Apparatus and method for designing codes by using polar and algebraic codes

An apparatus for designing a code, the apparatus comprising:

• a transceiver;
• and
• a controller that is operatively connected to the transceiver, wherein the controller is configured to:
• receive an information signal to be transmitted;
• identify a polar code defined as at least one information set,
• identify a parity matrix of the polar code,
• identify a vector corresponding to the polar code where the vector is related to at least one binarization vector corresponding to at least one exponent,
• identify a row that is representable in a way by linearly combining each row of the parity matrix among at least one row constituting the binarization matrix,
• identify a specific binarization matrix in which the representable row does not exist among at least one binarization matrix,
• generate a transformed parity matrix by adding the specific binarization matrix to the parity matrix,
• generate a pre-code corresponding to the transformed parity matrix,
• encode the information signal based on the generated pre-code and the polar code to generate an error-correction codeword, and
• control the transceiver to transmit the generated error-correction codeword over a communication channel.