I am stuck on formulating this optimization problem and would appreciate your thoughts on this.
A transmitter sends fixed data packet with $k$ bits of data. The cost of sending a data packet is $c$. I want to send $N$ bits of data. Each bit in the data packets has probability $p$ to be accepted or rejected. After each transmission I will know which bits have been successfully transmitted and accepted (and their locations too), and then I will re-transmit the remaining fragment of data bits in sequence again in another packet. What would be the expected number of packets for transmitting $N$ bits?
Any idea on how to model the problem? I am confused on whether this would be a case of a geometric distribution or beta distribution. Thanks.