Combining Reed-Solomon Codes and OFDM for Impulse Noise Mitigation: RS-OFDM

In this paper, a joint solution to the design problem of a good error-correcting code for an OFDM scheme with a low peak to average power ratio (PAPR) in the case of impulse noise is presented. The PAPR problem is tackled by decomposing the circulant channel matrix into parallel channels by using DFT matrices in a Galois field of odd characteristic, rather than in a complex field. The modulo operation inherent to this field then limits the power of the modulated signal. More importantly, it is explained how this OFDM scheme can be seamlessly merged with a Reed-Solomon (RS) code, which due to its maximal Hamming distance is the preferred code for impulse noise cancellation. The overall scheme, referred to as RS-OFDM, shows an error correcting code that is matched to the OFDM-modulator. It is shown that the optimal Hamming distance of the RS code is preserved not only by the OFDM modulator, but also by the channel