Patent ID: 7469373

Claim:
A method of detecting and correcting data bit errors in one or more received codewords transmitted through a communication channel comprising: first processing said one or more received codewords using a symbol detector; generating an output from said symbol detector; and second processing said output using a detector having 2 t states, said communication channel providing no intersymbol interference, said output comprising a hard decision output, ν, wherein v = arg ⁢ ⁢ max x ∈ { 0 , 1 } χ ⁢ ⁢ log ⁢ ⁢ P ⁡ ( ξ ⁢ ❘ ⁢ x ) = argmax x ∈ { 0 , 1 } χ ⁢ ∑ i = 1 i = χ ⁢ log ⁢ ⁢ P ( ξ i ⁢ ❘ ⁢ x i ) , said detector providing a soft decision output, log P(ξ i |ν i )−log P(ξ i | ν i ), for i=1, . . . , χ, said log P(ξ i |ν i )−log P(ξ i | ν i ), for i=1, . . . , χ equating to −(χ i |ν i ) 2 +(χ i − ν i ) 2 if noise added to said communication channel is additive white Gaussian, said detector using said hard and said soft decision outputs to correct said one or more received codewords, wherein a linear operator, Φ:{0,1} χ →{0,1} t , computes the parity syndrome value of said hard decision output such that Φ(Ε):=Φ(e 1 )⊕Φ(e 2 )⊕ . . . ⊕Φ(e n )=π, wherein the sum of the event weights represented by a set of error events associated with said parity syndrome value has a minimum value.