Combining soft-decision demodulation with bit erasure correction and weighting to reduce the effect of transmission errors in log-PCM

In the paper we analyse an improved soft-decision demodulation technique applied to ¿¿-law pulse code modulation (PCM). The PCM-encoded waveforms are transmitted over Gaussian and Rayleigh fading channels by means of coherent phase shift keying modulation. Received bits which are unreliable are identified by means of soft-decision demodulation and erased. Each bit in the PCM word is assigned its own erasure threshold. The thresholds are optimised and are thus theoretically determined as a function of input power level to the quantiser, channel type and signal/noise ratio, and the relative mean-square error power that occurs when a PCM word containing an erased bit is estimated by means of prediction or interpolation. The predicted or interpolated sample amplitude is used as an estimate of the missing speech amplitude. This procedure works well because of the redundancy in the decoded speech waveform. In previous work the estimate was used to replace the PCM word with an erased bit. In the present paper the estimate is used to decide the most likely value of the erased bit, thus correcting most of the erasures without introducing errors in the replaced word. The new soft demodulation algorithm performs significantly better than the previous one. A gain of several decibels in overall speech signal/noise ratio is typical both for Gaussian and Rayleigh fading channels. Compared to no soft demodulation, the improvement in required channel signal/noise ratio is up to about 4 dB for the Gaussian channel. The combination of bit-position weighting and soft demodulation is also analysed, as well as the combination of a PCM bit assignment more robust against transmission errors and soft demodulation. For both of these cases, the combined schemes yield improvements, but not as large as for unweighted transmission of the standard bit assignment plus the improvement of the weighting or the robust bit assignment.