Keith Saints

Algebraic-geometric codes and multidimensional cyclic codes: a unified theory and algorithms for decoding using Grobner bases

It is proved that any algebraic-geometric (AG) code can be expressed as a cross section of an extended multidimensional cyclic code. Both AG codes and multidimensional cyclic codes are described by a unified theory of linear block codes defined over point sets: AG codes are defined over the points of an algebraic curve, and an m-dimensional cyclic code is defined over the points in m-dimensional space. The power of the unified theory is in its description of decoding techniques using Grobner bases. In order to fit an AG code into this theory, a change of coordinates must be applied to the curve over which the code is defined so that the curve is in special position. For curves in special position, all computations can be performed with polynomials and this also makes it possible to use the theory of Grobner bases. Next, a transform is defined for AG codes which generalizes the discrete Fourier transform. The transform is also related to a Grobner basis, and is useful in setting up the decoding problem. In the decoding problem, a key step is finding a Grobner basis for an error locator ideal. For AG codes, multidimensional cyclic codes, and indeed, any cross section of an extended multidimensional cyclic code, Sakatas algorithm can be used to find linear recursion relations which hold on the syndrome array. In this general context, the authors give a self-contained and simplified presentation of Sakatas algorithm, and present a general framework for decoding algorithms for this family of codes, in which the use of Sakatas algorithm is supplemented by a procedure for extending the syndrome array.

The MSM5100/sup TM/ cdma2000 + AMPS + gpsOne/sup TM/ + Bluetooth multimode ASIC for 3G handsets

The MSM5100 ASIC forms the heart of a high-featured cdma2000 3G handset that is gpsOne position location capable. The gpsOne technology meets the accuracy requirements set by the FCC for E911 Phase II. This ASIC performs baseband processing for the spectrum of air interfaces supported: IS-2000 Release 0, IS-95A/B, AMPS, GPS, and Bluetooth 1.1. The ASIC itself is both a merging effort of two previous ASIC designs, MSM3300 and MSM5000, and the addition of new functionality. The new functionality includes USB speed enhancements and increased IS-2000 physical layer support. Also, several new VLSI challenges were met in creating this product, including our product in the 0.18 um process and integrated voltage regulators. Altogether, the MSM5100 makes a significant leap forward in 3G handset functionality.