Coding for Parallel Channels: Gallager Bounds for Binary Linear Codes with Applications to Repeat-Accumulate Codes and Variations

This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error probability are derived. These bounds are applied to various ensembles of turbo-like codes, focusing especially on repeat-accumulate codes and their recent variations which possess low encoding and decoding complexity and exhibit remarkable performance under iterative decoding. The framework of the second version of the Duman and Salehi (DS2) bounds is generalized to the case of parallel channels, along with the derivation of their optimized tilting measures. The connection between the generalized DS2 and the 1961 Gallager bounds, addressed by Divsalar and by Sason and Shamai for a single channel, is explored in the case of an arbitrary number of independent parallel channels. The generalization of the DS2 bound for parallel channels enables to re-derive specific bounds which were originally derived by Liu et al. as special cases of the Gallager bound. In the asymptotic case where we let the block length tend to infinity, the new bounds are used to obtain improved inner bounds on the attainable channel regions under ML decoding. The tightness of the new bounds for independent parallel channels is exemplified for structured ensembles of turbo-like codes. The improved bounds with their optimized tilting measures show, irrespectively of the block length of the codes, an improvement over the union bound and other previously reported bounds for independent parallel channels; this improvement is especially pronounced for moderate to large block lengths.Comment: Submitted to IEEE Trans. on Information Theory, June 2006 (57 pages, 9 figures

Capacity-achieving ensembles for the binary erasure channel with bounded complexity

We present two sequences of ensembles of non-systematic irregular repeat-accumulate codes which asymptotically (as their block length tends to infinity) achieve capacity on the binary erasure channel (BEC) with bounded complexity per information bit. This is in contrast to all previous constructions of capacity-achieving sequences of ensembles whose complexity grows at least like the log of the inverse of the gap (in rate) to capacity. The new bounded complexity result is achieved by puncturing bits, and allowing in this way a sufficient number of state nodes in the Tanner graph representing the codes. We also derive an information-theoretic lower bound on the decoding complexity of randomly punctured codes on graphs. The bound holds for every memoryless binary-input output-symmetric channel and is refined for the BEC.Comment: 47 pages, 9 figures. Submitted to IEEE Transactions on Information Theor

Quantum correlations of twophoton polarization states in the parametric down-conversion process

We consider correlation properties of twophoton polarization states in the parametric down-conversion process. In our description of polarization states we take into account the simultaneous presence of colored and white noise in the density matrix. Within the considered model we study the dependence of the von Neumann entropy on the noise amount in the system and derive the separability condition for the density matrix of twophoton polarization state, using Perec-Horodecki criterion and majorization criterion. Then the dependence of the Bell operator (in CHSH form) on noise is studied. As a result, we give a condition for determining the presence of quantum correlation states in experimental measurements of the Bell operator. Finally, we compare our calculations with experimental data [doi:10.1103/PhysRevA.73.062110] and give a noise amount estimation in the photon polarization state considered there.Comment: 10 pages, 7 figures; corrected typo

Distance Properties of Short LDPC Codes and their Impact on the BP, ML and Near-ML Decoding Performance

Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel are studied. Both random and structured LDPC codes are considered. In particular, the BP decoding is applied to the code parity-check matrices with an increasing number of redundant rows, and the convergence of the performance to that of the ML decoding is analyzed. A comparison of the simulated BP, ML, and near-ML performance with the improved theoretical bounds on the error probability based on the exact weight spectrum coefficients and the exact stopping size spectrum coefficients is presented. It is observed that decoding performance very close to the ML decoding performance can be achieved with a relatively small number of redundant rows for some codes, for both the BEC and the AWGN channels

Modulation of host cell processes by T3SS effectors

Two of the enteric Escherichia coli pathotypes-enteropathogenic E. coli (EPEC) and enterohaemorrhagic E. coli (EHEC)-have a conserved type 3 secretion system which is essential for virulence. The T3SS is used to translocate between 25 and 50 bacterial proteins directly into the host cytosol where they manipulate a variety of host cell processes to establish a successful infection. In this chapter, we discuss effectors from EPEC/EHEC in the context of the host proteins and processes that they target-the actin cytoskeleton, small guanosine triphosphatases and innate immune signalling pathways that regulate inflammation and cell death. Many of these translocated proteins have been extensively characterised, which has helped obtain insights into the mechanisms of pathogenesis of these bacteria and also understand the host pathways they target in more detail. With increasing knowledge of the positive and negative regulation of host signalling pathways by different effectors, a future challenge is to investigate how the specific effector repertoire of each strain cooperates over the course of an infection

Prevalence of Frailty in European Emergency Departments (FEED): an international flash mob study

Introduction Current emergency care systems are not optimized to respond to multiple and complex problems associated with frailty. Services may require reconfiguration to effectively deliver comprehensive frailty care, yet its prevalence and variation are poorly understood. This study primarily determined the prevalence of frailty among older people attending emergency care. Methods This cross-sectional study used a flash mob approach to collect observational European emergency care data over a 24-h period (04 July 2023). Sites were identified through the European Task Force for Geriatric Emergency Medicine collaboration and social media. Data were collected for all individuals aged 65 + who attended emergency care, and for all adults aged 18 + at a subset of sites. Variables included demographics, Clinical Frailty Scale (CFS), vital signs, and disposition. European and national frailty prevalence was determined with proportions with each CFS level and with dichotomized CFS 5 + (mild or more severe frailty). Results Sixty-two sites in fourteen European countries recruited five thousand seven hundred eighty-five individuals. 40% of 3479 older people had at least mild frailty, with countries ranging from 26 to 51%. They had median age 77 (IQR, 13) years and 53% were female. Across 22 sites observing all adult attenders, older people living with frailty comprised 14%. Conclusion 40% of older people using European emergency care had CFS 5 + . Frailty prevalence varied widely among European care systems. These differences likely reflected entrance selection and provide windows of opportunity for system configuration and workforce planning