mirror of https://github.com/saitohirga/WSJT-X.git
Fix several more typos; round 0.0266 to 0.027.
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6218 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
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@ -95,7 +95,8 @@ The JT65 mode has revolutionized amateur-radio weak-signal communication
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Since 2004, most JT65 decoders have used the patented Koetter-Vardy (KV)
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Since 2004, most JT65 decoders have used the patented Koetter-Vardy (KV)
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algebraic soft-decision decoder, licensed to K1JT and implemented in a
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algebraic soft-decision decoder, licensed to K1JT and implemented in a
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closed-source program for use in amateur radio applications.
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closed-source program for use in amateur radio applications.
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We describe here a new open-source alternative called the FT algotithm.
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We describe here a new open-source alternative called the Franke-Taylor
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(FT, or K9AN-K1JT) algorithm.
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It is conceptually simple, built around the well-known Berlekamp-Massey
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It is conceptually simple, built around the well-known Berlekamp-Massey
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errors-and-erasures algorithm, and performs at least as well as the KV
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errors-and-erasures algorithm, and performs at least as well as the KV
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decoder.
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decoder.
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@ -195,7 +196,7 @@ For the JT65 code,
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no more than 25 symbol errors.
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no more than 25 symbol errors.
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Any one of several well-known algebraic algorithms, such as the widely
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Any one of several well-known algebraic algorithms, such as the widely
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used Berlekamp-Massey (BM) algorithm, can carry out the decoding.
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used Berlekamp-Massey (BM) algorithm, can carry out the decoding.
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Two steps are ncessarily involved in this process, namely
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Two steps are necessarily involved in this process, namely
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\end_layout
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\end_layout
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\begin_layout Enumerate
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\begin_layout Enumerate
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@ -561,8 +562,8 @@ Examples 1 and 2 show that a random strategy for selecting symbols to erase
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\begin_inset Formula $X=40$
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\begin_inset Formula $X=40$
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\end_inset
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\end_inset
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incorrect symbols, as before, but suppose we know that 10 symbols are significa
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incorrect symbols, as before, but suppose we know that 10 received symbols
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ntly more reliable than the other 53.
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are significantly more reliable than the other 53.
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We might therefore protect the 10 most reliable symbols from erasure, selecting
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We might therefore protect the 10 most reliable symbols from erasure, selecting
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erasures from the smaller set of
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erasures from the smaller set of
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\begin_inset Formula $N=53$
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\begin_inset Formula $N=53$
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@ -573,8 +574,8 @@ ntly more reliable than the other 53.
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\begin_inset Formula $s=45$
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\begin_inset Formula $s=45$
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\end_inset
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\end_inset
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symbols are chosen randomly in this way, it is still necessary for the
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symbols are chosen randomly for erasure in this way, it is still necessary
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erased symbols to include at least 37 errors, as in Example 2.
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for the erased symbols to include at least 37 errors, as in Example 2.
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However, the probabilities are now much more favorable: with
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However, the probabilities are now much more favorable: with
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\begin_inset Formula $N=53$
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\begin_inset Formula $N=53$
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\end_inset
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\end_inset
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@ -622,7 +623,7 @@ reference "eq:hypergeometric_pdf"
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\end_inset
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\end_inset
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,
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,
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\begin_inset Formula $P(x\ge38)=0.0266$
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\begin_inset Formula $P(x\ge38)=0.027$
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\end_inset
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\end_inset
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.
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.
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@ -638,7 +639,7 @@ name "sec:The-decoding-algorithm"
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\end_inset
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\end_inset
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The FT decoding algorithm
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The Franke-Taylor decoding algorithm
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\end_layout
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\end_layout
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\begin_layout Standard
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\begin_layout Standard
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@ -647,8 +648,8 @@ Example 3 shows how reliable information about symbol quality should make
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In practice the number of errors in the received word is unknown, so we
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In practice the number of errors in the received word is unknown, so we
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use a stochastic algorithm to assign high erasure probability to low-quality
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use a stochastic algorithm to assign high erasure probability to low-quality
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symbols and relatively low probability to high-quality symbols.
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symbols and relatively low probability to high-quality symbols.
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As illustrated by Example 3, a good choice of these probabilities can increase
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As illustrated by Example 3, a good choice of erasure probabilities can
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the chance of a successful decode by many orders of magnitude.
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increase the chance of a successful decode by many orders of magnitude.
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\end_layout
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\end_layout
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\begin_layout Standard
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\begin_layout Standard
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@ -656,7 +657,7 @@ The FT algorithm uses two quality indices made available by a noncoherent
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64-FSK demodulator.
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64-FSK demodulator.
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The demodulator identifies the most likely value for each symbol based
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The demodulator identifies the most likely value for each symbol based
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on the largest signal-plus-noise power in 64 frequency bins.
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on the largest signal-plus-noise power in 64 frequency bins.
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The fraction of total power in the two bins containing the largest and
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The fractions of total power in the two bins containing the largest and
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second-largest powers (denoted by
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second-largest powers (denoted by
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\begin_inset Formula $p_{1}$
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\begin_inset Formula $p_{1}$
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\end_inset
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\end_inset
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@ -846,7 +847,7 @@ Make independent stochastic decisions about whether to erase each symbol
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\begin_layout Enumerate
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\begin_layout Enumerate
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Attempt errors-and-erasures decoding by using the BM algorithm and the set
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Attempt errors-and-erasures decoding by using the BM algorithm and the set
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of eraseures determined in step 2.
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of erasures determined in step 2.
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If the BM decoder is successful go to step 5.
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If the BM decoder is successful go to step 5.
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\end_layout
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\end_layout
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