Error correction code: Difference between revisions

Revision as of 19:30, 1 May 2018

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The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. ECC gives the receiver the ability to correct errors without needing a [[reverse channel]] to request retransmission of data, but at the cost of a fixed, higher forward channel bandwidth. ECC is therefore applied in situations where retransmissions are costly or impossible, such as one-way communication links and when transmitting to multiple receivers in [[multicast]]. For example, in the case of a satellite orbiting around [[Uranus]], a retransmission because of decoding errors can create a delay of 5 hours. ECC information is usually added to [[mass storage]] devices to enable recovery of corrupted data, is widely used in [[modem]]s, and is used on systems where the primary memory is [[ECC memory]].

ECC processing in a receiver may be applied to a digital bit stream or in the demodulation of a digitally modulated carrier. For the latter, ECC is an integral part of the initial [[Analog-to-digital converter|analog-to-digital conversion]] in the receiver. The [[Viterbi decoder]] implements a [[Error correction code#Types of ECC|soft-decision algorithm]] to demodulate digital data from an analog signal corrupted by noise. Many ECC codersencoders/decoders can also generate a [[bit-error rate]] (BER) signal which can be used as feedback to fine-tune the analog receiving electronics.

The maximum fractions of errors or of missing bits that can be corrected is determined by the design of the ECC code, so different forward error correcting codes are suitable for different conditions. In general, a stronger code induces more redundancy that needs to be transmitted using the available bandwidth, which reduces the effective bit-rate while improving the received effective signal-to-noise ratio. The [[noisy-channel coding theorem]] of Claude Shannon answers the question of how much bandwidth is left for data communication while using the most efficient code that turns the decoding error probability to zero. This establishes bounds on the theoretical maximum information transfer rate of a channel with some given base noise level. However, the proof is not constructive, and hence gives no insight of how to build a capacity achieving code. Fortunately, after years of research, some advanced ECC systems nowadays come very close to the theoretical maximum.

==How it works==