Subspace algorithms for error localization with quantized DFT codes

Recently, a class of real-number Bose-Chaudhuri-Hocquengem codes known as discrete Fourier transform (DFT) codes have been considered as joint source and channel codes for providing robustness to erasures and errors over wireless networks. We propose three subspace algorithms for error localization with quantized DFT codes. The algorithms are similar to the MUSIC, the minimum-norm, and the ESPRIT algorithms used in array signal processing for direction-of-arrival estimation. They provide different but related formulations of the error localizations by first partitioning a vector space into the channel error subspace and its orthogonal complement, the noise subspace. The locations of the errors are determined from either the error subspace eigenvectors or the noise subspace eigenvectors. We also present a brief performance analysis of the localization error in terms of the perturbation of the error subspace due to quantization. Simulation results show that their localization performances are similar, and they perform better than the coding-theoretic approach over a broad range of channel-error-to-quantization-noise ratios.