Analog network coding (ANC) is a throughput increasing technique for the two-way relay channel (TWRC) whereby two end nodes transmit simultaneously to a relay at the same time and band, followed by the relay broadcasting the received sum of signals to the end nodes. Coherent reception under ANC is challenging due to requiring oscillator synchronization for all nodes, a problem further exacerbated by Doppler shift. This work develops a noncoherent M-ary frequency-shift keyed (FSK) demodulator implementing ANC. The demodulator produces soft outputs suitable for use with capacity-approaching channel codes and supports information feedback from the channel decoder. A unique aspect of the formulation is the presence of an infinite summation in the received symbol probability density function. Detection and channel decoding succeed when the truncated summation contains a sufficient number of terms. Bit error rate performance is investigated by Monte Carlo simulation, considering modulation orders two, four and eight, channel coded and uncoded operation, and with and without information feedback from decoder to demodulator. The channel code considered for simulation is the LDPC code defined by the DVB-S2 standard. To our knowledge this work is the first to develop a noncoherent soft-output demodulator for ANC.