On dispersion of compound DMCs

Code for a compound discrete memoryless channel (DMC) is required to have small probability of error regardless of which channel in the collection perturbs the codewords. Capacity of the compound DMC has been derived classically: it equals the maximum (over input distributions) of the minimal (over channels in the collection) mutual information. In this paper the expression for the channel dispersion of the compound DMC is derived under certain regularity assumptions on the channel. Interestingly, dispersion is found to depend on a subtle interaction between the channels encoded in the geometric arrangement of the gradients of their mutual informations. It is also shown that the third-order term need not be logarithmic (unlike single-state DMCs). By a natural equivalence with compound DMC, all results (dispersion and bounds) carry over verbatim to a common message broadcast channel.National Science Foundation (U.S.) (CAREER Award CCF-12-53205)National Science Foundation (U.S.). Center for Science of Information (Grant Agreement CCF-0939370

Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error probabilities for various problems are bounded above by a non-vanishing constant and the spotlight is shone on achievable coding rates as functions of the growing blocklengths. This represents the study of asymptotic estimates with non-vanishing error probabilities. In Part I, after reviewing the fundamentals of information theory, we discuss Strassen's seminal result for binary hypothesis testing where the type-I error probability is non-vanishing and the rate of decay of the type-II error probability with growing number of independent observations is characterized. In Part II, we use this basic hypothesis testing result to develop second- and sometimes, even third-order asymptotic expansions for point-to-point communication. Finally in Part III, we consider network information theory problems for which the second-order asymptotics are known. These problems include some classes of channels with random state, the multiple-encoder distributed lossless source coding (Slepian-Wolf) problem and special cases of the Gaussian interference and multiple-access channels. Finally, we discuss avenues for further research.Comment: Further comments welcom

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced by Polyanskiy for the Multiple Access Channel (MAC) with a fixed, known number of transmitters, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario where neither the transmitters nor the receiver know which transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or RAC. Scheduled feedback of a finite number of bits is used to synchronize the transmitters. The decoder is tasked with determining from the channel output the number of active transmitters ($k$) and their messages but not which transmitter sent which message. The decoding procedure occurs at a time $n_t$ depending on the decoder's estimate $t$ of the number of active transmitters, $k$, thereby achieving a rate that varies with the number of active transmitters. Single-bit feedback at each time $n_i, i \leq t$, enables all transmitters to determine the end of one coding epoch and the start of the next. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require $2^k - 1$ simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion.Comment: Presented at ISIT18', submitted to IEEE Transactions on Information Theor

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced for the Multiple Access Channel (MAC) with a fixed, known number of transmitters by Polyanskiy, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario in which neither the transmitters nor the receiver know which or how many transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or RAC. Limited feedback is used to ensure that the collection of active transmitters remains fixed during each epoch. The decoder is tasked with determining from the channel output the number of active transmitters (k) and their messages but not which transmitter sent which message. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require 2^k - 1 simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion

New techniques for analysis of organic pollutants in drinking water

An abstractor packing prepared by coating Chromosorb G AW/DMCS with copper(II) chloride was effective for removal of amines from gas-chromatographic streams, but it did not affect the chromatographic behavior of nonamine compounds. By using pre-columns packed with the abstractor packing, solventless chromatograms were obtained for samples in pyridine. A method was developed for determining haloforms in drinking water by sorption of the haloforms on columns packed with acetylated XAD-2. A pre-column of the abstractor packing was used to remove the pyridine solvent from the samples containing the haloforms concentrated from waters. Detection limits for the four chloro-, bromo- haloforms in a 100-ml water sample using an electron capture detector were below 1 ppB. Addition of ascorbic acid to chlorinated waters was effective for stopping the production of haloforms. Design of the inlet allowed samples to be introduced to the capillary column in a Tracor model 550 gas chromatograph with or without splitting of the carrier-gas stream. An exit splitter was implemented that carried the effluent from the capillary column to two detectors. The capillary-column system was applied to the analysis of trace components in complex mixtures. Small columns packed with Florisil were used to fractionate mixtures of organic compounds by gravity-flow liquid chromatography. Three fractions of organic compounds were collected from the Florisil columns. The recovery and elution behavior of many organic compounds was investigated. Organic compounds from fifteen waters were fractionated on Florisil

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. As in the model recently introduced by Polyanskiy for the Multiple Access Channel (MAC) with a fixed, known number of transmitters, the channel is assumed to be invariant to permutations on its inputs, and all active transmitters employ identical encoders. Unlike the Polyanskiy model, in the proposed scenario, neither the transmitters nor the receiver knows which transmitters are active. We refer to this agnostic communication setup as the Random Access Channel (RAC). Scheduled feedback of a finite number of bits is used to synchronize the transmitters. The decoder is tasked with determining from the channel output the number of active transmitters, k, and their messages but not which transmitter sent which message. The decoding procedure occurs at a time n_t depending on the decoder’s estimate, t, of the number of active transmitters, k, thereby achieving a rate that varies with the number of active transmitters. Single-bit feedback at each time n_i, i ≤ t, enables all transmitters to determine the end of one coding epoch and the start of the next. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require 2^k - 1 simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion

Hemin availability induces coordinated DNA methylation and gene expression changes in Porphyromonas gingivalis.

Periodontal disease is a chronic inflammatory disease in which the oral pathogen Porphyromonas gingivalis plays an important role. Porphyromonas gingivalis expresses virulence determinants in response to higher hemin concentrations, but the underlying regulatory processes remain unclear. Bacterial DNA methylation has the potential to fulfil this mechanistic role. We characterized the methylome of P. gingivalis, and compared its variation to transcriptome changes in response to hemin availability. Porphyromonas gingivalis W50 was grown in chemostat continuous culture with excess or limited hemin, prior to whole-methylome and transcriptome profiling using Nanopore and Illumina RNA-Seq. DNA methylation was quantified for Dam/Dcm motifs and all-context N6-methyladenine (6mA) and 5-methylcytosine (5mC). Of all 1,992 genes analyzed, 161 and 268 were respectively over- and under-expressed with excess hemin. Notably, we detected differential DNA methylation signatures for the Dam "GATC" motif and both all-context 6mA and 5mC in response to hemin availability. Joint analyses identified a subset of coordinated changes in gene expression, 6mA, and 5mC methylation that target genes involved in lactate utilization and ABC transporters. The results identify altered methylation and expression responses to hemin availability in P. gingivalis, with insights into mechanisms regulating its virulence in periodontal disease. IMPORTANCE DNA methylation has important roles in bacteria, including in the regulation of transcription. Porphyromonas gingivalis, an oral pathogen in periodontitis, exhibits well-established gene expression changes in response to hemin availability. However, the regulatory processes underlying these effects remain unknown. We profiled the novel P. gingivalis epigenome, and assessed epigenetic and transcriptome variation under limited and excess hemin conditions. As expected, multiple gene expression changes were detected in response to limited and excess hemin that reflect health and disease, respectively. Notably, we also detected differential DNA methylation signatures for the Dam "GATC" motif and both all-context 6mA and 5mC in response to hemin. Joint analyses identified coordinated changes in gene expression, 6mA, and 5mC methylation that target genes involved in lactate utilization and ABC transporters. The results identify novel regulatory processes underlying the mechanism of hemin regulated gene expression in P. gingivalis, with phenotypic impacts on its virulence in periodontal disease