Transition probabilities of coded BPSK signals for hard-decision decoding with k-bit CSI in Nakagami-m fading channels

We evaluate a closed form expression of the transition probabilities used for calculating metric values and pairwise error probabilities of convolutional codes, equipped with coherent BPSK signals, for hard-decision decoding with k-bit channel state information (CSI) in slow varying frequency nonselective Nakagami-m fading channels. It's noted that 1-bit CSI is sufficient to take advantage of channel information tinder deep fadings.