Operating LDPC codes with zero shaping gap

Unequal transition probabilities between input and output symbols, input power constraints, or input symbols of unequal durations can lead to non-uniform capacity achieving input distributions for communication channels. Using uniform input distributions reduces the achievable rate, which is called the shaping gap. Gallager´s idea for reliable communication with zero shaping gap is to do encoding, matching, and jointly decoding and dematching. In this work, a scheme is proposed that consists in matching, encoding, decoding, and dematching. Only matching is channel specific whereas coding is not. Thus off-the-shelf LDPC codes can be applied. Analytical formulas for shaping and coding gap of the proposed scheme are derived and it is shown that the shaping gap can be made zero. Numerical results show that the proposed scheme allows to operate off-the-shelf LDPC codes with zero shaping gap and a coding gap that is unchanged compared to uniform transmission.