Real error and erasure correction with DFT codes for communication channels

This paper deals with the decoding of lowpass DFT codes in presence of both errors and erasures. First we consider the case when the codevectors are not quantized and present a coding theoretic algorithm as well as subspace based decoding algorithm. Then we consider the quantization of the codevectors and show the equivalence between the error and erasure correction, and the estimation of directions of arrival (DOA) of plane waves in array signal processing. This analogy leads to the introduction of an adaptation of the subspace based DOA estimation techniques to the problem of error and erasure correction in the real field. The adaptation incorporates a whitening operation, which is shown to be equivalent to the projection of the syndrome vector onto the orthogonal complement of the subspace spanned by the erasure locator vectors. Simulation results with a Gauss-Markov source reveal that the proposed subspace based algorithm is more efficient than the coding theoretic approach in localizing the errors.