ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV / Constrained codes also known as modulation codes are a key component in the digital magnetic recording systems. The constrained codes forbid particular input data patterns which lead to some of the dominant error events or higher media noise. In data recording systems, a concatenated approach toward the constrained code and error-correcting code (ECC) is typically used and the decoding is done independently. In this paper, we show the improvement in combining the decoding of the constrained code and the ECC using generalized belief propagation (GBP) algorithm. We consider the performance of a combined modulation constraints and the ECC on a binary symmetric channel (BSC). We show that combining demodulation and decoding results in a superior performance compared to concatenated schemes. Furthermore, we compute the capacity of the joint ECC and modulation codes for 1-D and 2-D constraints.