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Faster-than-Nyquist signaling introduces intersymbol interference, but increases the bit rate while preserving the signaling bandwidth. For sinc pulses, it has been established that with a small increase in the signaling rate beyond the Nyquist rate, there is no reduction in the minimum Euclidean distance for binary signaling. We generalize these observations to the family of raised-cosine pulses. The structure of the error events that reduce the minimum distance is examined, and constrained coding ideas are suggested that theoretically allow even faster signaling. Then we propose ways of achieving these gains practically by designing appropriate constrained codes and through equalization and iterative joint equalization and decoding (turbo equalization).