Block code

Practical definition

A block code is the primary type of channel coding which was used in earlier mobile communication systems. Simply it adds redundancy in order that at the receiver, one can decode with (theoretical) probability of zero errors, provided that the information rate (amount of transported information in bits per sec) would not exceed the channel capacity. The main characterisation of a block code is that it is a fixed length channel code (unlike source coding schemes such as Huffman coding, and unlike channel coding methods like convolutional encoding). Typically, a block code takes a k-digit information word, and transforms this into an n-digit codeword.

Theoretical definition

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

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

A[n,d]

The trade-off between efficiency (large informationrate) and correction capabilities can also be seen from the attempt to, given a fixed codeword length and a fixed correction capability (represented by the Hamming distance d) maximise the total amount of codewords. A[n,d] is the maximum number of codewords for a given codeword length n and Hamming distance d.