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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 encoders/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 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. After years of research, some advanced ECC systems nowadays {{when|date=August 2019}} come very close to the theoretical maximum.
==How it works==
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