New compression schemes for natural number sequences

Sapir Asraf, Yoav Gross, Shmuel Tomi Klein, Rivka Revivo, Dana Shapira

Abstract: 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 Cγ or Cδ 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.