Characterization of a Class of Error Correcting Frames for Robust Signal Transmission over Wireless Communication Channels

Joint source-channel coding has been introduced recently as an element of QoS support for IP-based wired and wireless multimedia. Indeed, QoS provisioning in a global mobility context with highly varying channel characteristics is all the most challenging and requires a loosening of the layer and source-channel separation principle. Overcomplete frame expansions have been introduced as joint source-channel codes for erasure channels, that is, to allow for a signal representation that would be resilient to erasures in wired and wireless channels. In this paper, we characterize a class of frames for error correction besides erasure recovery in such channels. We associate the frames with complex number codes and characterize them based on the BCH-like property of the parity check matrices of the associated codes. We show that, in addition to the BCH-type decoding, subspace-based algorithms can also be used to localize errors over such frame expansion coefficients. When the frame expansion coefficients are quantized, we modify these algorithms suitably and compare their performances in terms of the accuracy of error localization and the signal-to-noise ratio of the reconstructed signal. In particular, we compare the frames associated with lowpass DFT, DCT, and DST codes, which belong to the defined class, in terms of their error correction efficiency.