Patent ID: 7418649

Claim:
A method for encoding and decoding original messages in a high-rate erasure resilience coding application having a coded message space that is at least an order of magnitude larger than a number of original messages, the method comprising: performing high-rate Reed-Solomon erasure resilient code encoding and decoding operations on the original messages using a scalar vector multiplication and addition technique represented by the equation y=y+αx, where x and y are vectors of symbols of a Galois Field, GF(p), and where y is an order of the Galois Field, and where alpha, α, is a scalar number in GF(p), and where y is an update vector and x is a content vector; the scalar vector multiplication and addition technique further comprising: establishing a logarithm lookup table and an exponential lookup table in advance of the encoding and decoding operations; calculating a logarithm of alpha, α, using the logarithm lookup table; calculating a logarithm of an element of the content vector, x i ; testing whether the element of the content vector, x i , is equal to zero; for zero x i ; performing nothing; for non-zero x i , calculating an exponential of a sum of log(α) and a logarithm of the element of the content vector, x i , using the exponential lookup table to generate an intermediate result; generating an updated element of the update vector, y i , by adding on the Galois Field the intermediate result to a current element of the update vector, y i to obtain scalar vector multiplication and addition results; and using the scalar vector multiplication and addition results to encode the original messages and decode encoded messages to recover the original messages.