An extrinsic information transfer chart, commonly called an EXIT chart, is a technique to aid the construction of good iteratively-decoded
error-correcting codes
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...
(in particular
low-density parity-check (LDPC) codes and
Turbo code
In information theory, turbo codes (originally in French ''Turbocodes'') are a class of high-performance forward error correction (FEC) codes developed around 1990–91, but first published in 1993. They were the first practical codes to closely ...
s).
EXIT charts were developed by
Stephan ten Brink
Stephan may refer to:
* Stephan, South Dakota, United States
* Stephan (given name), a masculine given name
* Stephan (surname), a Breton-language surname
See also
* Sankt-Stephan
* Stefan (disambiguation)
* Stephan-Oterma
* Stephani
* Step ...
, building on the concept of
extrinsic information
In science and engineering, an intrinsic property is a property of a specified subject that exists itself or within the subject. An extrinsic property is not essential or inherent to the subject that is being characterized. For example, mass ...
developed in the Turbo coding community.
[Stephan ten Brink, Convergence of Iterative Decoding, Electronics Letters, 35(10), May 1999] An EXIT chart includes the response of elements of decoder (for example a convolutional decoder of a Turbo code, the LDPC parity-check nodes or the LDPC variable nodes). The response can either be seen as extrinsic information or a representation of the messages in
belief propagation.
If there are two components which exchange messages, the behaviour of the decoder can be plotted on a two-dimensional chart. One component is plotted with its input on the horizontal axis and its output on the vertical axis. The other component is plotted with its input on the vertical axis and its output on the horizontal axis. The decoding path followed is found by stepping between the two curves. For a successful decoding, there must be a clear swath between the curves so that iterative decoding can proceed from 0 bits of extrinsic information to 1 bit of extrinsic information.
A key assumption is that the messages to and from an element of the decoder can be described by a single number, the extrinsic information. This is true when decoding codes from a
binary erasure channel
In coding theory and information theory, a binary erasure channel (BEC) is a communications channel model. A transmitter sends a bit (a zero or a one), and the receiver either receives the bit correctly, or with some probability P_e receives a me ...
but otherwise the messages are often samples from a Gaussian distribution with the correct extrinsic information. The other key assumption is that the messages are independent (equivalent to an infinite block-size code without local structure between the components)
To make an optimal code, the two transfer curves need to lie close to each other. This observation is supported by the theoretical result that for capacity to be reached for a code over a binary-erasure channel there must be no area between the curves and also by the insight that a large number of iterations are required for information to be spread throughout all bits of a code.
References
* T. Richardson and R. Urbanke: "Modern Coding Theory" {{ISBN, 0-521-85229-3
External links
Lecture notes on EXIT charts(PDF)
Error detection and correction
Information theory