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Updating node information
In recent years, there has also been a great deal of work in studying the effects of alternative schedules for variable and constraint node update. The original technique that was used for decoding LDPC codes was known as flooding. This type of updates required that before updating a variable node, all constraint nodes needed to be updated and vice-versa. In later work by Vila Casado et al.,[9] alternative update techniques are studied in which variable nodes are updated with the newest available
check-node information.
The intuition behind these algorithms is that variable nodes whose value varies the most, are the ones that need to be updated first. Highly reliable nodes whose Log-likelihood ratio (LLR) magnitude is large and does not change significantly from one update to the next do not require updates with the same frequency of other nodes whose sign and magnitude fluctuate. These scheduling algorithms show great speed of convergence and lower-error floors than when the flooding is used. These lower error floors
are achieved due to the ability of the Informed Dynamic Scheduling (IDS)[9] algorithm to overcome trapping sets or near codewords.[10]
When non-flooding scheduling algorithms are used, an alternative definition of iteration is used. For an (n, k) LDPC code of rate k/n, a full iteration occurs when n variable and n ? k constraint nodes have been updated, no matter the order in which they were.
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.[11] 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.
The construction of a specific LDPC code after this optimisation falls into two main types of techniques:
Pseudo-random techniques
Combinatorial approaches
Construction by a pseudo-random approach builds on theoretical results that, for large block-size, a random construction gives good decoding performance.[7] In general, pseudo-random codes have complex encoders, however pseudo-random codes with the best decoders also can have simple encoders.[12] Various constraints are often applied to help the good properties expected at the theoretical limit of infinite block size to occur at a finite block size.
Combinatorial approaches can be used to optimise properties of small block-size LDPC codes or create codes with simple encoders.
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