Duality of Channel Encoding and Decoding - Part I: Rate-1 Binary Convolutional Codes

In this paper, we revisit the forward, backward and bidirectional Bahl-Cocke-Jelinek-Raviv (BCJR) soft-input soft-output (SISO) maximum a posteriori probability (MAP) decoding process of rate-1 binary convolutional codes. From this we establish some interesting explicit relationships between encoding and decoding of rate-1 convolutional codes. We observe that the forward and backward BCJR SISO MAP decoders can be simply represented by their dual SISO channel encoders using shift registers in the complex number field. Similarly, the bidirectional MAP decoding can be implemented by linearly combining the shift register contents of the dual SISO encoders of the respective forward and backward decoders. The dual encoder structures for various recursive and non-recursive rate-1 convolutional codes are derived.Comment: 32 pages, 20 figures, to appear in ET

Federal Aviation Administration's approach to engine rotor integrity

Sections of the U.S. Airworthiness Standards which contribute to rotor integrity are explored. Reports published under NASA's Rotor Burst Protection program are included in current FAA studies to determine the weight penalty for two different levels of increased containment, and the penalty associated with protecting critical structure and systems, the passenger cabin, and the flight deck by strategic location of armor shields or deflector plates. Findings of the two studies will be used to propose revisions to regulations to reduce uncontained rotor failures

Minimal realizations of linear systems: The "shortest basis" approach

Given a controllable discrete-time linear system C, a shortest basis for C is a set of linearly independent generators for C with the least possible lengths. A basis B is a shortest basis if and only if it has the predictable span property (i.e., has the predictable delay and degree properties, and is non-catastrophic), or alternatively if and only if it has the subsystem basis property (for any interval J, the generators in B whose span is in J is a basis for the subsystem C_J). The dimensions of the minimal state spaces and minimal transition spaces of C are simply the numbers of generators in a shortest basis B that are active at any given state or symbol time, respectively. A minimal linear realization for C in controller canonical form follows directly from a shortest basis for C, and a minimal linear realization for C in observer canonical form follows directly from a shortest basis for the orthogonal system C^\perp. This approach seems conceptually simpler than that of classical minimal realization theory.Comment: 20 pages. Final version, to appear in special issue of IEEE Transactions on Information Theory on "Facets of coding theory: From algorithms to networks," dedicated to Ralf Koette

MacWilliams Identities for Terminated Convolutional Codes

Shearer and McEliece [1977] showed that there is no MacWilliams identity for the free distance spectra of orthogonal linear convolutional codes. We show that on the other hand there does exist a MacWilliams identity between the generating functions of the weight distributions per unit time of a linear convolutional code C and its orthogonal code C^\perp, and that this distribution is as useful as the free distance spectrum for estimating code performance. These observations are similar to those made recently by Bocharova, Hug, Johannesson and Kudryashov; however, we focus on terminating by tail-biting rather than by truncation.Comment: 5 pages; accepted for 2010 IEEE International Symposium on Information Theory, Austin, TX, June 13-1

The Microbial Ecology of Bacterial Vaginosis: A Fine Scale Resolution Metagenomic Analysis

The vaginal microbiota play an important protective role in maintaining the health of women. Disruption of the mutualistic relationship that exists between bacterial communities in the vagina and their hosts can lead to bacterial vaginosis (BV), a condition in which lactic acid producing bacteria are supplanted by a diverse array of strictly anaerobic bacteria. BV has been shown to be an independent risk factor for adverse outcomes including preterm delivery and low infant birth weight, acquisition of sexually transmitted infections and HIV, and development of pelvic inflammatory disease. National surveys indicate the prevalence of BV among U.S. women is 29.2%, and yet, despite considerable effort, the etiology of BV remains unknown. Moreover, there are no broadly effective therapies for the treatment of BV, and reoccurrence is common. In the proposed research we will test the overarching hypothesis that vaginal microbial community dynamics and activities are indicators of risk to BV. To do this, we propose to conduct a high resolution prospective study in which samples collected daily from 200 reproductive-age women over two menstrual cycles are used to capture molecular events that take place before, during, and after the spontaneous remission of BV episodes. We will use modern genomic technologies to obtain the data needed to correlate shifts in vaginal microbial community composition and function, metabolomes, and epidemiological and behavioral metadata with the occurrence of BV to better define the syndrome itself and identify patterns that are predictive of BV. The three specific aims of the research are: (1) Evaluate the association between the dynamics of vaginal microbial communities and risk to BV by characterizing the community composition of vaginal specimens archived from a vaginal douching cessation study in which 33 women self-collected vaginal swabs twice-weekly for 16 weeks; (2) Enroll 135 women in a prospective study in which self-collected vaginal swab samples and secretions are collected daily along with data on the occurrence of BV, vaginal pH, and information on time varying habits and practices; (3) Apply model-based statistical clustering and classification approaches to associate the microbial community composition and function, with metadata and clinical diagnoses of BV. The large body of information generated will facilitate understanding vaginal microbial community dynamics, the etiology of BV, and drive the development of better diagnostic tools for BV. Furthermore, the information will enable a more personalized and effective treatment of BV and ultimately help prevent adverse sequelae associated with this highly prevalent disruption of the vaginal microbiome