alternative perspective where the event algebra is based on sequences. Order irrelevance is incorporated by considering fidelity criteria with a permutation-invariance property. These fidelity criteria cannot be stated in single-letter terms, thus calling the mathematical tractability into question. However, like the non-single-letter fidelity criteria in [@BergerY1972; @Kieffer1978b], our fidelity criteria are tractable and also bear semantic significance on several applications.

All logarithms use base 2, and all rates are thus given in bits. In this paper, rates are generally not normalized by the number of symbols $n$. The reason for this departure from convention will soon become clear: the total number of bits required in some problems scales sublinearly with $n$. We use standard asymptotic notation such as $o(\cdot)$, $O(\cdot)$, $\Omega(\cdot)$ and $\Theta(\cdot)$ [@OrlitskySVZ2006].

Outline
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The remainder of the paper is organized as follows. In Section \[sec:ordervalue\], we propose the transformation of a sequence into an order and a multiset of values, and we show that the order and values are independent when letters are produced i.i.d. Sections \[sec:entropyrate\] and \[sec:universal\] address lossless coding. First we consider lossless coding with known distribution for both finite and countably-infinite alphabets in Section \[sec:entropyrate\]. Section \[sec:universal\] considers the universal setting and provides 