A polynomial matrix is said to be locally invertible if it has an invertible subsequence map of equal size between its input and output sequence spaces. This paper examines the use of these matrices, which we call locally invertible encoders, for generating multidimensional convolutional codes. We discuss a novel method of encoding and inverting multidimensional sequences using the subsequence map. We also show that the overlapping symbols between consecutive input subsequences obtained during the sequence inversion can be used to determine if the received sequence is the same as the transmitted codeword.

In prokaryotes, Shine-Dalgarno (SD) sequences, nucleotides upstream from start codons on messenger RNAs (mRNAs) that are complementary to ribosomal RNA (rRNA), facilitate the initiation of protein synthesis. The location of SD sequences relative to start codons and the stability of the hybridization between the mRNA and the rRNA correlate with the rate of synthesis. Thus, accurate characterization of SD sequences enhances our understanding of how an organism's transcriptome relates to its cellular proteome. We implemented the Individual Nearest Neighbor Hydrogen Bond model for oligo-oligo hybridization and created a new metric, relative spacing (RS), to identify both the location and the hybridization potential of SD sequences by simulating the binding between mRNAs and single-stranded 16S rRNA 3' tails. In 18 prokaryote genomes, we identified 2,420 genes out of 58,550 where the strongest binding in the translation initiation region included the start codon, deviating from the expected location for the SD sequence of five to ten bases upstream. We designated these as RS+1 genes. Additional analysis uncovered an unusual bias of the start codon in that the majority of the RS+1 genes used GUG, not AUG. Furthermore, of the 624 RS+1 genes whose SD sequence was associated with a free energy release of less than -8.4 kcal/mol (strong RS+1 genes), 384 were within 12 nucleotides upstream of in-frame initiation codons. The most likely explanation for the unexpected location of the SD sequence for these 384 genes is mis-annotation of the start codon. In this way, the new RS metric provides an improved method for gene sequence annotation. The remaining strong RS+1 genes appear to have their SD sequences in an unexpected location that includes the start codon. Thus, our RS metric provides a new way to explore the role of rRNA-mRNA nucleotide hybridization in translation initiation.

A new method of computing the glottal pulse period of voiced speech is given. This algorithm is based on the mathematically derived fact that the amplitudes of the odd harmonics of a periodic function with period P are zero when the function is expanded in a Fourier series whose coefficients are determined by integrating over 2P instead of the usual P. It is shown that such a glottal pulse tracker is extremely sensitive to sudden short-lived shifts in the apparent frequency of the glottal pulse that circumscribe certain consonants in the speech stream. This method may therefore be used to segment these consonants for various analytical purposes. 1.

The option of obtaining education over networks is quickly becoming a reality for all those who have access to the Internet and the World Wide Web (WWW). However, at present, network-based education (NBE) over the WWW and the Internet in general faces a number of pitfalls. The problems range from inadequate end-user quality of service (QoS), to inadequate materials, to shortcomings in learning paradigms, and to missing or inappropriate student assessment and feedback mechanisms. In this paper, we discuss some major issues that, although mostly solved for NBE, still face Web-based education (WEE). These include the required workflow-oriented technological and quality of service support. In discussing the issues, we use examples from a wide-area NBE/WBE system called NovaNET and a WEE system called Web Lecture System (WLS). We recommend that WEE system developers construct operational user (workflow) profiles before building their content and interfaces. Our experience is that, especially for synchronous WEE systems, user-level round-trip keystroke delays should not exceed about 250 ms and the overall availability of the system (including network-related service failures) should be at least 0.95. We also suggest that a successful WEE system will have a sound auto-adaptive knowledge assessment component, a "virtual" laboratory capability, and a set of strong collaborative functions.

A locally invertible convolutional encoder has a local inverse defined as a full rank w/spl times/w matrix that specifies a one-to-one mapping between equal-length blocks of information and encoded bits. In this correspondence, it is shown that a rate-1/n convolutional encoder is nondegenerate and noncatastrophic if and only if it is locally invertible. Local invertibility is used to obtain upper and lower bounds on the number of consecutive zero-weight branches in a convolutional codeword. Further, existence of a local inverse can be used as an alternate test for noncatastrophicity instead of the usual approach involving computation of the greatest common divisor of n polynomials.

An important class of quality of service (QoS)-dependent network-based applications are computer-based education systems. A successful network-based education (NBE) system needs to provide appropriate QoS at the user level. This includes adequate end-to-end response delay and adequate system reliability and availability. This paper presents results from a reliability and availability evaluation of NovaNET. NovaNET is a successful low-overhead multimedia education system which serves thousands of users on a daily basis. We analyze eight years of failure data and examine correlations among system failure events. The NovaNET data are used to discuss practical bounds on the reliability and availability of an NBE system.

Table based error correction and decoding of rate one-half convolutional codes is described. A new class of fast-decodeable locally invertible convolutional codes based on a one-to-one mapping between information and encoded blocks of equal lengths is defined. The syndrome is used as an address to access a correction table which stores pre-computed correction information. The correction table generation process is described and a specific table based correction algorithm is given. Performance of this scheme is analyzed and simulation results are presented.>

Nonstationary channels (e.g., digital mobile communication channels) require adaptive error control schemes for reliable communication. On these channels, a particular transmission may encounter no errors. Hence, it is desirable to split an encoded sequence into subsequences that are sent in successive transmissions such that each subsequence contains all the information necessary to recover the original message in case of no errors. When errors are present, the subsequences are combined to perform error correction. We show that invertible convolutional codes have this property, and can be used to provide incremental redundancy in a variable-redundancy hybrid ARQ (VR-HARQ) scheme. Invertible convolutional codes provide an alternative to polynomial division otherwise required to extract the original message in convolutional VR-HARQ schemes.>