Efficient implementation of reed-solomon erasure resilient codes in high-rate applications

摘要

A new high-rate Reed-Solomon erasure resilient codes (ERC) system and method for generating and efficiently implementing novel Reed-Solomon erasure-resilient codes for use in high-rate applications. High-rate applications are applications where the number of coded messages is significantly higher (such as an order of magnitude) than the number of original messages. The new Reed-Solomon ERC system uses a novel scalar vector multiplication and addition technique and a novel direct inversion technique. The direct inversion technique uses specific generator matrices, including a modified Vandermonde Matrix and a Cauchy Matrix, to directly calculate an inverse of the sub-generator matrix of receiving ERC-coded messages, thereby reducing decoding computation. The scalar vector multiplication and addition technique generates new high-rate Reed-Solomon codes and performs scalar vector multiplication and addition on the Galois Field to speed up the Reed-Solomon erasure encoding/decoding operations. In effect, the new Reed-Solomon codes are “tuned” for maximum performance in the high-rate environment.