Final answer:
The question deals with a repeat each-bit error-correction strategy for transmitting data over a Binary Symmetric Channel (BSC). It involves repeating each information bit multiple times to reduce errors, thereby lowering the data rate to R=1/2n.
Step-by-step explanation:
If we suppose R=1/2n for some integer n and consider a repeat each bit 2n times strategy for communicating over a Binary Symmetric Channel (BSC), we are discussing an error-correcting method used in digital communications. The rate R of a code is the ratio of the number of information bits to the total number of bits transmitted. When R is equal to 1/2n, it means that for every bit of information, 2n bits are being sent.
The repeat each bit 2n times strategy is a simple form of error correction where each bit is duplicated multiple times to reduce the chances of error during transmission.
In this context, the Binary Symmetric Channel is a theoretical model used to represent a communication channel with two possible input and output bits—0 and 1—and where the probability of a bit flip (an error) is the same for both bits. By repeating each bit 2n times, if there is an error in the transmission, the receiver can perform a majority rule decoding to determine the original bit. If more than half of the received bits are 1's, then the original bit is assumed to be a 1, and vice versa for 0.
This method significantly increases the probability of correct bit transmission at the cost of decreased data rate, which is expressed by the rate R.