Frame-Theoretic Analysis of DFT Codes With Erasures

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 frametheoretic 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.