Turbo Decoding on the Binary Erasure Channel: Finite-Length Analysis and Turbo Stopping Sets

This paper is devoted to the finite-length analysis of turbo decoding over the binary erasure channel (BEC). The performance of iterative belief-propagation decoding of low-density parity-check (LDPC) codes over the BEC can be characterized in terms of stopping sets. We describe turbo decoding on the BEC which is simpler than turbo decoding on other channels. We then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure. Apply turbo decoding until the transmitted codeword has been recovered, or the decoder fails to progress further. Then the set of erased positions that will remain when the decoder stops is equal to the unique maximum-size turbo stopping set which is also a subset of the set of erased positions. Furthermore, we present some improvements of the basic turbo decoding algorithm on the BEC. The proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results. Finally, we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption, and an efficient enumeration algorithm of small-size turbo stopping sets for a particular interleaver. The solution is based on the algorithm proposed by Garello et al. in 2001 to compute an exhaustive list of all low-weight codewords in a turbo code.     

Sphere-packing bounds for convolutional codes

We introduce general sphere-packing bounds for convolutional codes. These improve upon the Heller (1968) bound for high-rate convolutional codes. For example, based on the Heller bound, McEliece (1998) suggested that for a rate (n - 1)/n convolutional code of free distance 5 with /spl nu/ memory elements in its minimal encoder it holds that n /spl les/ 2/sup (/spl nu/+1)/2/. A simple corollary of our bounds shows that in this case, n < 2/sup /spl nu//2/, an improvement by a factor of /spl radic/2. The bound can be further strengthened. Note that the resulting bounds are also highly useful for codes of limited bit-oriented trellis complexity. Moreover, the results can be used in a constructive way in the sense that they can be used to facilitate efficient computer search for codes.     

Improved algorithms for the determination of turbo-code weight distributions

We discuss algorithms for determining exactly the lower terms of the weight distribution of a turbo code. Several improvements on the recently introduced algorithm by Garello et al. are outlined. The techniques presented in this letter improve the observed asymptotic complexity by a factor proportional to the information length. As an example, the improved algorithm is applied to the determination of the minimum distance of all universal mobile telecommunications system turbo codes. We further apply the improved algorithm to high-rate turbo codes using high-rate nonpunctured constituent codes. To reduce complexity, the constituent codes are represented by a minimal information bit-oriented trellis.     

Promoting Bacillus cereus spore germination for subsequent inactivation by mild heat treatment

Sublethal heat treatment may activate dormant spores and thereby potentiate the conversion of spores to vegetative cells. As the germinated spore is known to possess lower heat resistance than its dormant counterpart, it has been postulated that double heat treatment, i.e., spore heat activation followed by germination and then by heat inactivation, can be used to control spores in foods. Production of refrigerated processed foods of extended durability often includes more than one heat treatment of the food components. This work simulates conventional heat treatment procedures and evaluates double heat treatment as a method to improve spore control in model food matrixes of meat broth and cream sauce. Bacillus cereus NVH 1230-88 spores were supplemented in food model matrixes and heat activated at 70°C and then heat inactivated at 80 or 90°C. The samples were held at 29 to 30°C for 1 h between primary and secondary heat treatments, to allow spore germination. Nutrients naturally present in the food matrixes, e.g., amino acids and inosine, could act as germinants that induce germination. The levels of germinants could be too low to produce effective germination within 1 h. Following primary heat treatment, some samples were therefore supplemented with a combination of L-alanine and inosine, a germinant mixture known to be effective for B. cereus spores. In both matrixes, a combination of double heat treatment (heat activation, germination, and inactivation) and addition of germinants gave a reduction in spore counts equivalent to or greater than that obtained with a single heat treatment for 12 min at 90°C. Addition of germinants was essential to induce effective germination in cream sauce during 1 h at 29 to 30°C, and germinants were therefore a crucial supplement to obtain an effect of double heat treatment in this matrix. These data will be valuable when setting up temperature-time-germinant combinations for an optimized spore reduction in mild-heat-treated foods.     

Recent Advances in Minimal Heat Processing of Fish: Effects on Microbiological Activity and Safety

Thermal processing is one of the most common methods for achieving safe convenience fish products with an extended shelf life. Designing a thermal process for such products, typically in the range of 60–95 °C for 10 to 30 min, is challenging since the heat load required for inactivating target microorganisms may cause undesirable quality changes in the lipid and protein fraction. Concern about the safety of some fish products exists, particularly when considering the potential abuse caused by storage temperature. New methods that focus on minimal heating or rapid heating of fish products are therefore of vital importance. The main aim for new developments is to reduce the overall thermal load by reducing the temperature gradients in the product or by targeting specific potentially infected areas. In both cases, alternative technologies to conventional autoclaves, combi-steamers or water baths are used for enhanced heat transfer, thereby providing more rapid heating and avoiding unnecessarily high heat loads on part of the product. Dielectric heating, Shaka technology and surface pasteurisation are technologies that meet these approaches, and are now available for industrial applications. Minimal processing often relies on the use of multiple sub-lethal stresses or processes to achieve a similar level of microbial control such as that traditionally achieved by using a single lethal stress. Most minimally processed products require refrigerated storage and distribution to maintain food safety.     

Effect of modified atmosphere packaging and superchilled storage on the shelf‐life of farmed ready‐to‐cook spotted wolf‐fish (Anarhichas minor)

Modified atmosphere packaging (MAP) combined with superchilling (?1°C) was evaluated as a mild preservation method for farmed spotted wolf‐fish (Anarhichas minor). Portions were packaged in air and in CO2:N2 (60%:40%) atmosphere with a gas:product ratio of approximately 1, at superchilled (?1.0°C ± 0.2°C) or chilled (+4.0°C ± 0.2°C) temperatures. A reduced bacterial growth (p < 0.001), measured as aerobic plate counts (APC) and psychrotrophic bacteria, was observed in modified atmosphere (MA) packaged wolf‐fish at both ?1°C and +4°C, compared to portions in air. MA‐packaged wolf‐fish had improved odour and flavour scores (p < 0.05), but also a higher drip loss than fish stored in air. A shelf‐life of 15 days was obtained at ?1°C for MA‐packaged fish compared to 8–10 days in air, and at 4°C the shelf‐life was 13 days in MA and 6–8 days in air. Copyright © 2006 John Wiley & Sons, Ltd.     

Characterisation of the dominant bacterial population in modified atmosphere packaged farmed halibut (Hippoglossus hippoglossus) based on 16S rDNA-DGGE

It is not well understood why Atlantic halibut (Hippoglossus hippoglossus) has longer shelf-life than most other white fish species. Our approach was to examine the microbiological diversity of the spoilage microbiota during modified atmosphere (MA) packaging of farmed Atlantic halibut. Portions were packaged with gas mixtures of CO(2):N(2) and CO(2):O(2) (50%:50%) and with air as a reference. The packages were stored at 4 degrees C and samples were taken 6 times during the 23 days of storage. Analyses with molecular techniques (PCR-DGGE) determined profiles of the bacterial populations in the various samples and sequencing detected the bacterial species present. In addition, samples were analysed for microbial, chemical and sensory parameters. The shelf-life was 10-13 days when stored in air and between 13 and 20 days for MA packages, with oxygen-enriched packages suggested as the better gas mixture, based on microbial growth and sensory scores. From sequence analyses of the bacterial population Photobacterium phosphoreum and Pseudomonas spp. were found to dominate in the halibut. Brochothrix thermosphacta was found in most samples at the end of the storage period. Shewanella putrefaciens was found sporadically and in low concentrations based on microbial methods, but not detected by PCR-DGGE.     

Stopping Set Analysis of Iterative Row-Column Decoding of Product Codes

In this paper, we introduce stopping sets for iterative row-column decoding of product codes using optimal constituent decoders. When transmitting over the binary erasure channel (BEC), iterative row-column decoding of product codes using optimal constituent decoders will either be successful, or stop in the unique maximum-size stopping set that is contained in the (initial) set of erased positions. Let C_p denote the product code of two binary linear codes C_c and C_r of minimum distances dc and d_r and second generalized Hamming weights d₂(C_c) and d₂(C_r), respectively. We show that the size s_min of the smallest noncode- word stopping set is at least mm(d_rd₂(C_c),d_cd₂(C_r)) > d_rd_c, where the inequality follows from the Griesmer bound. If there are no codewords in C_p with support set S, where S is a stopping set, then S is said to be a noncodeword stopping set. An immediate consequence is that the erasure probability after iterative row-column decoding using optimal constituent decoders of (finite-length) product codes on the BEC, approaches the erasure probability after maximum-likelihood decoding as the channel erasure probability decreases. We also give an explicit formula for the number of noncodeword stopping sets of size s_min, which depends only on the first nonzero coefficient of the constituent (row and column) first and second support weight enumerators, for the case when d₂(C_r) < 2d_r and d₂(C_c) < 2d_c. Finally, as an example, we apply the derived results to the product of two (extended) Hamming codes and two Golay codes.     

An interlaboratory study to find an alternative to the MPN technique for enumerating Escherichia coli in shellfish

Nine laboratories in eight countries tested 16 batches of common mussels (Mytilus edulis) over a 32 week period in order to find an alternative to the Most Probable Number (MPN) technique to enumerate E. coli. The alternatives investigated included the 3M Petrifilm system, the Merck Chromocult agar method and a Malthus conductance technique. The Petrifilm was found to be unsuitable and was subsequently dropped from the trial. After 669 analyses, a correlation of 0.83 was observed for log E. coli counts between the MPN and Chromocult methods and there was no significant evidence that either method tended to give higher readings than the other. The MPN was slightly better than the Chromocult method for repeatability but the Chromocult was slightly better for reproducibility. However, the observed differences are probably too small to be of practical importance. On the basis of these data therefore, the two methods appear equally suitable for E. coli enumeration in shellfish. There were poor correlations between these methods and the Malthus technique. A small but significant number of samples tested positive on the Malthus instrument but were recorded negative on the MPN and Chromocult tests. Subsequent analysis positively identified E. coli from these Malthus assays. After statistical analysis, errors were noted in both the MPN and Chromocult methods but it was found that there would be no statistical differences if the Chromocult agar were used as an alternative to the MPN technique.     

A review of modified atmosphere packaging of fish and fishery products – significance of microbial growth, activities and safety

Modified atmosphere packaging (MAP) extends shelf-life of most fishery products by inhibiting bacterial growth and oxidative reactions. The achievable extension of shelf-life depends on species, fat content, initial microbial population, gas mixture, the ratio of gas volume to product volume, and most importantly, storage temperature. The shelf-life of fishery products is usually limited by microbial activity, although for some fatty fishes or at superchilled storage, it can be limited by nonmicrobial activity. Packaging of fishery products under modified atmospheres (MA) increases shelf-life compared with those packaged under air, but confers little or no additional shelf-life increase compared with vacuum packaging. The specific spoilage organism (SSO) of MA packaged cod at 0 °C has been found to be Photobacterium phosphoreum . Whether or not this bacterium is the general SSO for all marine temperate fishes at different storage temperatures and under various CO₂/N₂/O₂ mixtures needs to be resolved. Without proper control of storage temperature, the benefits of MAP may be lost. Higher temperatures inevitably lead to less dissolved CO₂ in the product and consequently loss of inhibitory effect, which may result in higher microbial and enzymatic activity, and uncertainties concerning the microbial safety, as food-borne pathogens might be present in the product.