Let's consider a symbol source that generates symbols as following:
Fix a distribution for the symbols' lengths $P_L$ over $\mathbb{N}$ with finite mean $E(L)$. Generate $A$ independently and identically distributed (i.i.d.) random variables $L_1,L_2,...,L_A$ from $P_L$. We next generate a sequence of binary strings $X_a\in\{0,1\}^{L_a}$ for each $a\in\{1,2,...,A\}$. Starting with $a = 1$, choose $X_a$ uniformly at random from $\{0,1\}^{L_a}\setminus\{X_1,X_2,...,X_{a-1}\}$. Thus, each $X_a$ is a binary string of length $L_a$, called a source symbol. The source alphabet $\mathcal{X}\subset\{0,1\}^*$ (where $\{0,1\}^*$ denotes the set of all finite-length binary sequences) is defined as the union of all the source symbols $$\mathcal{X}\triangleq\{X_a\}_{a=1}^A$$
Note that $|\mathcal{X}|=A$ by construction. The author first assumes that $L$ is tightly concentrated around its mean, specifically that $P(E(L)/2\leq L\leq 2E(L)) = 1$. Furthermore, to ensure that the source alphabet generation is always well defined, he assumes that $2\leq A\leq 2^{E(L)/2-1}$.
What I don't understand is why the number of symbols is upper bounded by $2^{E(L)/2-1}$. This doesn't seem obvious from Markov or Kraft inequality. The paper is here.