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Additions to sfrsd document.
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6200 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
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@ -826,7 +826,8 @@ The decoder has a built-in table of symbol error probabilities derived from
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\emph on
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\emph on
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a-priori
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a-priori
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\emph default
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\emph default
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probability of symbol error that is expected based on the
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probability of symbol error that is expected based on a given symbol's
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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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@ -841,7 +842,8 @@ a-priori
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\emph default
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\emph default
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symbol error probabilities will be close to 1 for lower-quality symbols
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symbol error probabilities will be close to 1 for lower-quality symbols
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and closer to 0 for high-quality symbols.
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and closer to 0 for high-quality symbols.
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Recall, from Case 2, that the best performance was obtained when
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Recall, from Cases 2 and 3, that the best performance was obtained when
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\begin_inset Formula $n_{e}>X$
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\begin_inset Formula $n_{e}>X$
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\end_inset
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\end_inset
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@ -850,36 +852,74 @@ a-priori
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erasing a symbol is somewhat larger than the probability that the symbol
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erasing a symbol is somewhat larger than the probability that the symbol
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is incorrect.
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is incorrect.
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Empirically, it was determined that good performance of the SFRSD algorithm
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Empirically, it was determined that good performance of the SFRSD algorithm
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is obtained when the symbol erasure probability is somewhat larger than
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is obtained when the symbol erasure probability is a factor of
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the prior estimate of symbol error probability.
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It has been empirically determined that choosing the erasure probabilities
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to be a factor of
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\begin_inset Formula $1.3$
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\begin_inset Formula $1.3$
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\end_inset
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\end_inset
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larger than the symbol error probabilities gives the best results.
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larger than the symbol error probability.
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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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The SFRSD algorithm successively tries to decode the received word.
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The SFRSD algorithm successively tries to decode the received word using
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educated guesses at the symbols that should be erased.
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In each iteration, an independent stochastic erasure vector is generated
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In each iteration, an independent stochastic erasure vector is generated
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based on a-priori symbol erasure probabilities.
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based on the symbol erasure probabilities.
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Technically, the algorithm is a list-decoder, potentially generating a
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The guessed erasure vector is provided to the BM decoder along with the
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list of candidate codewords.
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received word.
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Each codeword on the list is assigned a quality metric, defined to be the
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If the BM decoder finds a candidate codeword, then the codeword is assigned
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soft distance between the received word and the codeword.
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a quality metric, defined to be the soft distance,
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\begin_inset Formula $d_{s}$
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\end_inset
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, between the received word and the codeword, where
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\begin_inset Formula
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\begin{equation}
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d_{s}=\sum_{i=1}^{n}(1+p_{1,i})\alpha_{i}.\label{eq:soft_distance}
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\end{equation}
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\end_inset
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and
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\begin_inset Formula $p_{1,i}$
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\end_inset
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is the fractional power associated with the i'th received symbol and
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\begin_inset Formula $\alpha_{i}=0$
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\end_inset
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if the i'th received symbol is the same as the corresponding symbol in
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the codeword, and
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\begin_inset Formula $\alpha_{i}=1$
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\end_inset
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if the i'th symbol in the received word and the codeword are different.
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This soft distance can be written as two terms, the first of which is just
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the Hamming distance between the received word and the codeword.
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The second term ensures that if two candidate codewords have the same Hamming
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distance from the received word, a smaller distance will be assigned to
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the one where the different symbols occurred in lower quality symbols.
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\end_layout
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\begin_layout Standard
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Technically, the algorithm is a list-decoder, potentially generating a list
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of candidate codewords.
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Among the list of candidate codewords found by this stochastic search algorithm
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Among the list of candidate codewords found by this stochastic search algorithm
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, only the one with the smallest soft-distance from the received word is
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, only the one with the smallest soft-distance from the received word is
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kept.
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kept.
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As with all such algorithms, a stopping criterion is necessary.
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As with all such algorithms, a stopping criterion is necessary.
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SFRSD accepts a codeword unconditionally if its soft distance is smaller
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SFRSD accepts a codeword unconditionally if its soft distance is smaller
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than an acceptance threshold,
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than an empirically determined acceptance threshold,
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\begin_inset Formula $d_{a}$
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\begin_inset Formula $d_{a}$
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\end_inset
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\end_inset
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.
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.
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A timeout is employed to limit the execution time of the algorithm.
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A timeout is employed to limit the execution time of the algorithm in cases
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where no codewords within soft distance
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\begin_inset Formula $d_{a}$
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\end_inset
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of the received word are found in a reasonable number of trials.
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\end_layout
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\end_layout
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\begin_layout Paragraph
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\begin_layout Paragraph
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@ -887,12 +927,14 @@ Algorithm
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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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For each symbol in the received word, find the erasure probability from
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For each symbol in the received word, define the erasure probability to
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the erasure-probability matrix and the
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be 1.3 times the a priori symbol-error probability determined by the soft-symbol
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information
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\begin_inset Formula $\{p_{1}\textrm{-rank},p_{2}/p_{1}\}$
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\begin_inset Formula $\{p_{1}\textrm{-rank},p_{2}/p_{1}\}$
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\end_inset
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\end_inset
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soft-symbol information.
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.
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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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