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

Unequal Error Protection Achieves Threshold Gains on BEC and BSC via Higher Fidelity Messages