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The parity bit may be used within another constituent code. In an example using the DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits.
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Tanner proved the following bounds Let be the rate of the resulting linear code, let the degree of the digit nodes be and the degree of the subcode nodes be .If each subcode node is associated with a linear code (n,k) with rate r = k/n, then the rate of the code is bounded by
Used as constituent code in 3GPP 25.212 Turbo Code. The example encoder is systematic because the input data is also used in the output symbols (Output 2). Codes with output symbols that do not include the input data are called non-systematic. Recursive codes are typically systematic and, conversely, non-recursive codes are typically non ...
Systematic codes have the advantage that the parity data can simply be appended to the source block, and receivers do not need to recover the original source symbols if received correctly – this is useful for example if error-correction coding is combined with a hash function for quickly determining the correctness of the received source ...
The form of Eq(12) is usually the goal of a sensitivity analysis, since it is general, i.e., not tied to a specific set of parameter values, as was the case for the direct-calculation method of Eq(3) or (4), and it is clear basically by inspection which parameters have the most effect should they have systematic errors. For example, if the ...
The normal deviate mapping (or normal quantile function, or inverse normal cumulative distribution) is given by the probit function, so that the horizontal axis is x = probit(P fa) and the vertical is y = probit(P fr), where P fa and P fr are the false-accept and false-reject rates.
Funnel plots, introduced by Light and Pillemer in 1984 [1] and discussed in detail by Matthias Egger and colleagues, [2] [3] are useful adjuncts to meta-analyses. A funnel plot is a scatterplot of treatment effect against a measure of study precision. It is used primarily as a visual aid for detecting bias or systematic heterogeneity.