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A channel-coded physical-layer network coding strategy is refined for practical operation. The system uses frequency-shift keying (FSK) modulation and operates noncoherently, providing advantages over coherent operation: there are no requirements for perfect power control, phase synchronism, or estimates of carrier-phase offset. In contrast with analog network coding, which relays received analog signals plus noise, the system relays digital network codewords, obtained by digital demodulation and channel decoding at the relay. The emphasis of this paper is on the relay receiver formulation. Closed-form expressions are derived that provide bitwise log-likelihood ratios, which may be passed through a standard error-correction decoder. The role of fading-amplitude estimates is investigated, and an effective fading-amplitude estimator is developed. Simulation results are presented for a Rayleigh block-fading channel, and the influence of block length is explored. An example realization of the proposed system demonstrates a 32.4% throughput improvement compared to a similar system that performs network coding at the link layer. By properly selecting the rates of the channel codes, this benefit may be achieved without requiring an increase in transmit power.