- Low complexity rate allocation (RA) algorithms for reliable transmission of progressively coded bit streams over noisy variable channels are presented. First, based on backward application of a Viterbi-like algorithm, a rate allocation algorithm is introduced, that can be applied to both variable channel packet length (VPP) and fixed channel packet (FPP) problems. The latter is presumably the first low-complexity algorithm. RA algorithms require packet error rates. We assume ideal known constant channel. We also consider the packet error approximation for undetermined BSC channels. For real-time applications, an efficient linear complexity two-directional local search algorithm is presented for FPP and then developed for VPP. It is achieved by sequential distortion improvement of an initial solution for optimal rates with neighboring lower and/or higher rates. It is observed that this fast rate allocation method is suitable for the transmission of multiple images over variable channels. Also, we have presented a rate allocation method that may be applied in variable channels with a first order Markov model. Since progressive image encoders suffer from error propagation, decoding must stop as soon as an erroneous packet is received. For reduction of this weakness, layered source coding and rate allocation are presented. Keywords: Joint Source channel coding, rate allocation, progressive codes, rate-compatible codes