This paper examines a coded Gaussian Minimum Shift Keying (GMSK) system which uses Reed-solomon (RS) codes in Additive White Gaussian Noise channels.The performance of GMSK and RS code combinations is compared with the constraint that the transmission bandwidth is constant. The coding gains were obtained using simulations and the best combination of GMSK and RS codes was found. Keywords—GMSK, R...

The cohomology ring of the complement of a central complex hyperplane arrangement is the well-studied Orlik-Solomon algebra. The homotopy group of the complement is interesting, complicated, and few results are known about it. We study the ranks for the lower central series of such a homotopy group via the linear strand of the minimal free resolution of the field C over the Orlik-Solomon algebra.

Solomon C., Miller L., Witten A., Usachenko J., Kleinman M., Balmes J. (2003) Particleand ozone exposure in allergic asthma: effect on airway cells and in-vitro allergen-induced cytokine expression. Am. J. Respir. Crit. Care Med. 166 (5). Power, K., Balmes, J., Solomon C. (2004) Decreased heart rate variability aftercontrolled human exposure to particles and ozone. Am. J. Respir. Cr...

In this paper, we present a new algorithm for decoding Reed-Solomon codes with both errors and erasures. The algorithm combines an efficient method for solving the Key Equation and a technique which separates the error locator polynomial from the erasure locator polynomial. The new algorithm is compared to two other efficient Reed-Solomon decoding algorithms and shown to be significantly faster...

In this correspondence, Sudan’s algorithm is modified into an efficient method to list-decode a class of codes which can be seen as a generalization of Reed–Solomon codes. The algorithm is specialized into a very efficient method for unique decoding. The code construction can be generalized based on algebraic-geometry codes and the decoding algorithms are generalized accordingly. Comparisons wi...

Epidermal nevi are congenital hamartomas of embryonal ectodermal origin classified on the basis of their main component. The compone keratinocytic. An estimated 1/3 of individuals with epidermal nevi have involvement of other organ systems; hence this condition is considered to be epidermal nevus syndrome. Solomon defined epidermal nevus syndrome as a sporadic neuro in the skin, brain, eyes and...

Abstract. The subset sum problem over finite fields is a well-known NPcomplete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a mathematical point of view. In several interesting cases, we obtain explicit or asymptotic formulas for the solution number. As a consequence, we obtain some resu...

DRAFT Last class, we saw a toy version of recovering from a mixture of two Reed-Solomon codewords the two polynomials in question. Now we turn to list decoding arbitrary received words with a bounded distance from the Reed-Solomon code using Sudan’s [6] algorithm. This algorithm decodes close to a fraction 1 of errors for low rates. Then we will see an improvement by Guruswami and Sudan [4] whi...

With increasing telemetry data rates, there is a need for faster Reed-Solomon and Convolutional on-board encoders than currently exist, both as self standing components and as integrated parts of future single chip telemetry systems. A radiation hard CCSDS Reed-Solomon and Convolutional Encoder (RESCUE) device has been developed along this line to meet current and future demands, being based on...

The interpolation step of Sudan’s list decoding of Reed-Solomon codes sets forth the problem of finding the minimal polynomial of the ideal of interpolating polynomials with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Gröbner bases of modules. In a special case, this algorithm is shown to be equivalent with the Berlekam...