In this paper, two fixed per-information symbol complexity lossless source coding algorithms are modified for estimation and incremental LT decoding over piecewise stationary memoryless channels (PSMC's) with a bounded number of abrupt changes in channel statistics. In particular, as a class of PSMC's, binary symmetric channels are considered with a crossover probability that changes a bounded number of times with no repetitions in the statistics. Simulation results are given which illustrate the benefits of using our algorithms, both in terms of probability of error and in terms of redundancy.