Syndrome decoding and performance analysis of DFT codes with bursty erasures

In this paper, we analyze the performance of DFT codes with bursty erasures in the framework of syndrome decoding. Bursty erasures give rise to a syndrome decoding matrix which has very large elements depending on the code parameters and the burst length. The largeness of the elements of the syndrome decoding matrix is studied by establishing various relationships between the syndrome decoding matrix, and the parity and the generator polynomial coefficients. With a suitable model for the quantization error, the reconstruction error performance of DFT codes in the context of the syndrome decoding is analyzed and then applied to the case of bursty erasures. Simulation results with a Gauss-Markov source verify the theoretical results obtained with the assumed quantization error model.