Energy Efficiency of Error Correction on Wireless Systems

called extension fields or Galois Fields denoted as GF(p w ). Operations on extension fields are simple in the case p = 2. The elements of GF(2 w ) are integers from zero to 2 w - 1. Addition and subtraction of GF(2 w ) are simple exclusive-OR operations. Multiplication and division are more complex and require two mapping tables, each of length 2 w . These two tables map an integer to its logarithm and its inverse logarithm in the Galois field. A table for the multiplication can be used as well if the number of field elements is not too large. Note that a multiplication in GF(2 8 ) already requires a 64 kB lookup table! Energy efficiency of the Reed-Solomon algorithm The encoding overhead depends on the number of source packets k, on the number redundant pa