Constraint gain

In digital storage systems where the input to the noisy channel is required to satisfy a modulation constraint, the constrained code and error-control code (ECC) are typically designed and decoded independently. The achievable rate for this situation is evaluated as the rate of average intersection of the constraint and the ECC. The gap from the capacity of the noisy constrained channel is called the constraint gain, which represents the potential improvement in combining the design and decoding of the constrained code and the ECC. The constraint gain is computed for various constraints over the binary-input additive white Gaussian noise (AWGN) channel (BIAWGNC) as well as over intersymbol interference (ISI) channels. Finally, it is shown that an infinite cascade of reverse concatenation with independent decoding of constraint and ECC has a capacity equal to the rate of average intersection.