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The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that 204 − 188 = 16 redundant octets (or bytes) are added to each block of 188 octets of useful information.
The code-rate is hence a real number. A low code-rate close to zero implies a strong code that uses many redundant bits to achieve a good performance, while a large code-rate close to 1 implies a weak code. The redundant bits that protect the information have to be transferred using the same communication resources that they are trying to protect.
Bob can perform this procedure using any two err-mails, so the erasure code in this example has a rate of 40%. Note that Alice cannot encode her telephone number in just one err-mail, because it contains six characters, and that the maximum length of one err-mail message is five characters.
The rate of a block code is defined as the ratio between its message length and its block length: R = k / n {\displaystyle R=k/n} . A large rate means that the amount of actual message per transmitted block is high.
The Reed–Solomon code is a [n, k, n − k + 1] code; in other words, it is a linear block code of length n (over F) with dimension k and minimum Hamming distance = + The Reed–Solomon code is optimal in the sense that the minimum distance has the maximum value possible for a linear code of size ( n , k ); this is known as the Singleton bound .
The code rate is the second number divided by the first, for our repetition example, 1/3. Hamming also noticed the problems with flipping two or more bits, ...
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Convolutional code with any code rate can be designed based on polynomial selection; [15] however, in practice, a puncturing procedure is often used to achieve the required code rate. Puncturing is a technique used to make a m/n rate code from a "basic" low-rate (e.g., 1/n) code. It is achieved by deleting of some bits in the encoder output.