Shuffle Exchange Network and de Bruijn’s Graph Shuffle Exchange graph Merge exchange into a single node De Bruijn Graph (label: shift left and add the label)

Same Graph, Another labeling on edges node x 1 x 0  x 0 (x 1  label)

 f f is either 0 or 1 For 0: shift 1: complement Note that each complete cycle of shift register corresponds to a HC of de Bruijns Graph

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 Shift Register => DeBruijn sequence  x 3 + x + 1 is irreducible x 3 + x is irreducible

 Shift Register => degenerated cycle x 3 + x 2 + x + 1 ? = (x 2 +1)(x+1) not irreducible 

 For 4 bit

Cycle decomposition based n   101  010

Conventional labeling