Irregular Product Codes

We introduce irregular product codes, a class of codes where each codeword is represented by a matrix and the entries in each row (column) of the matrix come from a component row (column) code. As opposed to standard product codes, we do not require that all component row codes nor all component column codes be the same. Relaxing this requirement can provide some additional attractive features such as allowing some regions of the codeword to be more error-resilient, providing a more refined spectrum of rates for finite lengths, and improved performance for some of these rates. We study these codes over erasure channels and prove that for any 0 < ε < 1, for many rate distributions on component row codes, there is a matching rate distribution on component column codes such that an irregular product code based on MDS codes with those rate distributions on the component codes has asymptotic rate 1 - ε and can decode on erasure channels having erasure probability <; ε (and having alphabet size equal to the alphabet size of the component MDS codes)

Generalized Codes on Graphs and Applications in Content Distribution

The contribution of this thesis is twofold. In the first part, we generalize and analyze two classes of error correcting codes: LDPC codes and product codes. We generalize graphical codes by considering checks being arbitrary codes instead of single parities. We analyze the performance of these codes under message passing decoding by using an extended density evolution over erasure channels. Further, we provide an optimal instance of these codes having rates arbitrarily close to the capacity of any binary symmetric channel where a belief propagation algorithm is used for decoding. The relation to other similar constructions is discussed as well. In a similar approach, we introduce irregular product codes, a class of codes where each codeword is represented by a matrix and the entries in each row (column) of the matrix come from a component row (column) code. Unlike product codes, we do not require that all component row and column codes be the same. This relaxation offers additional flexibility and features such as allowing some regions of the codeword to be more error-resilient, providing a more refined spectrum of rates for finite lengths, and improved performance for some of these rates. We study these codes over erasure channels and prove that for many rate distributions on component row codes, there is a matching rate distribution on component column codes such that an irregular product code based on MDS codes with those rate distributions on the component codes has an optimal asymptotic rate. In the second part we consider two novel applications of Raptor codes. Raptor codes are a class of fountain codes which present excellent performance, flexibility, and low decoding complexity over erasure channels. The data synchronization in an IP multicasting scenario involves reflecting changes from a content on a server to multiple clients efficiently. All these clients possess a slightly different copy of the content on the server. Existing methods are a direct extension of the point-to-point setting which is not necessarily optimal in terms of the total bandwidth usage in the multicast setting. We review this problem and its related information theoretic bounds. We propose and analyze an algorithm using Raptor codes which takes advantage of the multicast protocol to address this problem effectively. This method is close to optimal in terms of the amount of required transmitted information and the network usage. In another application, we show how to make satellite Digital Video Broadcasting resilient to signal jamming by distributing programs over multiple satellite links. However, leasing extra bandwidth on satellite links incurs supplementary cost to the broadcasting operator. In our solution we employ Raptor codes to make the bandwidth usage efficient and adaptive according to the link conditions. The proposed solution is fully compatible with the existing standards and infrastructure

Global mortality associated with 33 bacterial pathogens in 2019: a systematic analysis for the Global Burden of Disease Study 2019

Summary Background Reducing the burden of death due to infection is an urgent global public health priority. Previous studies have estimated the number of deaths associated with drug-resistant infections and sepsis and found that infections remain a leading cause of death globally. Understanding the global burden of common bacterial pathogens (both susceptible and resistant to antimicrobials) is essential to identify the greatest threats to public health. To our knowledge, this is the first study to present global comprehensive estimates of deaths associated with 33 bacterial pathogens across 11 major infectious syndromes. Methods We estimated deaths associated with 33 bacterial genera or species across 11 infectious syndromes in 2019 using methods from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, in addition to a subset of the input data described in the Global Burden of Antimicrobial Resistance 2019 study. This study included 343 million individual records or isolates covering 11 361 study-location-years. We used three modelling steps to estimate the number of deaths associated with each pathogen: deaths in which infection had a role, the fraction of deaths due to infection that are attributable to a given infectious syndrome, and the fraction of deaths due to an infectious syndrome that are attributable to a given pathogen. Estimates were produced for all ages and for males and females across 204 countries and territories in 2019. 95% uncertainty intervals (UIs) were calculated for final estimates of deaths and infections associated with the 33 bacterial pathogens following standard GBD methods by taking the 2·5th and 97·5th percentiles across 1000 posterior draws for each quantity of interest. Findings From an estimated 13·7 million (95% UI 10·9–17·1) infection-related deaths in 2019, there were 7·7 million deaths (5·7–10·2) associated with the 33 bacterial pathogens (both resistant and susceptible to antimicrobials) across the 11 infectious syndromes estimated in this study. We estimated deaths associated with the 33 bacterial pathogens to comprise 13·6% (10·2–18·1) of all global deaths and 56·2% (52·1–60·1) of all sepsis-related deaths in 2019. Five leading pathogens—Staphylococcus aureus, Escherichia coli, Streptococcus pneumoniae, Klebsiella pneumoniae, and Pseudomonas aeruginosa—were responsible for 54·9% (52·9–56·9) of deaths among the investigated bacteria. The deadliest infectious syndromes and pathogens varied by location and age. The age-standardised mortality rate associated with these bacterial pathogens was highest in the sub-Saharan Africa super-region, with 230 deaths (185–285) per 100 000 population, and lowest in the high-income super-region, with 52·2 deaths (37·4–71·5) per 100 000 population. S aureus was the leading bacterial cause of death in 135 countries and was also associated with the most deaths in individuals older than 15 years, globally. Among children younger than 5 years, S pneumoniae was the pathogen associated with the most deaths. In 2019, more than 6 million deaths occurred as a result of three bacterial infectious syndromes, with lower respiratory infections and bloodstream infections each causing more than 2 million deaths and peritoneal and intra-abdominal infections causing more than 1 million deaths. Interpretation The 33 bacterial pathogens that we investigated in this study are a substantial source of health loss globally, with considerable variation in their distribution across infectious syndromes and locations. Compared with GBD Level 3 underlying causes of death, deaths associated with these bacteria would rank as the second leading cause of death globally in 2019; hence, they should be considered an urgent priority for intervention within the global health community. Strategies to address the burden of bacterial infections include infection prevention, optimised use of antibiotics, improved capacity for microbiological analysis, vaccine development, and improved and more pervasive use of available vaccines. These estimates can be used to help set priorities for vaccine need, demand, and development

Adolescent transport and unintentional injuries: a systematic analysis using the Global Burden of Disease Study 2019

Background Globally, transport and unintentional injuries persist as leading preventable causes of mortality and morbidity for adolescents. We sought to report comprehensive trends in injury-related mortality and morbidity for adolescents aged 10-24 years during the past three decades. Methods Using the Global Burden of Disease, Injuries, and Risk Factors 2019 Study, we analysed mortality and disability-adjusted life-years (DALYs) attributed to transport and unintentional injuries for adolescents in 204 countries. Burden is reported in absolute numbers and age-standardised rates per 100 000 population by sex, age group (10-14, 15-19, and 20-24 years), and sociodemographic index (SDI) with 95% uncertainty intervals (UIs). We report percentage changes in deaths and DALYs between 1990 and 2019. Findings In 2019, 369 061 deaths (of which 214337 [58%] were transport related) and 31.1 million DALYs (of which 16.2 million [52%] were transport related) among adolescents aged 10-24 years were caused by transport and unintentional injuries combined. If compared with other causes, transport and unintentional injuries combined accounted for 25% of deaths and 14% of DALYs in 2019, and showed little improvement from 1990 when such injuries accounted for 26% of adolescent deaths and 17% of adolescent DALYs. Throughout adolescence, transport and unintentional injury fatality rates increased by age group. The unintentional injury burden was higher among males than females for all injury types, except for injuries related to fire, heat, and hot substances, or to adverse effects of medical treatment. From 1990 to 2019, global mortality rates declined by 34.4% (from 17.5 to 11.5 per 100 000) for transport injuries, and by 47.7% (from 15.9 to 8.3 per 100000) for unintentional injuries. However, in low-SDI nations the absolute number of deaths increased (by 80.5% to 42 774 for transport injuries and by 39.4% to 31 961 for unintentional injuries). In the high-SDI quintile in 2010-19, the rate per 100 000 of transport injury DALYs was reduced by 16.7%, from 838 in 2010 to 699 in 2019. This was a substantially slower pace of reduction compared with the 48.5% reduction between 1990 and 2010, from 1626 per 100 000 in 1990 to 838 per 100 000 in 2010. Between 2010 and 2019, the rate of unintentional injury DALYs per 100 000 also remained largely unchanged in high-SDI countries (555 in 2010 vs 554 in 2019; 0.2% reduction). The number and rate of adolescent deaths and DALYs owing to environmental heat and cold exposure increased for the high-SDI quintile during 2010-19. Interpretation As other causes of mortality are addressed, inadequate progress in reducing transport and unintentional injury mortality as a proportion of adolescent deaths becomes apparent. The relative shift in the burden of injury from high-SDI countries to low and low-middle-SDI countries necessitates focused action, including global donor, government, and industry investment in injury prevention. The persisting burden of DALYs related to transport and unintentional injuries indicates a need to prioritise innovative measures for the primary prevention of adolescent injury