Block code

Block code is the primary type of channel coding which was used in earlier Mobile communication systems. Simply it adds redundancy so that at the receiver, one can decode with (theoretical) probability of zero errors provided that the Rate(R) would not exceed the Channel Capacity.

In information theory, a block code is a code which encodes strings formed from an alphabet set ${\displaystyle S}$ into code words by encoding each letter of ${\displaystyle S}$ separately. Let ${\displaystyle (k_{1},k_{2},\ldots ,k_{m})}$ be a sequence of natural numbers each less than ${\displaystyle |S|}$. If ${\displaystyle S={s_{1},s_{2},\ldots ,s_{n}}}$ and a particular word ${\displaystyle W}$ is written as ${\displaystyle W=s_{k_{1}}s_{k_{2}}\ldots s_{k_{m}}}$, then the code word corresponding to ${\displaystyle W}$, namely ${\displaystyle C(W)}$, is

${\displaystyle C(W)=C(s_{k_{1}})C(s_{k_{2}})\ldots C(s_{k_{m}})}$.