Sparse approximations for joint source-channel coding

This paper considers the application of sparse approximations in a joint source-channel (JSC) coding framework. The considered JSC coded system employs a real number BCH code on the input signal before the signal is quantized and further processed. Under an impulse channel noise model, the decoding of error is posed as a sparse approximation problem. The orthogonal matching pursuit (OMP) and basis pursuit (BP) algorithms are compared with the syndrome decoding algorithm in terms of mean square reconstruction error. It is seen that, with a Gauss-Markov source and Bernoulli-Gaussian channel noise, the BP outperforms the syndrome decoding and the OMP at higher noise levels. In the case of image transmission with channel bit errors, the BP outperforms the other two decoding algorithms consistently.