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== Code construction ==
For large block sizes, LDPC codes are commonly constructed by first studying the behaviour of decoders. As the block size tends to infinity, LDPC decoders can be shown to have a noise threshold below which decoding is reliably achieved, and above which decoding is not achieved,<ref name=richardson01>{{cite journal |first1=T.J. |last1=Richardson |first2=M.A. |last2=Shokrollahi |first3=R.L. |last3=Urbanke |title=Design of capacity-approaching irregular low-density parity-check codes |journal=IEEE Transactions on Information Theory |volume=47 |issue=2 |pages=619–637 |date=February 2001 |doi=10.1109/18.910578|url=http://infoscience.epfl.ch/record/95795 }}</ref> colloquially referred to as the [[cliff effect]]. This threshold can be optimised by finding the best proportion of arcs from check nodes and arcs from variable nodes. An approximate graphical approach to visualising this threshold is an [[EXIT chart]].{{Citation needed|date=May 2023}}
The construction of a specific LDPC code after this optimization falls into two main types of techniques:{{Citation needed|date=May 2023}}
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*Combinatorial approaches
Construction by a pseudo-random approach builds on theoretical results that, for large block size, a random construction gives good decoding performance.<ref name=MacKay96/> In general, pseudorandom codes have complex encoders, but pseudorandom codes with the best decoders can have simple encoders.<ref name=richardson01b>{{cite journal |first1=T.J. |last1=Richardson |first2=R.L. |last2=Urbanke |title=Efficient encoding of low-density parity-check codes |journal=IEEE Transactions on Information Theory |volume=47 |issue=2 |pages=638–656 |date=February 2001 |doi=10.1109/18.910579 |url=http://infoscience.epfl.ch/record/95793 }}</ref> Various constraints are often applied to help ensure that the desired properties expected at the theoretical limit of infinite block size occur at a finite block size.{{Citation needed|date=May 2023}}
Combinatorial approaches can be used to optimize the properties of small block-size LDPC codes or to create codes with simple encoders.{{Citation needed|date=May 2023}}
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