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The output of pulse code modulation (PCM) encoder is statistically described; this description is used at the receiver to reduce the error of the received signal. Recently, PCM is the most important form of pulse modulation. Bit errors occur at the transmission of information through the communication system and the amount of error depends on the characteristics of the channel. In this paper, the voice message is sampled greater than Nyquist rate and quantized with scalar quantizer, then the quantized levels are encoded with resolution B bits assigned to each level. The binary data are mapped and transmitted over Gaussian noise channel. The system was designed without channel coding. At the receiver the statistical description is exploited to conceal the errors. The results show that a significant improvement gained in bit error rate that was reduced from 0.078 to 0.052 at 0 dB of E_b⁄N_0 by soft decoding, compared to hard decoding.

PCM --- Source Coding --- Hard Decoding --- Soft Decoding --- and MAP estimation.