Error correction code: Difference between revisions

Revision as of 00:23, 11 July 2019

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==Code-rate and the tradeoff between reliability and data rate==

{{See also|Bit rate#Information rate}}

The fundamental principle of ECC is to add redundant bits in order to help the decoder to find out the true message that was encoded by the transmitter. The code-rate of a given ECC system is defined as the rateratio between the number of information bits and the total number of bits (i.e. information plus redundancy bits) in a given communication package. 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. This causes a fundamental tradeoff between reliability and data rate.<ref>{{citation |author-first1=David |author-last1=Tse |author-first2=Pramod |author-last2=Viswanath |title=Fundamentals of Wireless Communication |publisher=[[Cambridge University Press]], UK |date=2005}}</ref> In one extreme, a strong code (with low code-rate) can induce an important increase in the receiver SNR decreasing the bit error rate, at the cost of reducing the effective data rate. On the other extreme, not using any ECC (i.e. a code-rate equal to 1) uses the full channel for information transfer purposes, at the cost of leaving the bits without any additional protection.