diff --git a/lib/sfrsd2/sfrsd_paper/sfrsd.lyx b/lib/sfrsd2/sfrsd_paper/sfrsd.lyx index acdd9b601..bb8fd1fbf 100644 --- a/lib/sfrsd2/sfrsd_paper/sfrsd.lyx +++ b/lib/sfrsd2/sfrsd_paper/sfrsd.lyx @@ -95,7 +95,8 @@ The JT65 mode has revolutionized amateur-radio weak-signal communication Since 2004, most JT65 decoders have used the patented Koetter-Vardy (KV) algebraic soft-decision decoder, licensed to K1JT and implemented in a closed-source program for use in amateur radio applications. - We describe here a new open-source alternative called the FT algotithm. + We describe here a new open-source alternative called the Franke-Taylor + (FT, or K9AN-K1JT) algorithm. It is conceptually simple, built around the well-known Berlekamp-Massey errors-and-erasures algorithm, and performs at least as well as the KV decoder. @@ -195,7 +196,7 @@ For the JT65 code, no more than 25 symbol errors. Any one of several well-known algebraic algorithms, such as the widely used Berlekamp-Massey (BM) algorithm, can carry out the decoding. - Two steps are ncessarily involved in this process, namely + Two steps are necessarily involved in this process, namely \end_layout \begin_layout Enumerate @@ -561,8 +562,8 @@ Examples 1 and 2 show that a random strategy for selecting symbols to erase \begin_inset Formula $X=40$ \end_inset - incorrect symbols, as before, but suppose we know that 10 symbols are significa -ntly more reliable than the other 53. + incorrect symbols, as before, but suppose we know that 10 received symbols + are significantly more reliable than the other 53. We might therefore protect the 10 most reliable symbols from erasure, selecting erasures from the smaller set of \begin_inset Formula $N=53$ @@ -573,8 +574,8 @@ ntly more reliable than the other 53. \begin_inset Formula $s=45$ \end_inset - symbols are chosen randomly in this way, it is still necessary for the - erased symbols to include at least 37 errors, as in Example 2. + symbols are chosen randomly for erasure in this way, it is still necessary + for the erased symbols to include at least 37 errors, as in Example 2. However, the probabilities are now much more favorable: with \begin_inset Formula $N=53$ \end_inset @@ -622,7 +623,7 @@ reference "eq:hypergeometric_pdf" \end_inset , -\begin_inset Formula $P(x\ge38)=0.0266$ +\begin_inset Formula $P(x\ge38)=0.027$ \end_inset . @@ -638,7 +639,7 @@ name "sec:The-decoding-algorithm" \end_inset -The FT decoding algorithm +The Franke-Taylor decoding algorithm \end_layout \begin_layout Standard @@ -647,8 +648,8 @@ Example 3 shows how reliable information about symbol quality should make In practice the number of errors in the received word is unknown, so we use a stochastic algorithm to assign high erasure probability to low-quality symbols and relatively low probability to high-quality symbols. - As illustrated by Example 3, a good choice of these probabilities can increase - the chance of a successful decode by many orders of magnitude. + As illustrated by Example 3, a good choice of erasure probabilities can + increase the chance of a successful decode by many orders of magnitude. \end_layout \begin_layout Standard @@ -656,7 +657,7 @@ The FT algorithm uses two quality indices made available by a noncoherent 64-FSK demodulator. The demodulator identifies the most likely value for each symbol based on the largest signal-plus-noise power in 64 frequency bins. - The fraction of total power in the two bins containing the largest and + The fractions of total power in the two bins containing the largest and second-largest powers (denoted by \begin_inset Formula $p_{1}$ \end_inset @@ -846,7 +847,7 @@ Make independent stochastic decisions about whether to erase each symbol \begin_layout Enumerate Attempt errors-and-erasures decoding by using the BM algorithm and the set - of eraseures determined in step 2. + of erasures determined in step 2. If the BM decoder is successful go to step 5. \end_layout