s well as the need to modu- late both data and voice for wireline and wireless transmission, let's end this digression and return to our discussion of the Nyquist relationship. MAXIMUM MODULATION RATE The Nyquist relationship states that the maximum rate at which data can be transmitted before one symbol interferes with another, a condition referred to as intersymbol inter- ference, must be less than or equal to twice the bandwidth in hertz. Understanding Light TABLE 2.5 Bit pair Phase change Potential Mapping of Bit Pairs into Phase Changes Because most transmission systems modulate or vary a signal, the Nyquist relationship limits the signaling rate, which is proportional to the available bandwidth. This explains why modem designers use differ- ent techniques to pack more bits into each baud to achieve a higher data transfer rate. Because the bandwidth of a telephone channel is fixed, a modem designer cannot exceed a given signaling rate before intersymbol interference adversely affects the data flow. Thus, to transmit more data, the modem designer must pack more bits into each signal change. In the telephone company infrastructure a bandwidth of 4 kHz is provided for a voice channel, which explains why the pulse-code modulation (PCM) sampling rate is 2 X 4 kHz or 8000 times per second. In addition to the Nyquist relationship which governs the signaling rate, there is a second constraint that limits the maximum achievable data rate obtainable on a copper transmission medium. That constraint is Shannon's law. SHANNON'S LAW In 1948, Professor Claude E. Shannon presented a paper concerning the relationship between coding and noise and com- puted the theoretical maximum bit rate capacity of a channel of band- width Win hertz as follows: where C = capacity in bits per second, bits/s W = bandwidth, Hz S = power of the transmitter N = power of thermal noise In 1948, a "perfect" telephone channel was considered to have an S/N ratio of 30 dB, which represents a value of 1000. The maximum data transmission for a telephon