Modem

Any interest in these proprietary improvements was destroyed during the lengthy introduction of the 28,800 bit/s V.34 standard. While waiting, several companies decided to release hardware and introduced modems they referred to as V.FAST. In order to guarantee compatibility with V.34 modems once the standard was ratified (1994), the manufacturers were forced to use more flexible parts, generally a DSP and microcontroller, as opposed to purpose-designed ASIC modem chips.
The ITU standard V.34 represents the culmination of the joint efforts. It employs the most powerful coding techniques including channel encoding and shape encoding. From the mere four bits per symbol (9.6 kbit/s), the new standards used the functional equivalent of 6 to 10 bits per symbol, plus increasing baud rates from 2,400 to 3,429, to create 14.4, 28.8, and 33.6 kbit/s modems. This rate is near the theoretical Shannon limit. When calculated, the Shannon capacity of a narrowband line is ${\displaystyle \text{bandwidth}\times {\log }_2(1+P_u/P_n)}$, with ${\displaystyle P_u/P_n}$ the (linear) signal-to-noise ratio. Narrowband phone lines have a bandwidth of 3,000 Hz so using ${\displaystyle P_u/P_n=1000}$ (SNR = 30 dB), the capacity is approximately 30 kbit/s.^[3]
Without the discovery and eventual application of trellis modulation, maximum telephone rates using voice-bandwidth channels would have been limited to 3,429 baud × 4 bit/symbol = approximately 14 kbit/s using traditional QAM.