presented results generalize, and improve upon, the probabilistic bounds of Kahale and Urbanke, as well as the deterministic upper bound of Bazzi, Mahdian, and Spielman, where only the dependence on the outer encoder’s free distance was proved