An optical error-correction code with spectrum domain decoding

We propose an optically (though not all-optically) decodable error-correction code. The structure of the proposed code is defined in the Fourier spectrum domain. The Fourier spectrum of the codewords has zeros. Thus, we can view any signal appearing in these spectrum zeros as the "syndrome", since the codewords have no energy in these spectrum zeros. The optical technique of the Fourier transform is used for fast decoding speed. The proposed code is nonlinear and of length eight. This code has a total of eight codewords (so the code rate is (log₂8)/8=3/8) and can correct 1.75 consecutive bit errors on average.