On the Design of a Novel Joint Network-Channel Coding Scheme for the Multiple Access Relay Channel

This paper proposes a novel joint non-binary network-channel code for the Time-Division Decode-and-Forward Multiple Access Relay Channel (TD-DF-MARC), where the relay linearly combines -- over a non-binary finite field -- the coded sequences from the source nodes. A method based on an EXIT chart analysis is derived for selecting the best coefficients of the linear combination. Moreover, it is shown that for different setups of the system, different coefficients should be chosen in order to improve the performance. This conclusion contrasts with previous works where a random selection was considered. Monte Carlo simulations show that the proposed scheme outperforms, in terms of its gap to the outage probabilities, the previously published joint network-channel coding approaches. Besides, this gain is achieved by using very short-length codewords, which makes the scheme particularly attractive for low-latency applications.Comment: 28 pages, 9 figures; Submitted to IEEE Journal on Selected Areas in Communications - Special Issue on Theories and Methods for Advanced Wireless Relays, 201

The serial harness interacting with a wall

The serial harnesses introduced by Hammersley describe the motion of a hypersurface of dimension d embedded in a space of dimension $d+1$. The height assigned to each site i of Z^d is updated by taking a weighted average of the heights of some of the neighbors of i plus a ``noise'' (a centered random variable). The surface interacts by exclusion with a ``wall'' located at level zero: the updated heights are not allowed to go below zero. We show that for any distribution of the noise variables and in all dimensions, the surface delocalizes. This phenomenon is related to the so called ``entropic repulsion''. For some classes of noise distributions, characterized by their tail, we give explicit bounds on the speed of the repulsion.Comment: 18 pages. Version almost identical to the one published in SP

On Secure Transmission over Parallel Relay Eavesdropper Channel

We study a four terminal parallel relay-eavesdropper channel which consists of multiple independent relay-eavesdropper channels as subchannels. For the discrete memoryless case, we establish inner and outer bounds on the rate-equivocation region. For each subchannel, secure transmission is obtained through one of the two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. The inner bound allows relay mode selection. For the Gaussian model we establish lower and upper bounds on the perfect secrecy rate. We show that the bounds meet in some special cases, including when the relay does not hear the source. We illustrate the analytical results through some numerical examples.Comment: 8 pages, Presented at the Forty-Eighth Annual Allerton Conference on Communication, Control, and Computing, September 29 - October 1, 2010, Monticello, IL, US

The microaerophilic microbiota of de-novo paediatric inflammatory bowel disease: the BISCUIT study

<p>Introduction: Children presenting for the first time with inflammatory bowel disease (IBD) offer a unique opportunity to study aetiological agents before the confounders of treatment. Microaerophilic bacteria can exploit the ecological niche of the intestinal epithelium; Helicobacter and Campylobacter are previously implicated in IBD pathogenesis. We set out to study these and other microaerophilic bacteria in de-novo paediatric IBD.</p> <p>Patients and Methods: 100 children undergoing colonoscopy were recruited including 44 treatment naïve de-novo IBD patients and 42 with normal colons. Colonic biopsies were subjected to microaerophilic culture with Gram-negative isolates then identified by sequencing. Biopsies were also PCR screened for the specific microaerophilic bacterial groups: Helicobacteraceae, Campylobacteraceae and Sutterella wadsworthensis.</p> <p>Results: 129 Gram-negative microaerophilic bacterial isolates were identified from 10 genera. The most frequently cultured was S. wadsworthensis (32 distinct isolates). Unusual Campylobacter were isolated from 8 subjects (including 3 C. concisus, 1 C. curvus, 1 C. lari, 1 C. rectus, 3 C. showae). No Helicobacter were cultured. When comparing IBD vs. normal colon control by PCR the prevalence figures were not significantly different (Helicobacter 11% vs. 12%, p = 1.00; Campylobacter 75% vs. 76%, p = 1.00; S. wadsworthensis 82% vs. 71%, p = 0.312).</p> <p>Conclusions: This study offers a comprehensive overview of the microaerophilic microbiota of the paediatric colon including at IBD onset. Campylobacter appear to be surprisingly common, are not more strongly associated with IBD and can be isolated from around 8% of paediatric colonic biopsies. S. wadsworthensis appears to be a common commensal. Helicobacter species are relatively rare in the paediatric colon.</p&gt

Densities of primes and realization of local extensions

In this paper we introduce new densities on the set of primes of a number field. If $K/K_0$ is a Galois extension of number fields, we associate to any element $x \in {\rm Gal}_{K/K_0}$ a density $\delta_{K/K_0,x}$ on primes of $K$. In particular, the density associated to $x = 1$ is the usual Dirichlet density on $K$. After establishing some properties of these densities, we use them to show that the maximal solvable extension of a number field unramified outside an almost Chebotarev set realize the maximal local extension at each prime lying outside this set.Comment: 19 pages; the main theorem appears now in a slightly generalized version compared to v1. A section recalling stable sets is added. Several small corrections are mad

Computationally Tractable Algorithms for Finding a Subset of Non-defective Items from a Large Population

In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main goal of a "non-defective subset recovery" algorithm is to identify a "subset" of non-defective items given the test outcomes. In this paper, we present a suite of computationally efficient and analytically tractable non-defective subset recovery algorithms. By analyzing the probability of error of the algorithms, we obtain bounds on the number of tests required for non-defective subset recovery with arbitrarily small probability of error. Our analysis accounts for the impact of both the additive noise (false positives) and dilution noise (false negatives). By comparing with the information theoretic lower bounds, we show that the upper bounds on the number of tests are order-wise tight up to a $\log^2K$ factor, where $K$ is the number of defective items. We also provide simulation results that compare the relative performance of the different algorithms and provide further insights into their practical utility. The proposed algorithms significantly outperform the straightforward approaches of testing items one-by-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate.Comment: In this revision: Unified some proofs and reorganized the paper, corrected a small mistake in one of the proofs, added more reference