In this paper, we propose a new probabilistic decoding method for the measurement-while-drilling telemetry system. The mud pulse telemetry system transmits the data from inside a borehole to the surface during drilling operations. The mud pulser is equipped with a mechanical valve, which partly shuts the mud stream for a short time, realizing modulation. The system modulates the drilling mud in the well, creating pressure pulses, which are sampled on the pressure sensor at the surface pump and further decoded into digital data. In our method, each detected pulse is assigned with reliability, calculated from informative pulse measures (rising edge slope, duration and delay to the previous pulse). Knowing a set of possible information packet lengths and reliability for each detected pulse, one can apply softdecision decoding to extract information with higher probability. This approach is similar to the Viterbi soft decoder, but in our case information is not encoded. The algorithm was implemented and validated in real wells. Field tests demonstrate 32 percent reduction in packet error rate in the real-life well on the 8750 meters depth borehole.

Power circuits are data structures which support efficient algorithms for highly compressed integers. Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the one-relator Baumslag group is in P. Before that the best known upper bound was non-elementary. In the present paper we provide new results for power circuits and we give new applications in algorithmic group theory: 1. We define a modified reduction procedure on power circuits which runs in quadratic time thereby improving the known cubic time complexity. 2. We improve the complexity of the Word Problem for the Baumslag group to cubic time thereby providing the first practical algorithm for that problem. (The algorithm has been implemented and is available in the CRAG library.) 3. The main result is that the Word Problem of Higman's group is decidable in polynomial time. The situation for Higman's group is more complicated than for the Baumslag group and forced us to advance the theory of Power Circuits.