Recently, the syndrome loss has been proposed to achieve "unsupervised learning" for neural network-based BCH/LDPC decoders. However, the design approach cannot be applied to polar codes directly and has not been evaluated under varying channels. In this work, we propose two modified syndrome losses to facilitate unsupervised learning in the receiver. Then, we first apply it to a neural network-based belief propagation (BP) polar decoder. With the aid of CRC-enabled syndrome loss, the BP decoder can even outperform conventional supervised learning methods in terms of block error rate. Secondly, we propose a jointly optimized syndrome-enabled blind equalizer, which can avoid the transmission of training sequences and achieve global optimum with 1.3 dB gain over non-blind minimum mean square error (MMSE) equalizer.