Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding

A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially-coupled GLDPC codes with BCH component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution (DE).Comment: 22 pages, this version accepted to the IEEE Transactions on Information Theor

On The Analysis of Spatially-Coupled GLDPC Codes and The Weighted Min-Sum Algorithm

This dissertation studies methods to achieve reliable communication over unreliable channels. Iterative decoding algorithms for low-density parity-check (LDPC) codes and generalized LDPC (GLDPC) codes are analyzed. A new class of error-correcting codes to enhance the reliability of the communication for high-speed systems, such as optical communication systems, is proposed. The class of spatially-coupled GLDPC codes is studied, and a new iterative hard- decision decoding (HDD) algorithm for GLDPC codes is introduced. The main result is that the minimal redundancy allowed by Shannon’s Channel Coding Theorem can be achieved by using the new iterative HDD algorithm with spatially-coupled GLDPC codes. A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with iterative decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. To the best of our knowledge, this is the first system that can approach the channel capacity using iterative HDD. The optimality of a codeword returned by the weighted min-sum (WMS) algorithm, an iterative decoding algorithm which is widely used in practice, is studied as well. The attenuated max-product (AttMP) decoding and weighted min-sum (WMS) decoding for LDPC codes are analyzed. Applying the max-product (and belief- propagation) algorithms to loopy graphs are now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence and/or the optimality of converged solutions. This work presents an analysis of both AttMP decoding and WMS decoding for LDPC codes which guarantees convergence to a fixed point when a weight factor, β, is sufficiently small. It also shows that, if the fixed point satisfies some consistency conditions, then it must be both a linear-programming (LP) and maximum-likelihood (ML) decoding solution

A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions

Low-density parity-check (LDPC) convolutional codes (or spatially-coupled codes) were recently shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this spectacular performance is now called threshold saturation via spatial coupling. This new phenomenon is characterized by the belief-propagation threshold of the spatially-coupled ensemble increasing to an intrinsic noise threshold defined by the uncoupled system. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled scalar recursions. Our approach is based on constructing potential functions for both the coupled and uncoupled recursions. Our results actually show that the fixed point of the coupled recursion is essentially determined by the minimum of the uncoupled potential function and we refer to this phenomenon as Maxwell saturation. A variety of examples are considered including the density-evolution equations for: irregular LDPC codes on the BEC, irregular low-density generator matrix codes on the BEC, a class of generalized LDPC codes with BCH component codes, the joint iterative decoding of LDPC codes on intersymbol-interference channels with erasure noise, and the compressed sensing of random vectors with i.i.d. components.Comment: This article is an extended journal version of arXiv:1204.5703 and has now been accepted to the IEEE Transactions on Information Theory. This version adds additional explanation for some details and also corrects a number of small typo

Antimicrobial resistance among migrants in Europe: a systematic review and meta-analysis

BACKGROUND: Rates of antimicrobial resistance (AMR) are rising globally and there is concern that increased migration is contributing to the burden of antibiotic resistance in Europe. However, the effect of migration on the burden of AMR in Europe has not yet been comprehensively examined. Therefore, we did a systematic review and meta-analysis to identify and synthesise data for AMR carriage or infection in migrants to Europe to examine differences in patterns of AMR across migrant groups and in different settings. METHODS: For this systematic review and meta-analysis, we searched MEDLINE, Embase, PubMed, and Scopus with no language restrictions from Jan 1, 2000, to Jan 18, 2017, for primary data from observational studies reporting antibacterial resistance in common bacterial pathogens among migrants to 21 European Union-15 and European Economic Area countries. To be eligible for inclusion, studies had to report data on carriage or infection with laboratory-confirmed antibiotic-resistant organisms in migrant populations. We extracted data from eligible studies and assessed quality using piloted, standardised forms. We did not examine drug resistance in tuberculosis and excluded articles solely reporting on this parameter. We also excluded articles in which migrant status was determined by ethnicity, country of birth of participants' parents, or was not defined, and articles in which data were not disaggregated by migrant status. Outcomes were carriage of or infection with antibiotic-resistant organisms. We used random-effects models to calculate the pooled prevalence of each outcome. The study protocol is registered with PROSPERO, number CRD42016043681. FINDINGS: We identified 2274 articles, of which 23 observational studies reporting on antibiotic resistance in 2319 migrants were included. The pooled prevalence of any AMR carriage or AMR infection in migrants was 25·4% (95% CI 19·1-31·8; I2 =98%), including meticillin-resistant Staphylococcus aureus (7·8%, 4·8-10·7; I2 =92%) and antibiotic-resistant Gram-negative bacteria (27·2%, 17·6-36·8; I2 =94%). The pooled prevalence of any AMR carriage or infection was higher in refugees and asylum seekers (33·0%, 18·3-47·6; I2 =98%) than in other migrant groups (6·6%, 1·8-11·3; I2 =92%). The pooled prevalence of antibiotic-resistant organisms was slightly higher in high-migrant community settings (33·1%, 11·1-55·1; I2 =96%) than in migrants in hospitals (24·3%, 16·1-32·6; I2 =98%). We did not find evidence of high rates of transmission of AMR from migrant to host populations. INTERPRETATION: Migrants are exposed to conditions favouring the emergence of drug resistance during transit and in host countries in Europe. Increased antibiotic resistance among refugees and asylum seekers and in high-migrant community settings (such as refugee camps and detention facilities) highlights the need for improved living conditions, access to health care, and initiatives to facilitate detection of and appropriate high-quality treatment for antibiotic-resistant infections during transit and in host countries. Protocols for the prevention and control of infection and for antibiotic surveillance need to be integrated in all aspects of health care, which should be accessible for all migrant groups, and should target determinants of AMR before, during, and after migration. FUNDING: UK National Institute for Health Research Imperial Biomedical Research Centre, Imperial College Healthcare Charity, the Wellcome Trust, and UK National Institute for Health Research Health Protection Research Unit in Healthcare-associated Infections and Antimictobial Resistance at Imperial College London

Surgical site infection after gastrointestinal surgery in high-income, middle-income, and low-income countries: a prospective, international, multicentre cohort study

Background: Surgical site infection (SSI) is one of the most common infections associated with health care, but its importance as a global health priority is not fully understood. We quantified the burden of SSI after gastrointestinal surgery in countries in all parts of the world. Methods: This international, prospective, multicentre cohort study included consecutive patients undergoing elective or emergency gastrointestinal resection within 2-week time periods at any health-care facility in any country. Countries with participating centres were stratified into high-income, middle-income, and low-income groups according to the UN's Human Development Index (HDI). Data variables from the GlobalSurg 1 study and other studies that have been found to affect the likelihood of SSI were entered into risk adjustment models. The primary outcome measure was the 30-day SSI incidence (defined by US Centers for Disease Control and Prevention criteria for superficial and deep incisional SSI). Relationships with explanatory variables were examined using Bayesian multilevel logistic regression models. This trial is registered with ClinicalTrials.gov, number NCT02662231. Findings: Between Jan 4, 2016, and July 31, 2016, 13 265 records were submitted for analysis. 12 539 patients from 343 hospitals in 66 countries were included. 7339 (58·5%) patient were from high-HDI countries (193 hospitals in 30 countries), 3918 (31·2%) patients were from middle-HDI countries (82 hospitals in 18 countries), and 1282 (10·2%) patients were from low-HDI countries (68 hospitals in 18 countries). In total, 1538 (12·3%) patients had SSI within 30 days of surgery. The incidence of SSI varied between countries with high (691 [9·4%] of 7339 patients), middle (549 [14·0%] of 3918 patients), and low (298 [23·2%] of 1282) HDI (p < 0·001). The highest SSI incidence in each HDI group was after dirty surgery (102 [17·8%] of 574 patients in high-HDI countries; 74 [31·4%] of 236 patients in middle-HDI countries; 72 [39·8%] of 181 patients in low-HDI countries). Following risk factor adjustment, patients in low-HDI countries were at greatest risk of SSI (adjusted odds ratio 1·60, 95% credible interval 1·05–2·37; p=0·030). 132 (21·6%) of 610 patients with an SSI and a microbiology culture result had an infection that was resistant to the prophylactic antibiotic used. Resistant infections were detected in 49 (16·6%) of 295 patients in high-HDI countries, in 37 (19·8%) of 187 patients in middle-HDI countries, and in 46 (35·9%) of 128 patients in low-HDI countries (p < 0·001). Interpretation: Countries with a low HDI carry a disproportionately greater burden of SSI than countries with a middle or high HDI and might have higher rates of antibiotic resistance. In view of WHO recommendations on SSI prevention that highlight the absence of high-quality interventional research, urgent, pragmatic, randomised trials based in LMICs are needed to assess measures aiming to reduce this preventable complication