V.34/28.8k and 33.6k

Any interest in these systems was destroyed during the lengthy introduction of the 28,800 bit/s V.34standard. 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.

Today, 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 4 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 \scriptstyle Bandwidth * log_2 (1 + P_u/P_n), with \scriptstyle P_u/P_n the signal-to-noise ratio. Narrowband phone lines have a bandwidth from 300-3,100 Hz, so using \scriptstyle P_u/P_n=10,000: capacity is approximately 35 kbit/s.

Without the discovery and eventual application of trellis modulation, maximum telephone rates would have been limited to 3,429 baud * 4 bit/symbol == approximately 14 kbit/s using traditional QAM.

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