*In the above communication system, if What governs ?*

Since AEP states,

*n*and taking antilog (log

*a*= log

_{2}

*a*⇒ for log

_{2}

*a*=

*c*,

*a*= 2

^{c}), we get

*⊂*

^{n}A_{ε}*such that*

^{n}X_{C}
Therefore, if *x ^{n}* ∈

^{n}A_{ε}*is the set of*

^{n}A_{ε}*x*for which lies within ±ε of the entropy

^{n}*H*(

*X*). ❶

**How typical**is the typical set^{n}A_{ε}?
It is typical enough that, for sufficiently large *n*

**How big**is the typical set^{n}A_{ε}?The size of a typical set is given by

*| is the cardinality of*

^{n}A_{ε}*.*

^{n}A_{ε}
Note that if *H*(*X*) < log_{2}|*X*| where log_{2}|*X*| is the maximum possible entropy, then * ^{n}A_{ε}* will frequently be a small fraction of

*which accounts for most of the*

^{n}X_{C}*that are emitted. ❸*

^{n}X_{C}

**What is the number of data–bits**required to form a typical set^{n}A_{ε}?If,

*l*∕

*n*is the number of .

Therefore, if *x _{i}* are equally probably

Then

**not**possible. For data compression to be possible, it needs to be

*Next:*

Summary (p:3) ➽