Simplified decoding techniques for linear block codes

Error correcting codes are combinatorial objects, designed to enable reliable transmission of digital data over noisy channels. They are ubiquitously used in communication, data storage etc. Error correction allows reconstruction of the original data from received word. The classical decoding algorithms are constrained to output just one codeword. However, in the late 50’s researchers proposed a relaxed error correction model for potentially large error rates known as list decoding. The research presented in this thesis focuses on reducing the computational effort and enhancing the efficiency of decoding algorithms for several codes from algorithmic as well as architectural standpoint. The codes in consideration are linear block codes closely related to Reed Solomon (RS) codes. A high speed low complexity algorithm and architecture are presented for encoding and decoding RS codes based on evaluation. The implementation results show that the hardware resources and the total execution time are significantly reduced as compared to the classical decoder. The evaluation based encoding and decoding schemes are modified and extended for shortened RS codes and software implementation shows substantial reduction in memory footprint at the expense of latency. Hermitian codes can be seen as concatenated RS codes and are much longer than RS codes over the same aphabet. A fast, novel and efficient VLSI architecture for Hermitian codes is proposed based on interpolation decoding. The proposed architecture is proven to have better than Kötter’s decoder for high rate codes. The thesis work also explores a method of constructing optimal codes by computing the subfield subcodes of Generalized Toric (GT) codes that is a natural extension of RS codes over several dimensions. The polynomial generators or evaluation polynomials for subfield-subcodes of GT codes are identified based on which dimension and bound for the minimum distance are computed. The algebraic structure for the polynomials evaluating to subfield is used to simplify the list decoding algorithm for BCH codes. Finally, an efficient and novel approach is proposed for exploiting powerful codes having complex decoding but simple encoding scheme (comparable to RS codes) for multihop wireless sensor network (WSN) applications.

Plasmid biology of natural Lactococcus lactis strains and molecular mechanisms of bacteriophage-host interaction

Lacticin 3147, enterocin AS-48, lacticin 481, variacin, and sakacin P are bacteriocins offering promising perspectives in terms of preservation and shelf-life extension of food products and should find commercial application in the near future. The studies detailing their characterization and bio-preservative applications are reviewed. Transcriptomic analyses showed a cell wall-targeted response of Lactococcus lactis IL1403 during the early stages of infection with the lytic bacteriophage c2, which is probably orchestrated by a number of membrane stress proteins and involves D-alanylation of membrane lipoteichoic acids, restoration of the physiological proton motive force disrupted following bacteriophage infection, and energy conservation. Sequencing of the eight plasmids of L. lactis subsp. cremoris DPC3758 from raw milk cheese revealed three anti-phage restriction/modification (R/M) systems, immunity/resistance to nisin, lacticin 481, cadmium and copper, and six conjugative/mobilization regions. A food-grade derivative strain with enhanced bacteriophage resistance was generated via stacking of R/M plasmids. Sequencing and functional analysis of the four plasmids of L. lactis subsp. lactis biovar. diacetylactis DPC3901 from raw milk cheese revealed genes novel to Lactococcus and typical of bacteria associated with plants, in addition to genes associated with plant-derived lactococcal strains. The functionality of a novel high-affinity regulated system for cobalt uptake was demonstrated. The bacteriophage resistant and bacteriocin-producing plasmid pMRC01 places a metabolic burden on lactococcal hosts resulting in lowered growth rates and increased cell permeability and autolysis. The magnitude of these effects is strain dependent but not related to bacteriocin production. Starters’ acidification capacity is not significantly affected. Transcriptomic analyses showed that pMRC01 abortive infection (Abi) system is probably subjected to a complex regulatory control by Rgg-like ORF51 and CopG-like ORF58 proteins. These regulators are suggested to modulate the activity of the putative Abi effectors ORF50 and ORF49 exhibiting topology and functional similarities to the Rex system aborting bacteriophage λ lytic growth.