A deletion channel is a communications channel model used in coding theory and information theory. In this model, a transmitter sends a bit (a zero or a one), and the receiver either receives the bit (with probability p {displaystyle p} ) or does not receive anything without being notified that the bit was dropped (with probability 1 − p {displaystyle 1-p} ). Determining the capacity of the deletion channel is an open problem. A deletion channel is a communications channel model used in coding theory and information theory. In this model, a transmitter sends a bit (a zero or a one), and the receiver either receives the bit (with probability p {displaystyle p} ) or does not receive anything without being notified that the bit was dropped (with probability 1 − p {displaystyle 1-p} ). Determining the capacity of the deletion channel is an open problem. The deletion channel should not be confused with the binary erasure channel which is much simpler to analyze. Let p {displaystyle p} be the deletion probability, 0 < p < 1 {displaystyle 0<p<1} . The iid binary deletion channel is defined as follows: Given a input sequence of n {displaystyle n} bits ( X i ) {displaystyle (X_{i})} as input, each bit in X n {displaystyle X_{n}} can be deleted with probability p {displaystyle p} . The deletion positions are unknown to the sender and the receiver. The output sequence ( Y i ) {displaystyle (Y_{i})} is the sequence of the ( X i ) {displaystyle (X_{i})} which were not deleted, in the correct order and with no errors. The capacity of the binary deletion channel (as an analytical expression of the deletion rate p {displaystyle p} ) is unknown. It has a mathematical expression. Several upper and lower bounds are known.