New compression schemes for natural number sequences

Elias and Fano independently proposed a quasi-succinct representation for monotonic integer sequences. When the standard deviation is high, one may use the well known Elias C_γ or C_δ codes, or Fibonacci codes, instead of the Unary code of the original Elias–Fano method. In case the integers are similar, not necessarily forming a monotonic sequence, we propose to apply the Haar transform as a preprocessing stage to convert the input into a more compressible form. Experimental results support the additional savings achieved by using our method.