I do generate a random codebook $\mathcal{C}$ by generating $2^{NC}$ codewords $X^N=[X_1\;X_2\;\cdots\;X_N]$ randomly and independently, each according to some distribution $p_{X^n}(x^n)=\Pi_{i=1}^n p_X(x_i)$ (i.e., the entries of each codeword are i.i.d.~ $p_X$.) The distribution $p_X$ has a finite alphabet $\mathcal{X}$. Now, consider a set $S\subseteq \{1,2,\cdots,N\}$, and define $Z^N=[Z_1\;Z_2\;\cdots\;Z_N]$, where $Z_i=X_i$ if $i\in S$ and $Z_i=``?"$ if $i\notin S$. We say that $X^N$ is consistent with $Z^N$ if $Z^N$ can be obtained from $X^N$ by changing some entries to $``?"$.
I need to show that $$ \rm{Pr}\{\text{A codebook } \mathcal{C}=C\text{ which satisfies that for any } Z^N, \text{the number of codewords consistent with } Z^N=M\}\geq 1-\gamma $$ for some small $\gamma$ and some fixed $M$.