A novel general bit-error rate (BER) expression for one-dimensional constellations is developed. The BER analysis is performed for bit patterns that form a labeling. The number of patterns for equally spaced M-PAM constellations with different BER is analyzed. The paper proves the equivalence of the symbol-based demodulator (SD) and the approximate bit-based demodulator (ABD) in terms of uncoded BER for any constellation and labeling. This equivalence allows the study of the ABD for one-dimensional constellations. A novel ready-to-use BER expression is introduced for any one-dimensional constellation and binary labeling. The analysis is performed for bit-patterns that form a labeling. The BER for a given labeling is expressed as an average of the BER for each bit position. The BER for the ABD and an M-PAM constellation with any labeling is derived. The paper generalizes this result to non-equally spaced constellations and derives a general BER expression for any one-dimensional constellation. The number of classes of patterns for M-PAM is derived, where each class has identical BER. The number of classes is given by a closed-form expression. The paper also presents the BER for different labelings of 4-PAM and 8-PAM, showing that the BER depends on the labeling. The results show that the BER for different labelings can be grouped into classes with identical BER at high SNR. The paper concludes that a general expression for the uncoded BER of one-dimensional constellations has been introduced, and a classification of patterns for equally spaced M-PAM constellations has been performed. The rule for combining patterns into a labeling remains for future investigation.A novel general bit-error rate (BER) expression for one-dimensional constellations is developed. The BER analysis is performed for bit patterns that form a labeling. The number of patterns for equally spaced M-PAM constellations with different BER is analyzed. The paper proves the equivalence of the symbol-based demodulator (SD) and the approximate bit-based demodulator (ABD) in terms of uncoded BER for any constellation and labeling. This equivalence allows the study of the ABD for one-dimensional constellations. A novel ready-to-use BER expression is introduced for any one-dimensional constellation and binary labeling. The analysis is performed for bit-patterns that form a labeling. The BER for a given labeling is expressed as an average of the BER for each bit position. The BER for the ABD and an M-PAM constellation with any labeling is derived. The paper generalizes this result to non-equally spaced constellations and derives a general BER expression for any one-dimensional constellation. The number of classes of patterns for M-PAM is derived, where each class has identical BER. The number of classes is given by a closed-form expression. The paper also presents the BER for different labelings of 4-PAM and 8-PAM, showing that the BER depends on the labeling. The results show that the BER for different labelings can be grouped into classes with identical BER at high SNR. The paper concludes that a general expression for the uncoded BER of one-dimensional constellations has been introduced, and a classification of patterns for equally spaced M-PAM constellations has been performed. The rule for combining patterns into a labeling remains for future investigation.