A variable-length channel quantizer for multicast networks with two users

We investigate the channel quantization problem for two-user multicast networks where the transmitter is equipped with multiple antennas and either receiver is equipped with only a single antenna. Our goal is to design a global quantizer to minimize the outage probability. It is known that any fixed-length quantizer with a finite-cardinality codebook cannot achieve the same minimum outage probability as the case where all nodes in the network know perfect channel state information (CSI). To achieve the minimum outage probability, we propose a variable-length global quantizer that knows perfect CSI and sends quantized CSI to the transmitter and receivers. With a random infinite-cardinality codebook, we prove that the proposed quantizer is able to achieve the minimum outage probability with a low average feedback rate. Numerical simulations also validate our theoretical analysis.