This work considers optimizing LDPC codes in the physical-layer network codedtwo-way relay channel using noncoherent FSK modulation. The error-rateperformance of channel decoding at the relay node during the multiple-accessphase was improved through EXIT-based optimization of Tanner graph variablenode degree distributions. Codes drawn from the DVB-S2 and WiMAX standards wereused as a basis for design and performance comparison. The computationalcomplexity characteristics of the standard codes were preserved in theoptimized codes by maintaining the extended irregular repeat-accumulate (eIRA).The relay receiver performance was optimized considering two modulation ordersM = {4, 8} using iterative decoding in which the decoder and demodulator refinechannel estimates by exchanging information. The code optimization procedureyielded unique optimized codes for each case of modulation order and availablechannel state information. Performance of the standard and optimized codes weremeasured using Monte Carlo simulation in the flat Rayleigh fading channel, anderror rate improvements up to 1.2 dB are demonstrated depending on systemparameters.
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