A desired information stream is recovered from a pair of independent bitstreams transmitted using quadrature modulation. One of the independent bitstreams is altered by an invertible alteration function prior to transmission. The quadrature modulated bitstreams are demodulated at a receiver to provide a demodulated I bitstream and a demodulated Q bitstream. One of the demodulated I and Q bitstreams is tentatively provided for decoding. The tentatively provided bitstream can be optionally inverted. One of the tentatively provided bitstream and the optionally inverted bitstream is decoded if it is desired to recover the bitstream that was not altered by the alteration function prior to transmission. One of the tentatively provided bitstream and the optionally inverted bitstream is decoded after applying the inverse of the alteration function thereto if it is desired to recover the bitstream that was altered by the alteration function prior to transmission. An error rate of data decoded during the decoding step is determined. If the error rate is not acceptable, different choices of the demodulated I and Q bitstreams with and without inversion are tried until an acceptable error rate is obtained.