Consider the repetition code R$25.$ One way of viewing this code is as a

concatenation of R$5$ with R$5.$ We first encode the source stream with

R$5,$ then encode the resulting output with R$5.$ We could call this code R$2\_5.$

This idea motivates an alternative decoding algorithm, in which we

decode the bits five at a time using the decoder for R$5$; then decode the

decoded bits from that first decoder using the decoder for R$5.$

Evaluate the probability of error for this decoder and compare it with the

probability of error for the optimal decoder for R$25.$

Do the concatenated encoder and decoder for R$2\_5$ have advantages over

those for R$25?$