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...

A new species of Nicrophorus in the nepalensis species-group, Nicrophorus efferens Sikes and Mousseau, is described from Bougainville Island in the Solomon Islands archipelago. It is distinguished from the known species of the genus Nicrophorus and its likely closest relative, Nicrophorus reticulatus Sikes and Madge, based on external morphology. A comparison among the four Nicrophorus species ...

Two architecturesfor universal Reed-Solomon decoders are given. These decoders, called time-domain decoders, work directly on the raw data word as received without the usual syndrome calculation or power-sum-symmetric functions Up to the limitations of the working registers, the decoders can decode any Reed-Solomon codeword or BCH codeword in the presence of both errors and erasures. Provision ...

Abstract— This paper presents FPGA implementation of the Reed-Solomon decoder for use in IEEE 802.16 WiMAX systems. The decoder is based on RS(255,239) code, and is additionally shortened and punctured according to the WiMAX specifications. A Simulink model based on the System Generator (Sysgen) library of low-level Xilinx blocks was used for simulation and hardware implementation. At the end, ...

This paper presents an algorithmic improvement to Sudan’s list-decoding algorithm for Reed-Solomon codes and its generalization to algebraic-geometric codes from Shokrollahi and Wasserman. Instead of completely factoring the interpolation polynomial over the function field of the curve, we compute sufficiently many coefficients of a Hensel development to reconstruct the functions that correspon...

The interpolation step of Sudan’s list decoding of Reed-Solomon codes sets forth the problem of finding the minimal polynomial of an ideal 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 Berlekamp-Massey algorithm for decodin...

391 Abstract— Detection and correction of errors in digital data is an important issue for the modern communication systems. Therefore an efficient error control code is needed to protect the digital data. In high speed communication system Reed-Solomon codes are widely used to provide error protection especially against the burst errors. Reed-Solomon codes are cyclic, non-binary codes. In this...

Although hookworm is highly prevalent in the Solomon Islands, the species involved are unknown. We initiated this study in response to finding Ancylostoma ceylanicum hookworm in a peacekeeper in Australia who had returned from the Solomon Islands. Kato-Katz fecal surveys performed in 2013 and 2014 in 2 village groups in East Malaita, Solomon Islands, identified hookworm-positive samples. These ...