We introduce a new graph parameter called generalized lettericity as a generalization of the lettericity parameter that was introduced two decades ago. Given a word $$w=w_1w_2\cdots w_n$$ of length $$|w|=n$$ over a finite alphabet  $$\varSigma $$ and a decoder set  $$\mathcal {D}$$ of words over  $$\varSigma $$ with length at least 2, we define a generalized letter graph $$G(\mathcal {D},w)$$ with respect to $$\mathcal {D}$$ and w. $$G(\mathcal {D},w)$$ has vertex set [n] and there is an edge between $$i