Noise-reducing codes for pulse-code modulation

Theory shows that a simple binary pulse-code modulation system does not make the maximum use of a communication channel of given bandwidth and signal/noise ratio. It is suggested that an improvement in output signal/noise ratio can be obtained by modifying the binary code so that errors in its different digits contribute equal amounts of noise power to the output. The noise contributions of the digits can be equalized by using a greater number of pulses to transmit the more significant digits. However, the resulting increase in bandwidth introduces additional noise which more than offsets the reduced error liability of the digits and so causes a worsening of the output signal/noise ratio. An attempt to equalize the noise contributions of the digits by using a code with a different base for each digit also fails. It is possible to make the digits of a binary code group contribute equally to the output noise by varying the pulse height or length from digit to digit. An improvement in output signal/noise ratio is then obtained over a range of input signal/noise ratios. The system using pulses of different heights is less complicated than that using different pulse lengths; however, it is more complex than a system using the simple binary code, and it is doubtful if the improvement in signal/noise ratio justifies the additional complexity.