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The effect of digital errors in PCM encoded speech signals transmitted over a noisy channel is reduced by using soft decision demodulation at the receiver. The reliability information supplied by the soft decision demodulator is used to point out likely transmission errors, especially in the most significant PCM bits. When a likely transmission error is identified, the corresponding PCM word is rejected by the receiver and replaced by a predictor estimate or an interpolation estimate if delayed decisions are used. We have analyzed soft decision demodulation schemes for standard PCM encoded speech signals transmitted over the Gaussian channel with coherent PSK (phase shift keying). A signal to noise ratio gain in of the order of 1-2 dB is Obtained at low input signal levels. The gain depends on the performance of the predictor or, alternatively, the interpolator. No modifications of the transmitter are required to obtain this improvement. The suggested soft decision schemes are optional at the receiver. The comparisons are made with hard decision demodulation.