Subspace-Based Error and Erasure Correction with DFT Codes for Wireless Channels

This paper deals with the decoding of lowpass discrete Foruier transform (DFT) codes in the presence of both errors and erasures. We propose a subspace-based approach for the error localization that is similar to the subspace approaches followed in the array signal processing for direction-of-arrival (DOA) estimation. The basic idea is to divide a vector space into two orthogonal subspaces of which one is spanned by the error locator vectors. The locations of the errors are estimated from the spanning eigenvectors of the complement subspace. However, unlike the subspace approach in DOA estimation, which is similar to estimating the subspaces from the syndrome covariance matrix after a projection, in the proposed approach, the subspaces are estimated from the modified syndrome covariance matrix after a whitening transform. Simulation results with a Gauss–Markov source reveal that the proposed algorithm is more efficient than the coding theoretic approach on impulsive channels as well as the subspace approach with projection on lossy channels.