Now the encoding of amplitudes in PCM is not linear. At low amplitudes an increment of 1 in the PCM byte value represents a much smaller increment (delta) in analog signal amplitude than would be the case if the amplitude being sampled were much higher. Thus for low amplitudes it's difficult to distinguish between adjacent byte values. To make it easier to do this (for 56k modems) certain PCM codes representing very low amplitudes are not used. This gives a larger delta between possible amplitudes and makes correct detection of them by your modem easier. Thus half of the amplitude levels are not used (in the downstream direction) by V.90 or V.92. This is tantamount to each symbol (valid amplitude level) representing 7 bits instead of 8. This is where 56k comes from: 7 bits/symbol x 8k symbols/sec = 56k bps. Of course each amplitude symbol is actually generated by 8-bits but only 128 bytes of the possible 256 bytes are actually used by the ISP sender. There is a code table mapping these 128 8-bit bytes to the 128 7-bit bytes. It's not just a simple mapping like ignoring the last bit. Thus to send 7 normal data bytes (8-bits) will take 8 of the above mentioned bytes.
But it's a little more complicated that this. If the line conditions are not nearly perfect or if the direction is upstream (V.92 only), then even fewer possible levels (symbols) are used resulting in speeds under 56k. Also due to US government rules prohibiting high power levels on phone lines, certain high amplitudes levels can't be used resulting in only about 53.3k at best for "56k" modems in the downstream direction.
Note that the digital part of the telephone network is bi-directional. Two such circuits are used for a phone call, one in each direction. For V.90, the 56k signal is only used in one of these directions: from your ISP to your PC (called the "downstream" direction). For this V.90, the other direction (upstream, from your home/office to the ISP) uses the conventional phase-amplitude modulation scheme with a maximum of 36.6kbps (and not 53.3kbps). For V.92, this upstream direction also uses the PCM method and supports up to 48 kbps. The analog portion of the circuit from your home/office to the nearest telephone Co. office was never intended to be bi-directional since it's only a single twisted pair. But due to sophisticated cancellation methods it's able to convey data simultaneously in both directions as explained in the next subsection. It's claimed that with V.92, it's almost impossible to get maximum thruput in both directions simultaneously due to the difficulties of bi-directional flow on a single circuit.
