a practical method of adapting trellis encoding for the downstream signal on pcm modems the trellis encoder described is simply the v 34 adapted for 1d symbols it describes improvements the receiver can make to make the trellis decoding less sensitive to the proportionally spaced pcm coded symbols it also describes the effect low and high noise signals has on the use of trellis encoding coding gain for pcm coded symbol the incorporation of trellis encoding has significant advantages for high noise signals and as such should be incorporated into the pcm modem specification because of its small benefits for low noise signals though the specification should allow the negotiation of no trellis encoding the pcm receiver should determine the acceptability of using trellis encoding a recursive process in accordance with an embodiment of the invention is shown in fig2 making reference to fig1 which shows an information processing system in a 1d trellis encoding device in accordance with the foregoing description in the process illustrated in fig2 a transmit output is assigned 100 to a transmit symbol concurrently a subset label is assigned 110 to the transmit symbol n 1 subset labels are stored 120 for n 1 transmit symbols thus an nth transmit symbol is formed 130 such that an associated nth subset label is partially determined by a combination of an output of an error reduction correction algorithm and said n 1 stored subset labels the transmit symbols.