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where we assume that the correspondence between filters and transmitted sequences has already been defined.
In a scenario with ten hops, though we can verify the poor performance obtained by comparing the received and transmitted sequences, we also appreciate a delay of the received image compared to the real image (notice that both webcams aim at a same target for comparison purposes).
Inclusion of these non-plant sequences into the phylogeny should then place horizontally transmitted sequences within the plant clan, while vertically related sequences should form a distinct clan outside the whole plant family in unrooted phylogenies.
Let and be the corresponding transmitted sequences.
Several techniques have been proposed to reduce the PAR, such as clipping [14], companding [15], selected mapping (SLM) [16], partial transmitted sequences [17], and Walsh code reassignment techniques [1, 18].
It was shown how the HNN can be used to decode single codewords, but the HNN decoder can be extended in order to detect ML transmitted sequences of codewords.
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The metrics are used to guide the tree search to find the most likely transmitted sequence.
The path metric governs the search through the tree to find the most likely transmitted sequence.
This sequence is then oversampled with rate r, given as s ⌣ r = r s ⌣ ⊗ r, and inserted to the transmit pulse shape filter to obtain transmitted sequence x.
Finally, the proposed precoding technique is detailed in Algorithm 2. Regarding the receiver side, we propose an efficient decision technique based on the MAP estimator to recover the transmitted sequence X as it will be explained in the next section.
Suppose frequency offset has been estimated and compensated perfectly, transmitted sequence in band 'b' can be expressed as S b = { s b ( 0 ), s b ( 1 ), ⋯, s b ( n - 1 ), s b ( n ), s b ( n + 1 ), ⋯ } ; n ≥ 0. (1).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com