diff --git a/lib/ftrsd/ftrsd_paper/ftdata-100000.dat b/lib/ftrsd/ftrsd_paper/ftdata-100000.dat index f262b0ea4..b0bdce3f5 100644 --- a/lib/ftrsd/ftrsd_paper/ftdata-100000.dat +++ b/lib/ftrsd/ftrsd_paper/ftdata-100000.dat @@ -3,7 +3,7 @@ snr psuccess 100000 trials r6315 -26.5 0.007 x -26.0 0.057 -25.5 0.207 --25.0 0.531 +-25.0 0.531 0.67 -24.5 0.822 -24.0 0.953 -23.5 0.99423 diff --git a/lib/ftrsd/ftrsd_paper/ftrsd.lyx b/lib/ftrsd/ftrsd_paper/ftrsd.lyx index 24cb9605e..73c2e23a6 100644 --- a/lib/ftrsd/ftrsd_paper/ftrsd.lyx +++ b/lib/ftrsd/ftrsd_paper/ftrsd.lyx @@ -122,7 +122,23 @@ Introduction and Motivation \end_layout \begin_layout Standard -To be written... +The following paragraph may not belong here - feel free to get rid of it, + change it, whatever. +\end_layout + +\begin_layout Standard +The Franke-Taylor (FT) decoder described herein is a probabilistic list-decoder + that has been optimized for use in the short block-length, low-rate Reed-Solomo +n code used in JT65. + The particular approach that we have developed has a number of desirable + properties, not the least of which is its conceptual simplicity. + The decoding performance and complexity scale in a useful way, providing + steadily increasing soft-decision decoding gain as a tunable computational + complexity parameter is increased over more than 5 orders of magnitude. + The fact that the algorithm requires a large number of independent decoding + trials should also make it possible to obtain significant performance gains + through parallelization. + \end_layout \begin_layout Section @@ -341,18 +357,52 @@ Statistical Framework \begin_layout Standard The FT algorithm uses the estimated quality of received symbols to generate lists of symbols considered likely to be in error, thus enabling decoding - of received words with more than 25 errors. - + of received words with more than 25 errors using the errors-and-erasures + capability of the BM decoder. + Algorithms of this type are generally called +\begin_inset Quotes eld +\end_inset + +reliability based +\begin_inset Quotes erd +\end_inset + + or +\begin_inset Quotes eld +\end_inset + +probabilistic +\begin_inset Quotes erd +\end_inset + + decoding methods +\begin_inset CommandInset citation +LatexCommand cite +key "key-1" + +\end_inset + +. + These algorithms generally involve some amount of educating guessing about + which received symbols are in error. + The guesses are informed by quality metrics, also known as +\begin_inset Quotes eld +\end_inset + +soft-symbol +\begin_inset Quotes erd +\end_inset + + metrics, associated with the received symbols. + To illustrate why it is absolutely essential to use such soft-symbol informatio +n to identify symbols that are most likely to be in error it helps to consider + what would happen if we tried to use completely random guesses, ignoring + any available soft-symbol information. \end_layout \begin_layout Standard -(SF: provide brief overview of literature survey and discuss the inspiration - for the FT approach). -\end_layout - -\begin_layout Standard -As a specific example, consider a received JT65 word with 23 correct symbols - and 40 errors. +As a specific example, we will consider a received JT65 word with 23 correct + symbols and 40 errors. We do not know which symbols are in error. Suppose that the decoder randomly selects \begin_inset Formula $s=40$ @@ -398,7 +448,7 @@ tric probability distribution. \end_inset as the number of errors in the symbols actually erased. - In an ensemble of many received words, + In an ensemble of many received words \begin_inset Formula $X$ \end_inset @@ -406,7 +456,15 @@ tric probability distribution. \begin_inset Formula $x$ \end_inset - will be random variables. + will be random variables but for this example we will assume that +\begin_inset Formula $X$ +\end_inset + + is known and that only +\begin_inset Formula $x$ +\end_inset + + is random. The conditional probability mass function for \begin_inset Formula $x$ \end_inset @@ -1081,6 +1139,17 @@ Make independent stochastic decisions about whether to erase each symbol Attempt errors-and-erasures decoding by using the BM algorithm and the set of erasures determined in step 2. If the BM decoder produces a candidate codeword, go to step 5. +\begin_inset Foot +status open + +\begin_layout Plain Layout +Our implementation of the FT-algorithm is based on the excellent open-source + BM decoder written by Phil Karn, KA9Q. +\end_layout + +\end_inset + + \end_layout \begin_layout Enumerate @@ -1133,7 +1202,63 @@ An acceptable codeword with \end_inset has been found. - Declare a successful decode and return this codeword . + Declare a successful decode and return this codeword. +\end_layout + +\begin_layout Standard +The inspiration for the FT decoding algorithm came from a number of sources, + particularly references +\begin_inset CommandInset citation +LatexCommand cite +key "key-2" + +\end_inset + + and +\begin_inset CommandInset citation +LatexCommand cite +key "key-3" + +\end_inset + + and the textbook by Lin and Costello +\begin_inset CommandInset citation +LatexCommand cite +key "key-1" + +\end_inset + +. + After developing this algorithm, we became aware that our approach is conceptua +lly similar to a +\begin_inset Quotes eld +\end_inset + +stochastic erasures-only list decoding algorithm +\begin_inset Quotes erd +\end_inset + +, described in reference +\begin_inset CommandInset citation +LatexCommand cite +key "key-4" + +\end_inset + +. + The algorithm in +\begin_inset CommandInset citation +LatexCommand cite +key "key-4" + +\end_inset + + is applied to higher-rate Reed-Solomon codes on a binary-input channel + over which BPSK-modulated symbols are transmitted. + Our 64-ary input channel with 64-FSK modulation required us to develop + our own unique methods for assigning erasure probabilities and for defining + an acceptance criteria to select the best codeword from the list of candidates. + \end_layout \begin_layout Section @@ -1650,10 +1775,23 @@ Summary \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem +label "1" key "key-1" \end_inset +Error Control Coding, 2nd edition, Shu Lin and Daniel J. + Costello, Pearson-Prentice Hall, 2004. +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +label "2" +key "key-2" + +\end_inset + "Stochastic Chase Decoding of Reed-Solomon Codes", Camille Leroux, Saied Hemati, Shie Mannor, Warren J. Gross, IEEE Communications Letters, Vol. @@ -1664,7 +1802,8 @@ key "key-1" \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem -key "key-2" +label "3" +key "key-3" \end_inset @@ -1686,7 +1825,8 @@ GLOBECOM \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem -key "key-3" +label "4" +key "key-4" \end_inset @@ -1707,7 +1847,8 @@ Stochastic Erasure-Only List Decoding Algorithms for Reed-Solomon Codes, \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem -key "key-4" +label "5" +key "key-5" \end_inset @@ -1723,7 +1864,8 @@ key "key-4" \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem -key "key-5" +label "6" +key "key-6" \end_inset