With the probability of that sequence occurring, and summing over all four possible sequences:ĪverageBitsPerSequence =&\, P(HH) \times 1 \text \, + \\
#Digital coin flip code#
We can now calculate how many bits we need to send, on average, per coin flip, by multiplying each sequence's code length Applying the standard Huffman coding scheme we obtain these Huffman coding assigns a code to each sequence such that more probable (frequent) sequences are assigned shorter codes, in anĪttempt to reduce the number of bits we need to send on average. In our example B=`3/4`, and we will consider sequences of just two coin flips hence there are just four possible sequences.
Is given by the following equation (from Estimating a Biased Coin):
The probability of any given coin flip sequence S consisting of h head and t tail flips, and for a coin with bias B, Optimal and the simpler but generally less efficient Huffman coding. On average per flip, most notably Arithmetic coding, which is near the receiverĬan produce an infinite sequence of coin flips that exactly match the actual coin.įor values of B other than 0, 1 and 0.5 there exist schemes for communicating our sequence of coin flips with less than one bit If B is exactly 0 or 1 then no bits need to be transmitted at all i.e. a fair coin) then both outcomes are equally likely and it is still necessary to If B is known and is exactly one half (i.e. Note that this method works regardless of the value of B, and therefore B does not need to be known to the We can represent the outcome of each flip with a binary 1 (heads) or 0 (tails), therefore on average it takes one bit of information (known as the Bernoulli process) and transmit each outcome to a reciever. To identify random samples from that distribution.Ĭonsider a coin with probability B (for bias) of flipping heads. Shannon entropy is defined for a given discrete probability distribution it measures how much information is required, on average,
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