A data shuffler apparatus for shuffling input bits includes a plurality of bit shufflers each inputting corresponding two bits x0 and x1 of the input bits and outputting a vector {x0′, x1′} such that a number of 1's at bit x0′ over time is within ±1 of a number of 1's at bit x1′. At least two 4-bit vector shufflers input the vectors {x0′, x1′}, and output 4-bit vectors, each 4-bit vector corresponding to a combination of corresponding two vectors {x0′, x1′} produced by the bit shufflers, such that the 4-bit vector shufflers operate on the vectors {x0′, x1′} in the same manner as the bit shufflers operate on the bits x0 and x1. The current state of the bit shufflers is updated based on a next state of the 4-bit vector shufflers.