abstract systems and methods are disclosed for communicating signals by receiving a k symbol long input block from a 2 m ary source channel encoding the input block into a 2 m ary non binary low density parity check codeword of length n and mapping each 2 m ary symbol to a point in a signal constellation comprised of 2 m points wherein a non binary ldpc code is used as the component code for forward error correction in a coded modulation scheme capable of achieving optical fiber communication at rates beyond 100 gb s application_number US 201213441808 A description fig1 a shows an exemplary transmitter configuration of a system using 4d nb ldpc cm scheme a 2 m ary source channel provides inputs to a 2 m ary low density parity check ldpc encoder 102 the output of the encoder 102 is provided to a mapper 104 that drives a modulator 106 fig1 b shows an exemplary receiver configuration of a system using 4d nb ldpc cm scheme a coherent detector 120 receives signals from a fiber and drives a maximum a posteriori map detector 122 the output of the map detector 122 in turn is provided to the 2 m ary low density parity check ldpc decoder 124 corresponding to the encoder 102 at the transmitter the transmitter and receiver configurations and the operating principles of the proposed scheme can be described as follows first of all a 2 m ary m gt 1 ldpc n k code is an.