Prof. Dr.-Ing. Werner Henkel
This report studies the encoding of Reed-Solomon codes with consecutive time and DFT domain redundancy. Many data transmission schemes rely on Reed-Solomon codes for error correction, therefore a thorough comprehension of their properties would be very constructive. An arbitrary number of redundant zeros in both time and DFT domain codewords were considered for all the encoding methods. In order to enforce the respective number of zeros, the equations that the information and codeword symbols should satisfy were determined. We concluded that the time domain encoding methods are the straightforward methods for controlling the redundancy of the codeword in both domains. The time domain redundancy directly depends on the number of information symbols whereas the DFT domain redundancy depends on the degree of the generator polynomial. However, controlling the codeword redundancy when using the DFT domain encoding method is not as simple. Enforcing an arbitrary number of zeros in the codeword in time domain requires a solution of a system of equations. Since the error-correction capability of Reed-Solomon codes depends on the codeword redundancy, further standard investigations of the error correction patterns for time/DFT Reed-Solomon codes could be a next step in our analysis.
[Report] Encoding of a DFT (Reed-Solomon like) code with consecutive time and frequency domain redundancy