Asymptotic MAP upper bounds for LDPC codes

This paper aims at computing tight upper bounds for the maximum a posteriori threshold of low-density parity check codes in the asymptotic blocklength regime for the transmission over binary-input memoryless symmetric-output channels. While these bounds are already known, we propose a novel derivation based on a completely different approach: based solely on the concept of the chain rule and the conditional entropy, resorting to the concentration theorem for the code ensemble to compute the syndrome entropy with low complexity employing density evolution.