Performance analysis and recursive syndrome decoding of DFT codes for bursty erasure recovery
Packet loss is a common phenomenon in current image processing (IP) networks. Current network protocols manage this problem by retransmitting the lost packets. However, the delay due to the retransmission of the lost packets may be inappropriate for many real-time applications. Therefore, a better approach to resolve this problem is to recover the lost data from the received packets using some error control coding scheme. The conventional error control coding is based on a tandem source and channel coding framework, where the message signal is first compactly represented using a rate-distortion criterion, and then, the error correcting bits are appended to it. As an alternative, joint source-channel codes that can perform as good as, or better than, the tandem source and channel coding are being considered. In particular, lowpass discrete Fourier transform (DFT) codes have been studied as joint source-channel codes. This paper is dedicated to the analysis of lowpass DFT codes with bursty erasures. The analysis aims at studying the performance of lowpass DFT codes when consecutive samples of a DFT codevector are erased due to packet losses. It is known that lowpass DFT codes are highly sensitive to quantization error when there are consecutive erasures. This phenomenon is studied in the context of syndrome decoding. Bursty erasures give rise to a syndrome-decoding matrix that has very large elements depending on the code parameters and the burst length. The size 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 lowpass DFT codes is analyzed and then applied to the case of bursty erasures. The paper also proposes a recursive syndrome decoding algorithm to improve on the normal syndrome decoding of lowpass DFT codes in the case of bursty erasures. The proposed algorithm aims at recovering the quantized values of the erased samples based on a cost computed using the statistics of the codevector and of the quantization error.