CGU‐frame‐based representations and their connection with Reed—Solomon and DCT/DST coding schemes

Abstract

SUMMARYWe investigate the use of overcomplete frame representations to correct errors occurring over burst-based transmission channels or channels leading to isolated errors. We show that when the overcomplete signal representation is based on a class of frames, called cyclic geometrically uniform (CGU) finite frames, the family of frames containing finite harmonic frames (both in C M and R M ), this representation becomes equivalent to a Reed-Solomon (RS) coding scheme. Hence, introducing an RS decoding procedure at the receiver, leads to remove the errors introduced by the transmission channel and consequently results in a quasi-perfect reconstructed signal. The advantage of this approach is to exploit the RS coding scheme without using it explicitly at the transmitter, which would lead to a robust and low complexity transmission. Furthermore, we prove that the discrete cosine transform (DCT) coding is a special case of CGU-framebased representations and this property holds also true for the discrete sine transform (DST) coding scheme.Simulation results are presented to confirm our claims.