This paper presents a general framework for combined source-channel coding within the context of subband coding. The unequal importance of subbands in reconstruction of the source is exploited by an appropriate allocation of source and channel coding rates for the coding and transmission of subbands over a noisy channel. For each subband, the source coding rate as well as the level of protection (quantified by the channel coding rate) are jointly chosen to minimize the total end-to-end mean-squared distortion suffered by the source. This allocation of source and channel coding rates is posed as a constrained optimization problem, and solved using a generalized bit allocation algorithm. The optimal choice of source and channel coding rates depends on the state of the physical channel. These results are extended to transmission over fading channels using a finite state model, where every state corresponds to an additive white Gaussian noise (AWGN) channel. A coding strategy is also developed that minimizes the average distortion when the channel state is unavailable at the transmitter. Experimental results are provided that demonstrate application of these combined source-channel coding strategies on video sequences.