An apparatus for communicating signals from a well logging tool to a recording unit is disclosed. The logging tool includes a transmitter comprising a source of digital bits representing measurements made by the tool, an encoder connected to the source of digital bits for transforming groups of the digital bits into multivalued symbols, a first in-phase filter and a first quadrature filter connected to the encoder so that first coordinates of the symbols are filtered in the in-phase filter, second coordinates of the symbols are filtered in the quadrature filter, the filters having responses forming a Hilbert transform pair, a digital subtractor connected to the first filters for calculating a difference between outputs of the filters, and a digital-to-analog converter connected to the output of the subtractor for generating signals to be communicated to the recording unit over a communication channel.The recording unit includes a receiver comprising an analog-to-digital converter to receive and digitize signals from the communication channel, a second in-phase filter and a second quadrature filter connected to the analog-to-digital converter, the second filters respectively having substantially the same response characteristics as the first in-phase and quadrature filters, a decision feedback equalizer connected to the second filters for correcting timing and distortion errors in the signals from the logging tool and demodulating the multivalued symbols, and a decoder connected to the equalizer for converting demodulated multivalued symbols output from the equalizer into the groups of bits conducted to the encoder in the logging tool.