of multisets and sequences of letters of size $n$ drawn from an alphabet $\mathcal{X}$. When $\mathcal{X}$ is discrete, we take it to be the (possibly-infinite) set $\{1,\,2,\,\ldots,|\mathcal{X}|\}$ without loss of generality. In addition to standard uses of parentheses, we will also use parentheses and braces to distinguish between sequences and multisets. For the ordered sequence $X_1,\,X_2,\,\ldots,\,X_n$ that is often denoted $X_1^n$ in the information theory literature, we write $(X_i)_{i=1}^n$. When these $n$ symbols are taken as an unordered multiset, we write $\{X_i\}_{i=1}^n$. The range limits are often omitted. We will refer to the distribution that describes $(X_i)_{i=1}^n$ as the parent distribution.

There are two perspectives that can be taken to relate (order-irrelevant) source coding of $\{X_i\}_{i=1}^n$ with (standard) source coding of $(X_i)_{i=1}^n$. In either case we take the sample space $\Omega$ to be the set of all sequences $\mathcal{X}^n$. Under the first perspective, which we take when discussing lossless coding, we define the event algebra, $\mathcal{F}$, based on permutation-invariant equivalence classes of sequences, rather than the sequences themselves. Since events are defined in terms of multisets, the source coding problem is formally no different than the standard one, though the results are interestingly different.

For lossy coding, we take an 