A log-likelihood ratio (LLR) for a bit bi in a message is determined by generating a first term, including by summing LLRs corresponding to bits in a first codeword having a specified value. The first codeword has a corresponding first message and bit bi of the first message corresponds to a 0. A second term is generated, including by summing LLRs corresponding to bits in a second codeword having the specified value. The second codeword has a corresponding second message and bit bi of the second message corresponds to a 1. The LLR for bit bi in the message is generated based at least in part on the first term and the second term.