K Distribution

Definition

A sequence $x_i$ of period $P$ is $k$-distributed to $v$-bit accuracy if:

• The series $({\text{trunc}}_v(x),\dots ,{\text{trunc}}_v(x_{i+k+1}))$ for $0\le i<P$ has each combination of bits ($2^{kv}$ total) occur the same number of times (except for the all-zero combination)
• Where ${\text{trunc}}_v(x)$ is the Truncation Function

Intuition

Taking the v-bit truncations of each element of the stream and plotting it out in a distribution, allows Uniform Continuous Probability Distribution