Generalized and Extended Subspace Algorithms for Error Correction with Quantized DFT Codes

Discrete Fourier transform (DFT) codes have been used to provide robustness against errors and erasures in various applications. This paper focuses on improving error localization of the Bose-Chaudhuri-Hocquenghem (BCH) DFT codes. First, we analyze how the subspace-based error localization outperforms the coding-theoretic one. Then, we propose an extension of the subspace-based error localization, based on additional syndrome, that improves the existing one and is naturally suitable for rate-adaptive distributed source coding (DSC). Further, we propose a new generic subspace-based algorithm to decode BCH-DFT codes. The proposed approach generalizes the encoding and decoding of this important class of DFT codes. It introduces many different decoding matrices for a DFT code; this diversity is then used to diminish the effect of the quantization noise and thus to improve the decoding. Finally, the extended and generalized approaches are combined to maximize the decoding gain. Simulation results demonstrate the capability of the proposed algorithms to perform significantly better than the existing subspace-based error localization, in the presence of quantization noise.