Title :
Frame-theoretic analysis of DFT codes with erasures
Author :
Rath, Gagan ; Guillemot, Christine
Author_Institution :
IRISA/INRIA, France
Abstract :
Discrete Fourier transform (DFT) codes have been used as joint source-channel codes in order to provide robustness against channel errors and erasures. This paper presents a frame-theoretic analysis of lowpass DFT codes with erasures. First, it is shown that such codes make a special class of frames. Then, the message reconstructions by the frame-theoretic signal space projection and coding-theoretic syndrome decoding of erasures are analyzed, and their equivalence is proved. The error performance of lowpass DFT codes is analyzed using the frame theory. The analysis helps in classifying the subframes of a DFT frame into several classes. This classification leads to the development of packetization criteria in order to guarantee minimum mean square reconstruction error and, thus, to minimize the effect of the quantization error. Simulation results substantiate the presented theory and the proposed packetization schemes.
Keywords :
combined source-channel coding; discrete Fourier transforms; error correction codes; error statistics; least mean squares methods; quantisation (signal); DFT codes; channel errors; coding-theoretic syndrome decoding; erasures; frame-theoretic analysis; frame-theoretic signal space projection; joint-source channel codes; message reconstructions; minimum mean square reconstruction error; packetization criteria; quantization error; robustness; Channel coding; Communication systems; Decoding; Degradation; Discrete Fourier transforms; Error correction; Fourier transforms; Quantization; Redundancy; Signal processing;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2003.821106