A method of encoding for optical transmission of information includes encoding information with a generalized low-density parity-check (GLDPC) code for providing coding gains, and constructing the GLDPC code with a Reed-Muller RM code as a component code, the component code being decodable using a maximum posterior probability (MAP) decoding. In a preferred embodiment, the GLDPC code includes a codeword length of substantially 4096, an information word length of substantially 3201, a lower-bound on minimum distance of substantially greater than or equal to 16, a code rate of substantially 0.78 and the RM component code includes an order of substantially 4 and an r parameter of substantially 6.