For the second FEC layer : every ASCII character is encoded as one of 64 possible Walsh functions ( or vectors of a Hadamard matrix ).
12.
The 2nd Walsh function is constructed from the 2nd bit of the 1st symbol, the 3rd bit of the 2nd symbol, and so on.
13.
Applications of the Walsh functions can be found wherever digit representations are used, including speech recognition, medical and biological image processing, and digital holography.
14.
The Walsh matrix ( and Walsh functions ) are used in computing the Walsh transform and have applications in the efficient implementation of certain signal processing operations.
15.
Walsh functions, the Walsh system, the Walsh series, and the fast Walsh Hadamard transform are all named after the American mathematician Joseph L . Walsh.
16.
It was proved that piecewise-constant functions can be represented within each of nine bases ( including the Walsh functions basis ) as finite sums of binary functions, when weighted with proper coefficients.
17.
Bit interleaving : The Walsh function for the first character in a block is constructed from the 1st bit of the 1st symbol, the 2nd bit of the 2nd symbol, and so on.
18.
This method is compared with the alternative method for enhancing the maximum throughput using aggregation of a smaller number of Walsh functions, but with a higher constellation alphabet size ( multi-level modulation ).
19.
In order to avoid simple transmitted patterns ( like a constant tone ) and to minimize the chance for a false lock at the synchronizer the characters encoded into the Walsh function pass through a scrambler and interleaver.
20.
The Olivia transmission system is constructed of two layers : the lower, modulation and forward error correcting ( FEC ) code layer is a classical multiple frequency-shift keying ( MFSK ) while the higher layer is a forward error correcting code based on Walsh functions.
