Rapid Encoding of Run Lengths and Pyramid Cubic Lattices

We can encode rare events with overhead about 1.56 bits/event. The contribution of the overhead to the total length of the code is negligible. The encoding and decoding time counted in operations over bits per bit of the code does not depend on the number of appearances of the events. We present also algorithms of the same speed which enumerate the pyramid cubic lattices with overhead about 1.56 bits/dimension. The overhead is the pay for reaching the ultimate (to within a constant factor) encoding and decoding speed.