Signal processing techniques in error control systems

Several standard signal processing techniques may be effectively applied in the design and mechanization of optimum encoders and decoders in error control systems that employ block error-correcting codes. Many of the approaches rely upon generalized transforms that resemble the Walsh functions. They use a fast algorithm that is developed over a subspace in the generalized frequency domain. The decoder performs error correction with a code which contains
k
information symbols by numerically combining the output from (
k+1
) finite impulse response (FIR) type of filters. These filters use weights that are directly related to the transforms of the system's transition probabilities. Each filter weights the transforms of the received digits over (
k+1
) special subsets in the frequency domain.