Analysis of complementary codes using FIR digital filtering theory for achieving reduced computational decoding

The author attempts to show how the generation and compression of complementary codes can be based on a specific single-input-multiple-output FIR (finite impulse response) digital filter structure. Driving this filter with a unit pulse yields both the code and its complement as the response simultaneously. A decoder is then derived as an FIR digital filter which is matched to the coder filter. The significance of this technique lies in the relative ease with which the decoder structure may be identified for arbitrary coder structures. This then leads to decoding algorithms with reduced computational requirements. An example is presented which shows how calculations on the order of N² may be reduced to a number on the order of Nlog₂N