  Because of their capacity-approaching performance, graph-based codes have a
wide range of applications, including communications and storage. In these
codes, unequal error protection (UEP) can offer performance gains with limited
rate loss. Recent empirical results in magnetic recording (MR) systems show
that extra protection for the parity bits of a low-density parity-check (LDPC)
code via constrained coding results in significant density gains. In
particular, when UEP is applied via more reliable parity bits, higher fidelity
messages of parity bits are spread to all bits by message passing algorithm,
enabling performance gains. Threshold analysis is a tool to measure the
effectiveness of a graph-based code or coding scheme. In this paper, we provide
a theoretical analysis of this UEP idea using extrinsic information transfer
(EXIT) charts in the binary erasure channel (BEC) and the binary symmetric
channel (BSC). We use EXIT functions to investigate the effect of change in
mutual information of parity bits on the overall coding scheme. We propose a
setup in which parity bits of a repeat-accumulate (RA) LDPC code have lower
erasure or crossover probabilities than input information bits. We derive the
a-priori and extrinsic mutual information functions for check nodes and
variable nodes of the code. After applying our UEP setup to the information
functions, we formulate a linear programming problem to find the optimal degree
distribution that maximizes the code rate under the decoding convergence
constraint. Results show that UEP via higher fidelity parity bits achieves up
to about $17\%$ and $28\%$ threshold gains on BEC and BSC, respectively.
