Consider the following signal encoding technique. Binary data are presented as input, am$,$ for m $=1,2,3,....$ Two levels of processing occur. First, a new set of binary num$-$

bers are produced:

b$0=0$

b$=1$a$+$b $2$mod$2$ m m m$-1$

These are then encoded as

cm $=$bm $-$bm$-1$

On reception, the original data are recovered by am $=$ cm mod $2$

Verify that the received values of am equal the transmitted values of am$.$

What sort of encoding is this?