Progressive source coding for a power constrained Gaussian channel

We consider the progressive transmission of a lossy source across a power constrained Gaussian channel using binary phase-shift keying modulation. Under the theoretical assumptions of infinite bandwidth, arbitrarily complex channel coding, and lossless transmission, we derive the optimal channel code rate and the optimal energy allocation per transmitted bit. Under the practical assumptions of a low complexity class of algebraic channel codes and progressive image coding, we numerically optimize the choice of channel code rate and the energy per bit allocation. This model provides an additional degree of freedom with respect to previously proposed schemes, and can achieve a higher performance for sources such as images. It also allows one to control bandwidth expansion or reduction.