Finding the complete path and weight enumerators of convolutional codes

A method for obtaining the complete path enumerator T(D, L, I) of a convolutional code is described. A system of algebraic equations is solved, using a new algorithm for computing determinants, to obtain T(D, L, I) for the (7,1/2) NASA standard code. Generating functions, derived from T(D, L, I) are used to upper bound Viterbi decoder error rates. This technique is currently feasible for constraint length K less than 10 codes. A practical, fast algorithm is presented for computing the leading nonzero coefficients of the generating functions used to bound the performance of constraint length K less than 20 codes. Code profiles with about 50 nonzero coefficients are obtained with this algorithm for the experimental K = 15, rate 1/4, code in the Galileo mission and for the proposed K = 15, rate 1/6, 2-dB code

The Extended Invariant Factor Algorithm with Application to the Forney Analysis of Convolutional Codes

In his celebrated paper on the algebraic structure of convolutional codes, Forney showed that by using the invariant-factor theorem, one can transform an arbitrary polynomial generator matrix for an (n, k) convolutional code C into a basic (and ultimately a minimal) generator matrix for C. He also showed how to find a polynomial inverse for a basic generator matrix for C, and a basic generator matrix for the dual code C^⊥. In this paper, we will discuss efficient ways to do all these things. Our main tool is the “entended invariant factor algorithm,” which we introduce here

Quantization effects in Viterbi decoding rate 1/n convolutional codes

A Viterbi decoder's performance loss due to quantizing data from the additive white Gaussian noise (AWGN) channel is studied. An optimal quantization scheme and branch metric calculation method are presented. The uniformly quantized channel capacity C(sub u)(q) is used to determine the smallest number of quantization bits q that does not cause a significant loss. The quantizer stepsize which maximizes C(sub u)(q) almost minimizes the decoder bit error rate (BER). However, a slightly larger stepsize is better, like the value that minimizes the Bhattacharyya bound. The range and renormalization of state metrics is analyzed, in particular for K = 15 decoders such as the Big Viterbi Decoder (BVD) for the Galileo mission. These results are required to design reduced hardware complexity Viterbi decoders with a negligible quantization loss

Compressed/reconstructed test images for CRAF/Cassini

A set of compressed, then reconstructed, test images submitted to the Comet Rendezvous Asteroid Flyby (CRAF)/Cassini project is presented as part of its evaluation of near lossless high compression algorithms for representing image data. A total of seven test image files were provided by the project. The seven test images were compressed, then reconstructed with high quality (root mean square error of approximately one or two gray levels on an 8 bit gray scale), using discrete cosine transforms or Hadamard transforms and efficient entropy coders. The resulting compression ratios varied from about 2:1 to about 10:1, depending on the activity or randomness in the source image. This was accomplished without any special effort to optimize the quantizer or to introduce special postprocessing to filter the reconstruction errors. A more complete set of measurements, showing the relative performance of the compression algorithms over a wide range of compression ratios and reconstruction errors, shows that additional compression is possible at a small sacrifice in fidelity

Optimal normal bases in GF(pn)

AbstractIn this paper the use of normal bases for multiplication in the finite fields GF(pn) is examined. We introduce the concept of an optimal normal basis in order to reduce the hardware complexity of multiplying field elements. Constructions for these bases in GF(2n) and extensions of the results to GF(pn) are presented. This work has applications in crytography and coding theory since a reduction in the complexity of multiplying and exponentiating elements of GF(2n) is achieved for many values of n, some prime

Truncation effects in Viterbi decoding

Practical Viterbi decoders often fall significantly short of full maximum likelihood decoding performance because of survivor truncation effects. In the present work the authors study the tradeoff between truncation length and performance loss for the two most common variations of Viterbi's algorithm: best-state decoding (BSD) and fixed-state decoding (FSD). It is found that FSD survivors should be about twice as long as BSD survivors for comparable performance

Axonal remodeling for motor recovery after traumatic brain injury requires downregulation of γ-aminobutyric acid signaling

Remodeling of the remnant neuronal network after brain injury possibly mediates spontaneous functional recovery; however, the mechanisms inducing axonal remodeling during spontaneous recovery remain unclear. Here, we show that altered γ-aminobutyric acid (GABA) signaling is crucial for axonal remodeling of the contralesional cortex after traumatic brain injury. After injury to the sensorimotor cortex in mice, we found a significant decrease in the expression of GABAAR-α1 subunits in the intact sensorimotor cortex for 2 weeks. Motor functions, assessed by grid walk and cylinder tests, spontaneously improved in 4 weeks after the injury to the sensorimotor cortex. With motor recovery, corticospinal tract (CST) axons from the contralesional cortex sprouted into the denervated side of the cervical spinal cord at 2 and 4 weeks after the injury. To determine the functional implications of the changes in the expression of GABAAR-α1 subunits, we infused muscimol, a GABA R agonist, into the contralesional cortex for a week after the injury. Compared with the vehicle-treated mice, we noted significantly inhibited recovery in the muscimol-treated mice. Further, muscimol infusion greatly suppressed the axonal sprouting into the denervated side of the cervical spinal cord. In conclusion, recovery of motor function and axonal remodeling of the CST following cortical injury requires suppressed GABAAR subunit expression and decreased GABAergic signaling

Induction of Blood Brain Barrier Tight Junction Protein Alterations by CD8 T Cells

Disruption of the blood brain barrier (BBB) is a hallmark feature of immune-mediated neurological disorders as diverse as viral hemorrhagic fevers, cerebral malaria and acute hemorrhagic leukoencephalitis. Although current models hypothesize that immune cells promote vascular permeability in human disease, the role CD8 T cells play in BBB breakdown remains poorly defined. Our laboratory has developed a novel murine model of CD8 T cell mediated central nervous system (CNS) vascular permeability using a variation of the Theiler's virus model of multiple sclerosis. In previous studies, we observed that MHC class II−/− (CD4 T cell deficient), IFN-γR−/−, TNF-α−/−, TNFR1−/−, TNFR2−/−, and TNFR1/TNFR2 double knockout mice as well as those with inhibition of IL-1 and LTβ activity were susceptible to CNS vascular permeability. Therefore, the objective of this study was to determine the extent immune effector proteins utilized by CD8 T cells, perforin and FasL, contributed to CNS vascular permeability. Using techniques such as fluorescent activated cell sorting (FACS), T1 gadolinium-enhanced magnetic resonance imaging (MRI), FITC-albumin leakage assays, microvessel isolation, western blotting and immunofluorescent microscopy, we show that in vivo stimulation of CNS infiltrating antigen-specific CD8 T cells initiates astrocyte activation, alteration of BBB tight junction proteins and increased CNS vascular permeability in a non-apoptotic manner. Using the aforementioned techniques, we found that despite having similar expansion of CD8 T cells in the brain as wildtype and Fas Ligand deficient animals, perforin deficient mice were resistant to tight junction alterations and CNS vascular permeability. To our knowledge, this study is the first to demonstrate that CNS infiltrating antigen-specific CD8 T cells have the capacity to initiate BBB tight junction disruption through a non-apoptotic perforin dependent mechanism and our model is one of few that are useful for studies in this field. These novel findings are highly relevant to the development of therapies designed to control immune mediated CNS vascular permeability