An ultrasonic element has a membrane formed as a thin walled portion of a substrate, on which a piezoelectric vibrator is formed. The receiver includes a zero-intermediate frequency converter for demodulating one of the plurality of multipath propagated signals to produce a demodulated signal; and a sampling module for sampling the demodulated signal. A parallel recursion unit is operative to recursively calculate a first plurality of parity check values for the message based on the intermediate vector and to recursively calculate a second plurality of parity check values for the message based on the intermediate vector.