An ISA modem manufactured to conform to the V.34 protocol.

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In 1980, Gottfried Ungerboeck from IBM Zurich Research Laboratory applied channel coding techniques to search for new ways to increase the speed of modems. His results were astonishing but only conveyed to a few colleagues.[2] In 1982, he agreed to publish what is now a landmark paper in the theory of information coding.[citation needed] By applying parity check coding to the bits in each symbol, and mapping the encoded bits into a two-dimensional diamond pattern, Ungerboeck showed that it was possible to increase the speed by a factor of two with the same error rate. The new technique was called mapping by set partitions, now known as trellis modulation.
Error correcting codes, which encode code words (sets of bits) in such a way that they are far from each other, so that in case of error they are still closest to the original word (and not confused with another) can be thought of as analogous to sphere packing or packing pennies on a surface: the further two bit sequences are from one another, the easier it is to correct minor errors.
V.32bis was so successful that the older high-speed standards had little to recommend them. USR fought back with a 16,800 bit/s version of HST, while AT&T introduced a one-off 19,200 bit/s method they referred to as V.32ter, but neither non-standard modem sold well.
V.34/28.8k and 33.6k[edit source | editbeta]


An ISA modem manufactured to conform to the V.34 protocol.
Any interest in these systems 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.
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 \text{bandwidth} \times \log_2 (1 + P_u/P_n), with P_u/P_n the (linear) signal-to-noise ratio. Narrowband phone lines have a bandwidth of 3000 Hz so using P_u/P_n=1000 (SNR = 24 dB), the capacity is approximately 24 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