$5\mathrm{.}5.$ 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 numbers are produced: b$0=0$ bm $=1$am $+$ bm$-12$mod $2$ These are then encoded as cm $=$ bm$-$ bm$-1$ On reception, the original data are recovered by am $=$ cm mod $2$ a$.$ Verify that the received values of am equal the transmitted values of am$.$ b$.$ What sort of encoding is this?