LDPC codes satisfying the (0,k) constraint

In this paper, we use a stochastic expectation-maximization method to illustrate how to come close to achieving the capacity of the noisy (0,k) constrained additive white Gaussian noise (AWGN) channels. We use the bit-flipping-based constrained coding system proposed by Vasic and Pedagani, to transmit (0,k) constrained low-density parity check (LDPC) codewords over an AWGN channel. In the original approach of Vasic and Pedagani, if the number of flipped bits is large, the message-passing decoder of the LDPC codes fails to correct all the errors, and the system is prone to an error floor. We propose a flip decoder that exploits the information from the message-passing decoder to correct the flipped bits. We illustrate that the message-passing decoder and the flip decoder together correct both the channel and flip errors and achieve rates close to the noisy (0,k) channel capacity.