passband transmission case, a signal with passband bandwidth W can be converted to an equivalent baseband signal (using undersampling or a superheterodyne receiver), with upper cut-off frequency W/2. If double-sideband modulation schemes such as QAM, ASK, PSK or OFDM are used, this results in a maximum symbol rate of W symbols/s, and in that the modulation efficiency can not exceed N (bit/s)/Hz. If digital single-sideband modulation is used, the passband signal with bandwidth W corresponds to a baseband message signal with baseband bandwidth W, resulting in a maximum symbol rate of 2W and an attainable modulation efficiency of 2N (bit/s)/Hz. Example 3: A 16QAM modem has an alphabet size of M = 16 alternative symbols, with N = 4 bit/symbol or bpcu. Since QAM is a form of double sideband passband transmission, the spectral efficiency cannot exceed N = 4 (bit/s)/Hz. Example 4: The 8VSB (8-level vestigial sideband) modulation scheme used in the ATSC digital television standard gives N=3 bit/symbol or bpcu. Since it can be described as nearly single-side band, the modulation efficiency is close to 2N = 6 (bit/s)/Hz. In practice, ATSC transfers a gross bit rate of 32 Mbit/s over a 6 MHz wide channel, resulting in a modulation efficiency of 32/6 = 5.3 (bit/s)/Hz. Example 5: The downlink of a V.92 modem uses a pulse-amplitude modulation with 128 signal levels, resulting in N = 7 bit/symbol. Since the transmitted signal before passband filtering can be considered as baseband transmission, the spectral efficiency cannot exceed 2N = 14 (bit/s)/Hz over the full baseband channel (0 to 4 kHz). As seen above, a higher spectral efficiency is achieved if we consider the smaller passband bandwidth. If a forward error correction code is used, the spectral efficiency is reduced from the uncoded modulation efficiency figure. Example 6: If a forward error correction (FEC) code with code rate 1/2 is added, meaning that the encoder input bit rate is one half the encoder output rate, the spectral efficiency is 50% of the modulation efficiency. In exchange for this reduction in spectral efficiency, FEC usually reduces the bit-error rate, and typically enables operation at a lower signal-to-noise ratio (SNR). An upper bound for the spectral efficiency possible without bit errors in a channel with a certain SNR, if ideal error coding and modulation is assumed, is given by the Shannon–Hartley theorem. Example 7: If the SNR is 1, corresponding to 0