After a study, it was determined that it is necessary to change the forward error correction scheme to a new one that is non$-$systematic.

For this new scheme, specific properties are required that are obtained by transforming the previous encoder, where:

The first column of G corresponds to the first column of the identity matrix.

Columns $2$ and $3$ of G correspond to the first columns of the parity matrix.

Columns $4$ and $5$ of G correspond to columns $2$ and $3$ of the identity matrix.

Column $6$ of G is the last column of the parity matrix.

Column $7$ is the last column of the identity matrix.

The new matrix H is formed from the matrix of the systematic code by executing the same permutations of columns that were applied in G$.$

After a study, it was determined that it is necessary to change the forward error correction scheme to a new one that is non$-$systematic.

For this new scheme, specific properties are required that are obtained by transforming the previous encoder, where:

The first column of G corresponds to the first column of the identity matrix.

Columns $2$ and $3$ of G correspond to the first columns of the parity matrix.

Columns $4$ and $5$ of G correspond to columns $2$ and $3$ of the identity matrix.

Column $6$ of G is the last column of the parity matrix.

Column $7$ is the last column of the identity matrix.

The new matrix H is formed from the matrix of the systematic code by executing the same permutations of columns that were applied in G$.$

Considering the new non$-$systematic encoder, what is the channel coding obtained if the bit sequence $11000011$ is obtained at the output of the source encoder?

The coded sequences are: Answer

and Response

$.$

Note: You must place them in the same order as they were received.

Considering the matrix H of the non$-$systematic encoder above, what would be the sequence of bits that would be delivered to the source decoder if the sequence $00010111010110$ is received?

The decoded sequences are: Answer

and Response

$.$

Note: You must place them in the same order as they were received.