The outer convolutional coding of the signals used to transmit mobile-handheld (M/H) service data within digital-television (DTV) signals is subjected to anti-Gray coding, either before or after its interleaving, but before its inner convolutional coding. In a receiver for such M/H-service data, portions of the trellis decoded DTV signal containing soft decisions concerning symbol-interleaved convolutionally coded M/H-service data are recoded for a Gray-code mapping of symbols to modulation levels. This is done either before or after symbol de-interleaving, but before decoding the outer convolutional coding. Soft decisions concerning extrinsic information to be fed back to the ⅔ trellis decoder to close a turbo decoding loop are derived from soft decisions as to the M/H-service data, which derivation includes re-coding for a binary-code mapping of symbols to modulation levels. Each re-coding procedure can be performed using ROM, but preferably is performed using simple digital logic.