Start VN and CN indexing from zero

src/thesis/chapters/4_decoding_under_dems.tex

@@ -474,9 +474,8 @@ and is difficult to predict beforehand.
 We briefly reintroduce the notation important for the definition of the windows.
 We use the variables $n,m \in \mathbb{N}$ to describe the number of
 \acp{vn} and \acp{cn} respectively.
-We index the \acp{vn} using the variable $i \in \mathcal{I} := \left\{
-1,\ldots,n \right\}$ and the \acp{cn} using the variable $j \in
-\mathcal{J} := \left\{ 1, \ldots, m \right\}$.
+We index the \acp{vn} using the variable $i \in \mathcal{I} :=
+[0:n-1]$ and the \acp{cn} using the variable $j \in \mathcal{J} := [ 0 : m-1]$.
 Finally, we call $\mathcal{N}_\text{V}(i) = \left\{ i\in \mathcal{I}:
 \bm{H}_{j,i} = 1 \right\}$ and $\mathcal{N}_\text{C}(j) := \left\{ j
 \in \mathcal{J} : \bm{H}_{j,i} = 1 \right\}$ the neighborhoods of the
@@ -487,9 +486,8 @@ check matrix of the underlying code, from which the \ac{dem} was generated.
 % How we get the corresponding rows
 
 We begin by describing the sets of \acp{cn} relevant to each window.
-For indexing, we use the variable $\ell \in \left\{
-0,\ldots,n_\text{win} - 1 \right\}$, where $n_\text{win} \in \mathbb{N}$
-is the number of windows.
+For indexing, we use the variable $\ell \in [0:n_\text{win} - 1]$,
+where $n_\text{win} \in \mathbb{N}$ is the number of windows.
 Because we defined the step size $F$ as the number of syndrome
 extraction rounds to skip, the first \ac{cn} of window $\ell$ should have index
 $\ell F m$.