Patent ID: 6993098

Claim:
An apparatus comprising: means for receiving an (x,y) coordinate of a modulated signal; means for determining a first value according to an equation −2x(Î i −Î j ), wherein Î i is an I component of a first symbol closest to the (x,y) coordinate and Î j is the I component of a second symbol closest to the (x,y) coordinate with a bit value opposite of the corresponding bit value of the first symbol; means for determining a second value according to an equation 2y({circumflex over (Q)} i −{circumflex over (Q)} j ), wherein {circumflex over (Q)} i is Q component of the first symbol and {circumflex over (Q)} j is the Q component of the second symbol; means for determining a third value equivalent to the sum of A 0 (Î i 2 +{circumflex over (Q)} i 2 ) and −A 0 (Î j 2 +{circumflex over (Q)} j 2 ), wherein A 0 is a minimum amplitude; means for determining a log-likelihood ratio (LLR) as a sum of the first value, the second value, and the third value; and means for transmitting the LLR to a decoder.