In DaniWi/Channelcoding: channelcoding
knitr::opts_chunk$set(echo = FALSE)
colorOrig <- "gray"
colorParity1 <- "orange"
colorParity2 <- "violet"
binVector <- function(n, min.length) {
result <- integer()
i <- 0
while (n != 0) {
result <- c(n %% 2, result)
n = n %/% 2
i <- i + 1
}
zeros <- rep(0, times = min.length)
result <- c(zeros, result)
return(paste(tail(result,min.length), collapse = ""))
}
decToBin <- function(x) { if (all(x<2)) x else paste(decToBin(x%/%2), x%%2, sep="") }
octalToDec <- function(x) {
res <- numeric()
for(j in 1:length(x)) {
dec <- 0
i <- 0
while (x[j] > 0) {
dec <- dec + (x[j] %% 10) * (8^i)
i <- i + 1
x[j] <- x[j] %/% 10
}
res[j] <- dec
}
return(res)
}
# returns an ordering of the state numbers for a nice state diagram
ordering <- function(num.states, next.state) {
#next.state <- matrix(rep(0:(num.states-1), each = 2), ncol = 2)
result <- integer(1)
n <- 0
for (i in 2:num.states) {
n0 <- next.state[n+1,1]
n1 <- next.state[n+1,2]
if (n0 %in% result) {
n <- n1
}
else if (n1 %in% result) {
n <- n0
}
else {
n <- if (n0 > n1) n0 else n1
}
result <- c(result, n)
}
return(result)
}
gcd <- function(n, m) {
if (n == 0 && m == 0) return(0)
n <- abs(n); m <- abs(m)
if (m > n) {
t <- n; n <- m; m <- t
}
while (m > 0) {
t <- n
n <- m
m <- t %% m
}
return(n)
}
node.short <- 18
node.long <- 33
decimal.digits <- 1
dots <- function (v, node) if(length(v) > node) ", ..." else ""
if (params$encoder$rsc == TRUE) {
art.coder <- "Rekursiver"
} else {
art.coder <- "Nicht-Rekursiver"
}
if (params$encoder$rsc == FALSE) {
generator.matrix <-
paste0(decToBin(octalToDec(params$encoder$generators)), " \\\\ ", collapse = "")
generator.print <- paste0("(", paste(params$encoder$generators, collapse="_8,"),
"_8) = \\begin{pmatrix}", generator.matrix, "\\end{pmatrix}")
} else {
generator.print <-
paste0("\\left(1,",
paste0("\\frac{",
head(params$encoder$generators, length(params$encoder$generators) - 1), "_8}{",
tail(params$encoder$generators, 1), "_8}", collapse = ","), "\\right)")
}
#cut off the parameters
orig <- paste0(
paste0(head(round(params$orig, decimal.digits), node.short), collapse = ", "), dots(params$orig, node.short))
parity1 <- paste0(
paste0(head(round(params$parity1, decimal.digits), node.short), collapse = ", "), dots(params$parity1, node.short))
parity2 <- paste0(
paste0(head(round(params$parity2, decimal.digits), node.short), collapse = ", "), dots(params$parity2, node.short))
origI <- paste0(
paste0(head(round(params$origI, decimal.digits), node.short), collapse = ", "), dots(params$origI, node.short))
decode2 <- paste0(
paste0(head(round(params$decode2, decimal.digits), node.short), collapse = ", "), dots(params$decode2, node.short))
decode2I <- paste0(
paste0(head(round(params$decode2I, decimal.digits), node.short), collapse = ", "), dots(params$decode2I, node.short))
decode1 <- paste0(
lapply(lapply(params$decode1,
function(x) {head(round(x, decimal.digits), node.short)}),
function(x) {paste0(x, collapse = ", ")}),
lapply(params$decode1, function(x) {dots(x, node.short)}))
decode1I <- paste0(
lapply(lapply(params$decode1I,
function(x) {head(round(x, decimal.digits), node.short)}),
function(x) {paste0(x, collapse = ", ")}),
lapply(params$decode1I, function(x) {dots(x, node.short)}))
decode2Back <- paste0(
lapply(lapply(params$decode2Back,
function(x) {head(round(x, decimal.digits), node.short)}),
function(x) {paste0(x, collapse = ", ")}),
lapply(params$decode2Back, function(x) {dots(x, node.short)}))
decode2IBack <- paste0(
lapply(lapply(params$decode2IBack,
function(x) {head(round(x, decimal.digits), node.short)}),
function(x) {paste0(x, collapse = ", ")}),
lapply(params$decode2IBack, function(x) {dots(x, node.short)}))
resultHard <- paste0(
lapply(lapply(params$tempResultHard,
function(x) {head(x, node.short)}),
function(x) {paste0(x, collapse = ", ")}),
lapply(params$tempResultHard, function(x) {dots(x, node.short)}))
resultSoft <- paste0(
lapply(lapply(params$tempResultSoft,
function(x) {head(round(x, decimal.digits), node.short)}),
function(x) {paste0(x, collapse = ", ")}),
lapply(params$tempResultSoft, function(x) {dots(x, node.short)}))
Faltungskodierer Informationen
r art.coder Kodierer- Anzahl von Ausgängen : $$N=
r params$encoder$N$$
- Länge des Schieberegisters : $$M=
r params$encoder$M$$
- Generatoren : $$
r generator.print$$
Faltungskodierer Matrix : Nächster Zustand
\begin{center}
next.table <- params$encoder$next.state
colnames(next.table) <- c("Bit 0", "Bit 1")
row.counter <- rep(0:(dim(next.table)[1]-1))
rownames(next.table) <- paste("Zustand ", row.counter)
knitr::kable(next.table, format="latex", align="c")
\end{center}
Faltungskodierer Matrix : Ausgangsbits
\begin{center}
output.table <- params$encoder$output
output.table <- matrix(decToBin(as.vector(output.table)), ncol = ncol(output.table))
colnames(output.table) <- c("Bit 0", "Bit 1")
row.counter <- rep(0:(dim(next.table)[1]-1))
rownames(output.table) <- paste("Zustand ", row.counter)
knitr::kable(output.table, format="latex", align="c")
\end{center}
Faltungskodierer Matrix : Zustandsdiagramm
num.states <- 2^params$encoder$M
state.order <- ordering(num.states, params$encoder$next.state)
## STATE DIAGRAM
tikz.diagram <- ""
# state diagram nodes
for (s in 0:(num.states-1)) {
xpos <- 2.5*sin(s*2*pi/num.states)
ypos <- 2.5*cos(s*2*pi/num.states)
position <- paste0(xpos,",",ypos)
name <- paste(binVector(state.order[s+1], params$encoder$M),collapse = "")
state <- paste0("\\node[state] (state",state.order[s+1],") at (",position,") {",name,"};")
tikz.diagram <- paste(tikz.diagram, state)
}
# state diagram connections
for (s in 0:(num.states-1)) {
this.state <- paste0("(state",s,")")
n_next.state.0 <- params$encoder$next.state[s+1,1]
n_next.state.1 <- params$encoder$next.state[s+1,2]
str_next.state.0 <- paste0("(state",n_next.state.0,")")
str_next.state.1 <- paste0("(state",n_next.state.1,")")
label.value.0 <- paste(binVector(params$encoder$output[s+1,1],params$encoder$N),collapse = "")
label.value.1 <- paste(binVector(params$encoder$output[s+1,2],params$encoder$N),collapse = "")
# indices of the states in the ordering vector (1 based)
this.ordering.index <- which(state.order == s)
next.0.ordering.index <- which(state.order == n_next.state.0)
next.1.ordering.index <- which(state.order == n_next.state.1)
# if edges do not go to neighbour, set label near start
# to avoid label crossings
near.0 <- ""
near.1 <- ""
distance.to.0 <- abs(this.ordering.index - next.0.ordering.index)
distance.to.1 <- abs(this.ordering.index - next.1.ordering.index)
if (distance.to.0 > 1 && distance.to.0 < num.states-1) {
near.0 <- ",near start"
}
if (distance.to.1 > 1 && distance.to.1 < num.states-1) {
near.1 <- ",near start"
}
# 2nd check in previous if clause necessary because if state numbers
# are in first and last position of the ordering, they have distance
# num.states-1 but are neighbours in the state diagram
label.0 <- paste0("node [sloped, above",near.0,"] {",label.value.0,"}")
label.1 <- paste0("node [sloped, above",near.1,"] {",label.value.1,"}")
# in case of a loop
angle <- (90-(this.ordering.index-1)*360/num.states) %% 360
angle.out <- (angle + 15) %% 360
angle.in <- (angle - 15) %% 360
if (n_next.state.0 == s) {
# loop with input bit 0
loop <- paste0("[looseness=8,out=",angle.out,",in=",angle.in,"]")
if (sin(angle*pi/180) < 0) {
label.0 <- paste0("node [sloped, below",near.0,"] {",label.value.0,"}")
}
edge.0 <- paste("\\draw[->]",this.state,"to",loop,label.0,this.state,";")
}
else {
# 'normal' edge to other node
bend <- ""
if (params$encoder$next.state[n_next.state.0+1,1] == s || params$encoder$next.state[n_next.state.0+1,2] == s) {
# there is a connection back -> bend the edge
bend <- "[bend left=15]"
}
edge.0 <- paste("\\draw[->]",this.state,"to",bend,label.0,str_next.state.0,";")
}
if (n_next.state.1 == s) {
# loop with input bit 1
loop <- paste0("[looseness=8,out=",angle.out,",in=",angle.in,"]")
if (sin(angle*pi/180) < 0) {
label.1 <- paste0("node [sloped, below",near.1,"] {",label.value.1,"}")
}
edge.1 <- paste("\\draw[->, dashed]",this.state,"to",loop,label.1,this.state,";")
}
else {
# 'normal' edge to other node
bend <- ""
if (params$encoder$next.state[n_next.state.1+1,1] == s || params$encoder$next.state[n_next.state.1+1,2] == s) {
# there is a connection back -> bend the edge
bend <- "[bend left=15]"
}
edge.1 <- paste("\\draw[->, dashed]",this.state,"to",bend,label.1,str_next.state.1,";")
}
tikz.diagram <- paste(tikz.diagram, edge.0, edge.1)
}
\begin{center}
\begin{tikzpicture}[>=stealth, font=\scriptsize]
\tikzstyle{state} = [draw, circle, inner sep=1mm, minimum size=8mm, font=\footnotesize]
r tikz.diagram
\end{tikzpicture}
\end{center}
Turbo-Dekodierer Informationen
- Interleaver : (
r head(params$permutation, node.long)``r dots(params$permutation, node.long))
\vspace*{6mm}
- Koderate : $$\frac{1}{3}$$
\vspace*{6mm}
- Dekodierungsiterationen :
r params$iterations
Turbodekodierung ohne Punktierung
\begin{center}
\begin{tikzpicture}[node distance=8mm, inner sep=2mm, outer sep=0,
=stealth, font=\tiny, align=center]
\tikzstyle{decoderStyle} = [rectangle, draw]
\tikzstyle{deinterleaverStyle} = [rectangle, draw, node distance=4mm]
\tikzstyle{startEndStyle} = [rectangle, draw]
\tikzstyle{demultiplexerStyle} = [deinterleaverStyle]
\tikzstyle{showStyle} = [decoderStyle, thick, draw=red, text=red, inner sep=1mm, overlay, fill=white]
\tikzstyle{showDrawStyle} = [->, red, thick]
\node [node distance=4mm] (demultiplexerTemp) {};
\node [demultiplexerStyle, rotate=90] (demultiplexer) at (demultiplexerTemp.west) {Demultiplexer};
\node [decoderStyle] (decoder1) [above right=of demultiplexerTemp] {SISO\ Dekodierer 1};
\node [deinterleaverStyle] (interleaver1) [right=of decoder1] {$I$};
\node [deinterleaverStyle] (interleaver2) [above=4mm of interleaver1] {$I^{-1}$};
\node [deinterleaverStyle] (interleaver3) [below=4mm of interleaver1] {$I$};
\node [decoderStyle, node distance=4mm] (decoder2) [right=of interleaver3] {SISO\ Dekodierer 2};
\node [deinterleaverStyle] (interleaver4) [right=of decoder2] {$I^{-1}$};
\node [deinterleaverStyle] (finalCalculation) [right=of interleaver4] {$=$};
\node [startEndStyle] (start) [left=of demultiplexerTemp] {Input};
\node [startEndStyle, node distance=5mm] (end) [right=of finalCalculation] {Output};
\draw [->] (start.east) -- node (afterInput) {} (demultiplexer.north);
\draw [->] (decoder1.east) -- node (afterDecoder1) {}(interleaver1.west);
\draw [->] (interleaver3.east) -- node (afterInterleaver3) {} (decoder2.west);
\draw [->] (decoder2.east) -- node (afterDecoder2) {} (interleaver4.west);
\draw [->] (interleaver4.east) -- node (afterInterleaver4) {} (finalCalculation.west);
\draw [->] (finalCalculation.east) -- node (afterFinalCalculation) {} (end.west);
\draw [->] ($(decoder2.east)+(0,+.2)$) -| ++(.2,.7) node (afterDecoder2Back) {} |- (interleaver2.east);
\visible<1-5>{
\draw [<-, lightgray] ($(decoder1.west)+(0,+.2)$) -| ++(-.2,.7) |- node [near end] (afterInterleaver2) {} (interleaver2.west);
}
\alt<1-5>{
\draw [<-] ($(decoder1.west)+(0,+.2)$) -- ++(-1.1,0) node [near end, above=-0.1] {$\left(0,0,\cdots \right)$};
} {
\draw [<-, lightgray] ($(decoder1.west)+(0,+.2)$) -- ++(-1.1,0) node [near end, above=-0.1] {$\left(0,0,\cdots \right)$};
}
\visible<6->{
\draw [<-] ($(decoder1.west)+(0,+.2)$) -| ++(-.2,.7) |- node [near end] (afterInterleaver2) {} (interleaver2.west);
}
\draw [->] (interleaver1.east) -| ++(+.2,-.7) node [midway] (afterInterleaver1) {} |- ($(decoder2.west)+(0,+.2)$);
\draw [->] ($(demultiplexer.south)+(0,+.4)$) -| ++(+.15,+.2) node (afterDemOrig) {} |- (decoder1.west);
\draw [->] (demultiplexer.south) -| ++(+.3,+.4) node (afterDemParity1) {} |- ($(decoder1.west)+(0,-.2)$);
\draw [->] (afterDemOrig) |- node [near end] (afterDemOrigInterl) {} (interleaver3.west);
\draw [<-] ($(decoder2.west)+(0,-.2)$) -| ++(-.2,-.3)|- node [near end] (afterDemParity2) {} ($(demultiplexer.south)+(0,-.4)$);
\begin{scope}[on background layer]
\node [draw, fit=(decoder1) (decoder2) (demultiplexer) (interleaver1) (interleaver2) (interleaver3) (interleaver4) (finalCalculation)] (background) {};
\end{scope}
\visible<1-4>{
\node [below =4mm of decoder2] {Iteration 1};
}
multipl.color <- character()
vec <- head(round(params$code, decimal.digits), node.short)
for (i in c(0:((length(vec) / 3) - 1))) {
temp <- paste0(
"\\textcolor{", colorOrig, "}{", vec[i * 3 + 1], "}, ",
"\\textcolor{", colorParity1, "}{", vec[i * 3 + 2], "}, ",
"\\textcolor{", colorParity2, "}{", vec[i * 3 + 3], "}",
collapse = ""
)
if (i == ((length(vec) / 3) - 1)) {
multipl.color <- paste0(multipl.color, temp, collapse = "")
} else {
multipl.color <- paste0(multipl.color, temp, ", ", collapse = "")
}
}
% AfterDemultiplexer
\visible<2>{
\node [showStyle] (showAboveCenterTop) [above=9mm of background] {r multipl.color``r dots(params$code, node.short)};
\draw [showDrawStyle] (showAboveCenterTop) -- (afterInput.center);
\node [showStyle] (showAboveCenter) [above=3mm of background, text=`r colorOrig`] {`r orig`};
\draw [showDrawStyle] (showAboveCenter) -- (afterDemOrig.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background, text=`r colorParity1`] {`r parity1`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemParity1.center);
\node [showStyle] (showBelowCenter) [below=3mm of background, text=`r colorParity2`] {`r parity2`};
\draw [showDrawStyle] (showBelowCenter) -- (afterDemParity2.center);
}
% AfterDemulitplexer, AfterInterleaver2 - AfterDecoder1
\visible<3>{
\node [showStyle] (showAboveCenterTop) [above=9mm of background] {r decode1[[1]]};
\draw [showDrawStyle] (showAboveCenterTop) -- (afterDecoder1.center);
\node [showStyle] (showAboveCenter) [above=3mm of background] {`r orig`};
\draw [showDrawStyle] ($(showAboveCenter.south)+(-.5,0)$) -- (afterDemOrig.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {`r parity1`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemParity1.center);
}
% AfterDecoder1, AfterDemultiplexer - AfterInterleaver1, 2
\visible<4>{
\node [showStyle] (showAboveCenterTop) [above=9mm of background] {r decode1[[1]]};
\draw [showDrawStyle] (showAboveCenterTop) -- (afterDecoder1.center);
\node [showStyle] (showAboveCenter) [above=3mm of background] {`r decode1I[[1]]`};
\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver1.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {`r orig`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemOrigInterl.center);
\node [showStyle] (showBelowCenter) [below=3mm of background] {`r origI`};
\draw [showDrawStyle] (showBelowCenter) -- (afterInterleaver3.center);
}
tikz.string <- character()
if (params$iterations > 1) {
for (i in c(1:(params$iterations - 1))) {
#AfterInterleaver1, 2, AfterDemultiplexer - AfterDecoder2Back
slide1 <- paste0(
"\\visible<", 5 + 4 * (i - 1),
">{ \\node [showStyle] (showAboveCenterTop) [above=9mm of background] {",
parity2,
"}; \\draw [showDrawStyle] (showAboveCenterTop) -- (afterDemParity2.center); \\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {",
decode2Back[[i]],
"}; \\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDecoder2Back.center); \\node [showStyle] (showAboveCenter) [above=3mm of background] {",
decode1I[[i]],
"}; \\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver1.center); \\node [showStyle] (showBelowCenter) [below=3mm of background] {",
origI,
"}; \\draw [showDrawStyle] (showBelowCenter) -- (afterInterleaver3.center);}",
collapse = ""
)
# AfterDecoder2Back - AfterInterleaver2
slide2 <- paste0(
"\\visible<", 6 + 4 * (i - 1),
">{ \\node [showStyle] (showAboveCenterTop) [above=9mm of background] {",
decode2IBack[[i]],
"}; \\draw [showDrawStyle] (showAboveCenterTop) -- (afterInterleaver2.center); \\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {",
decode2Back[[i]],
"}; \\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDecoder2Back.center);}",
collapse = ""
)
# AfterDemulitplexer, AfterInterleaver2 - AfterDecoder1
slide3 <- paste0(
"\\visible<", 7 + 4 * (i - 1),
">{ \\node [showStyle] (showAboveCenterTop) [above=9mm of background] {",
decode2IBack[[i]],
"}; \\draw [showDrawStyle] (showAboveCenterTop) -- (afterInterleaver2.center); \\node [showStyle] (showAboveCenter) [above=3mm of background] {",
orig,
"}; \\draw [showDrawStyle] (showAboveCenter) -- (afterDemOrig.center); \\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {",
parity1,
"}; \\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemParity1.center); \\node [showStyle] (showBelowCenter) [below=3mm of background] {",
decode1[[i + 1]],
"}; \\draw [showDrawStyle] (showBelowCenter) -- (afterDecoder1.center);}",
collapse = ""
)
# AfterDecoder1, AfterDemultiplexer - AfterInterleaver1, 2
slide4 <- paste0(
"\\visible<", 8 + 4 * (i - 1),
">{ \\node [showStyle] (showAboveCenterTop) [above=9mm of background] {",
decode1[[i + 1]],
"}; \\draw [showDrawStyle] (showAboveCenterTop) -- (afterDecoder1.center); \\node [showStyle] (showAboveCenter) [above=3mm of background] {",
decode1I[[i + 1]],
"}; \\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver1.center); \\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {",
orig,
"}; \\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemOrigInterl.center); \\node [showStyle] (showBelowCenter) [below=3mm of background] {",
origI,
"}; \\draw [showDrawStyle] (showBelowCenter) -- (afterInterleaver3.center);}",
collapse = ""
)
counter <- paste0(
"\\visible<", 5 + 4 * (i - 1), "-", 8 + 4 * (i - 1),
">{\\node [below =4mm of decoder2] {Iteration ", i + 1 ,"};}"
)
output <- paste0(
"\\visible<", 5 + 4 * (i - 1), "-", 8 + 4 * (i - 1),
">{\\node [below =15mm of background, font=\\small, overlay] {Output : (", resultHard[[i]],")};}"
)
tikz.string <- paste0(tikz.string, slide1, slide2, slide3, slide4, counter, output, collapse = "")
}
}
r tikz.string
%END
\visible<r params$iterations * 4 + 1-r params$iterations * 4 + 3>{
\node [below =4mm of decoder2] {Iteration r params$iterations};
}
\visible<r params$iterations * 4 + 1-r params$iterations * 4 + 3>{
\node [below =15mm of background, font=\small, overlay] {Output : (r resultHard[[params$iterations]])};
}
% AfterInterleaver1, 2, AfterDemultiplexer - AfterDecoder2
\visible<r params$iterations * 4 + 1>{
\node [showStyle] (showAboveCenterTop) [above=9mm of background] {r parity2};
\draw [showDrawStyle] (showAboveCenterTop) -- (afterDemParity2.center);
\node [showStyle] (showAboveCenter) [above=3mm of background] {`r decode1I[[params$iterations]]`};
\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver1.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {`r decode2`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDecoder2.center);
\node [showStyle] (showBelowCenter) [below=3mm of background] {`r origI`};
\draw [showDrawStyle] (showBelowCenter) -- (afterInterleaver3.center);
}
% AfterDecoder2 - AfterInterleaver4
\visible<r params$iterations * 4 + 2>{
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {r decode2};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDecoder2.center);
\node [showStyle] (showAboveCenter) [above=3mm of background] {`r decode2I`};
\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver4.center);
}
% AfterInterleaver4 - AfterFinalCalculation
\visible<r params$iterations * 4 + 3>{
\node [showStyle] (showAboveCenter) [above=3mm of background] {r decode2I};
\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver4.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {`r resultSoft[[params$iterations]]`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterFinalCalculation.center);
}
\end{tikzpicture}
\end{center}
Terminierung
term.string <- paste0(
"- Output mit Terminierung : (",
paste0(head(params$tempResultHard[[params$iterations]], length(params$tempResultHard[[params$iterations]]) - params$encoder$M), collapse = ", "),
"\\textcolor{orange}{, ",
paste0(tail(params$tempResultHard[[params$iterations]], params$encoder$M), collapse = ", "),
"})",
"\\vspace*{6mm}",
"\n- Output ohne Terminierung : (",
paste0(params$result$output.hard, collapse = ", "),
")"
)
if (length(params$result$output.hard) > node.long) {
term.string <- "Da der Output zu lang ist, kann die Terminierung leider nicht angezeigt werden!"
}
r term.string
DaniWi/Channelcoding documentation built on May 6, 2019, 1:23 p.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
knitr::opts_chunk$set(echo = FALSE)
colorOrig <- "gray" colorParity1 <- "orange" colorParity2 <- "violet" binVector <- function(n, min.length) { result <- integer() i <- 0 while (n != 0) { result <- c(n %% 2, result) n = n %/% 2 i <- i + 1 } zeros <- rep(0, times = min.length) result <- c(zeros, result) return(paste(tail(result,min.length), collapse = "")) } decToBin <- function(x) { if (all(x<2)) x else paste(decToBin(x%/%2), x%%2, sep="") } octalToDec <- function(x) { res <- numeric() for(j in 1:length(x)) { dec <- 0 i <- 0 while (x[j] > 0) { dec <- dec + (x[j] %% 10) * (8^i) i <- i + 1 x[j] <- x[j] %/% 10 } res[j] <- dec } return(res) } # returns an ordering of the state numbers for a nice state diagram ordering <- function(num.states, next.state) { #next.state <- matrix(rep(0:(num.states-1), each = 2), ncol = 2) result <- integer(1) n <- 0 for (i in 2:num.states) { n0 <- next.state[n+1,1] n1 <- next.state[n+1,2] if (n0 %in% result) { n <- n1 } else if (n1 %in% result) { n <- n0 } else { n <- if (n0 > n1) n0 else n1 } result <- c(result, n) } return(result) } gcd <- function(n, m) { if (n == 0 && m == 0) return(0) n <- abs(n); m <- abs(m) if (m > n) { t <- n; n <- m; m <- t } while (m > 0) { t <- n n <- m m <- t %% m } return(n) }
node.short <- 18 node.long <- 33 decimal.digits <- 1 dots <- function (v, node) if(length(v) > node) ", ..." else "" if (params$encoder$rsc == TRUE) { art.coder <- "Rekursiver" } else { art.coder <- "Nicht-Rekursiver" } if (params$encoder$rsc == FALSE) { generator.matrix <- paste0(decToBin(octalToDec(params$encoder$generators)), " \\\\ ", collapse = "") generator.print <- paste0("(", paste(params$encoder$generators, collapse="_8,"), "_8) = \\begin{pmatrix}", generator.matrix, "\\end{pmatrix}") } else { generator.print <- paste0("\\left(1,", paste0("\\frac{", head(params$encoder$generators, length(params$encoder$generators) - 1), "_8}{", tail(params$encoder$generators, 1), "_8}", collapse = ","), "\\right)") }
#cut off the parameters orig <- paste0( paste0(head(round(params$orig, decimal.digits), node.short), collapse = ", "), dots(params$orig, node.short)) parity1 <- paste0( paste0(head(round(params$parity1, decimal.digits), node.short), collapse = ", "), dots(params$parity1, node.short)) parity2 <- paste0( paste0(head(round(params$parity2, decimal.digits), node.short), collapse = ", "), dots(params$parity2, node.short)) origI <- paste0( paste0(head(round(params$origI, decimal.digits), node.short), collapse = ", "), dots(params$origI, node.short)) decode2 <- paste0( paste0(head(round(params$decode2, decimal.digits), node.short), collapse = ", "), dots(params$decode2, node.short)) decode2I <- paste0( paste0(head(round(params$decode2I, decimal.digits), node.short), collapse = ", "), dots(params$decode2I, node.short)) decode1 <- paste0( lapply(lapply(params$decode1, function(x) {head(round(x, decimal.digits), node.short)}), function(x) {paste0(x, collapse = ", ")}), lapply(params$decode1, function(x) {dots(x, node.short)})) decode1I <- paste0( lapply(lapply(params$decode1I, function(x) {head(round(x, decimal.digits), node.short)}), function(x) {paste0(x, collapse = ", ")}), lapply(params$decode1I, function(x) {dots(x, node.short)})) decode2Back <- paste0( lapply(lapply(params$decode2Back, function(x) {head(round(x, decimal.digits), node.short)}), function(x) {paste0(x, collapse = ", ")}), lapply(params$decode2Back, function(x) {dots(x, node.short)})) decode2IBack <- paste0( lapply(lapply(params$decode2IBack, function(x) {head(round(x, decimal.digits), node.short)}), function(x) {paste0(x, collapse = ", ")}), lapply(params$decode2IBack, function(x) {dots(x, node.short)})) resultHard <- paste0( lapply(lapply(params$tempResultHard, function(x) {head(x, node.short)}), function(x) {paste0(x, collapse = ", ")}), lapply(params$tempResultHard, function(x) {dots(x, node.short)})) resultSoft <- paste0( lapply(lapply(params$tempResultSoft, function(x) {head(round(x, decimal.digits), node.short)}), function(x) {paste0(x, collapse = ", ")}), lapply(params$tempResultSoft, function(x) {dots(x, node.short)}))
Faltungskodierer Informationen
r art.coderKodierer- Anzahl von Ausgängen : $$N=
r params$encoder$N$$ - Länge des Schieberegisters : $$M=
r params$encoder$M$$ - Generatoren : $$
r generator.print$$
Faltungskodierer Matrix : Nächster Zustand
\begin{center}
next.table <- params$encoder$next.state colnames(next.table) <- c("Bit 0", "Bit 1") row.counter <- rep(0:(dim(next.table)[1]-1)) rownames(next.table) <- paste("Zustand ", row.counter) knitr::kable(next.table, format="latex", align="c")
\end{center}
Faltungskodierer Matrix : Ausgangsbits
\begin{center}
output.table <- params$encoder$output output.table <- matrix(decToBin(as.vector(output.table)), ncol = ncol(output.table)) colnames(output.table) <- c("Bit 0", "Bit 1") row.counter <- rep(0:(dim(next.table)[1]-1)) rownames(output.table) <- paste("Zustand ", row.counter) knitr::kable(output.table, format="latex", align="c")
\end{center}
Faltungskodierer Matrix : Zustandsdiagramm
num.states <- 2^params$encoder$M state.order <- ordering(num.states, params$encoder$next.state) ## STATE DIAGRAM tikz.diagram <- "" # state diagram nodes for (s in 0:(num.states-1)) { xpos <- 2.5*sin(s*2*pi/num.states) ypos <- 2.5*cos(s*2*pi/num.states) position <- paste0(xpos,",",ypos) name <- paste(binVector(state.order[s+1], params$encoder$M),collapse = "") state <- paste0("\\node[state] (state",state.order[s+1],") at (",position,") {",name,"};") tikz.diagram <- paste(tikz.diagram, state) } # state diagram connections for (s in 0:(num.states-1)) { this.state <- paste0("(state",s,")") n_next.state.0 <- params$encoder$next.state[s+1,1] n_next.state.1 <- params$encoder$next.state[s+1,2] str_next.state.0 <- paste0("(state",n_next.state.0,")") str_next.state.1 <- paste0("(state",n_next.state.1,")") label.value.0 <- paste(binVector(params$encoder$output[s+1,1],params$encoder$N),collapse = "") label.value.1 <- paste(binVector(params$encoder$output[s+1,2],params$encoder$N),collapse = "") # indices of the states in the ordering vector (1 based) this.ordering.index <- which(state.order == s) next.0.ordering.index <- which(state.order == n_next.state.0) next.1.ordering.index <- which(state.order == n_next.state.1) # if edges do not go to neighbour, set label near start # to avoid label crossings near.0 <- "" near.1 <- "" distance.to.0 <- abs(this.ordering.index - next.0.ordering.index) distance.to.1 <- abs(this.ordering.index - next.1.ordering.index) if (distance.to.0 > 1 && distance.to.0 < num.states-1) { near.0 <- ",near start" } if (distance.to.1 > 1 && distance.to.1 < num.states-1) { near.1 <- ",near start" } # 2nd check in previous if clause necessary because if state numbers # are in first and last position of the ordering, they have distance # num.states-1 but are neighbours in the state diagram label.0 <- paste0("node [sloped, above",near.0,"] {",label.value.0,"}") label.1 <- paste0("node [sloped, above",near.1,"] {",label.value.1,"}") # in case of a loop angle <- (90-(this.ordering.index-1)*360/num.states) %% 360 angle.out <- (angle + 15) %% 360 angle.in <- (angle - 15) %% 360 if (n_next.state.0 == s) { # loop with input bit 0 loop <- paste0("[looseness=8,out=",angle.out,",in=",angle.in,"]") if (sin(angle*pi/180) < 0) { label.0 <- paste0("node [sloped, below",near.0,"] {",label.value.0,"}") } edge.0 <- paste("\\draw[->]",this.state,"to",loop,label.0,this.state,";") } else { # 'normal' edge to other node bend <- "" if (params$encoder$next.state[n_next.state.0+1,1] == s || params$encoder$next.state[n_next.state.0+1,2] == s) { # there is a connection back -> bend the edge bend <- "[bend left=15]" } edge.0 <- paste("\\draw[->]",this.state,"to",bend,label.0,str_next.state.0,";") } if (n_next.state.1 == s) { # loop with input bit 1 loop <- paste0("[looseness=8,out=",angle.out,",in=",angle.in,"]") if (sin(angle*pi/180) < 0) { label.1 <- paste0("node [sloped, below",near.1,"] {",label.value.1,"}") } edge.1 <- paste("\\draw[->, dashed]",this.state,"to",loop,label.1,this.state,";") } else { # 'normal' edge to other node bend <- "" if (params$encoder$next.state[n_next.state.1+1,1] == s || params$encoder$next.state[n_next.state.1+1,2] == s) { # there is a connection back -> bend the edge bend <- "[bend left=15]" } edge.1 <- paste("\\draw[->, dashed]",this.state,"to",bend,label.1,str_next.state.1,";") } tikz.diagram <- paste(tikz.diagram, edge.0, edge.1) }
\begin{center} \begin{tikzpicture}[>=stealth, font=\scriptsize] \tikzstyle{state} = [draw, circle, inner sep=1mm, minimum size=8mm, font=\footnotesize]
r tikz.diagram
\end{tikzpicture} \end{center}
Turbo-Dekodierer Informationen
- Interleaver : (
r head(params$permutation, node.long)``r dots(params$permutation, node.long)) \vspace*{6mm} - Koderate : $$\frac{1}{3}$$ \vspace*{6mm}
- Dekodierungsiterationen :
r params$iterations
Turbodekodierung ohne Punktierung
\begin{center} \begin{tikzpicture}[node distance=8mm, inner sep=2mm, outer sep=0,
=stealth, font=\tiny, align=center]
\tikzstyle{decoderStyle} = [rectangle, draw] \tikzstyle{deinterleaverStyle} = [rectangle, draw, node distance=4mm] \tikzstyle{startEndStyle} = [rectangle, draw] \tikzstyle{demultiplexerStyle} = [deinterleaverStyle] \tikzstyle{showStyle} = [decoderStyle, thick, draw=red, text=red, inner sep=1mm, overlay, fill=white] \tikzstyle{showDrawStyle} = [->, red, thick]
\node [node distance=4mm] (demultiplexerTemp) {}; \node [demultiplexerStyle, rotate=90] (demultiplexer) at (demultiplexerTemp.west) {Demultiplexer}; \node [decoderStyle] (decoder1) [above right=of demultiplexerTemp] {SISO\ Dekodierer 1}; \node [deinterleaverStyle] (interleaver1) [right=of decoder1] {$I$}; \node [deinterleaverStyle] (interleaver2) [above=4mm of interleaver1] {$I^{-1}$}; \node [deinterleaverStyle] (interleaver3) [below=4mm of interleaver1] {$I$}; \node [decoderStyle, node distance=4mm] (decoder2) [right=of interleaver3] {SISO\ Dekodierer 2}; \node [deinterleaverStyle] (interleaver4) [right=of decoder2] {$I^{-1}$}; \node [deinterleaverStyle] (finalCalculation) [right=of interleaver4] {$=$}; \node [startEndStyle] (start) [left=of demultiplexerTemp] {Input}; \node [startEndStyle, node distance=5mm] (end) [right=of finalCalculation] {Output};
\draw [->] (start.east) -- node (afterInput) {} (demultiplexer.north); \draw [->] (decoder1.east) -- node (afterDecoder1) {}(interleaver1.west); \draw [->] (interleaver3.east) -- node (afterInterleaver3) {} (decoder2.west); \draw [->] (decoder2.east) -- node (afterDecoder2) {} (interleaver4.west); \draw [->] (interleaver4.east) -- node (afterInterleaver4) {} (finalCalculation.west); \draw [->] (finalCalculation.east) -- node (afterFinalCalculation) {} (end.west);
\draw [->] ($(decoder2.east)+(0,+.2)$) -| ++(.2,.7) node (afterDecoder2Back) {} |- (interleaver2.east); \visible<1-5>{ \draw [<-, lightgray] ($(decoder1.west)+(0,+.2)$) -| ++(-.2,.7) |- node [near end] (afterInterleaver2) {} (interleaver2.west); } \alt<1-5>{ \draw [<-] ($(decoder1.west)+(0,+.2)$) -- ++(-1.1,0) node [near end, above=-0.1] {$\left(0,0,\cdots \right)$}; } { \draw [<-, lightgray] ($(decoder1.west)+(0,+.2)$) -- ++(-1.1,0) node [near end, above=-0.1] {$\left(0,0,\cdots \right)$}; } \visible<6->{ \draw [<-] ($(decoder1.west)+(0,+.2)$) -| ++(-.2,.7) |- node [near end] (afterInterleaver2) {} (interleaver2.west); } \draw [->] (interleaver1.east) -| ++(+.2,-.7) node [midway] (afterInterleaver1) {} |- ($(decoder2.west)+(0,+.2)$); \draw [->] ($(demultiplexer.south)+(0,+.4)$) -| ++(+.15,+.2) node (afterDemOrig) {} |- (decoder1.west); \draw [->] (demultiplexer.south) -| ++(+.3,+.4) node (afterDemParity1) {} |- ($(decoder1.west)+(0,-.2)$); \draw [->] (afterDemOrig) |- node [near end] (afterDemOrigInterl) {} (interleaver3.west); \draw [<-] ($(decoder2.west)+(0,-.2)$) -| ++(-.2,-.3)|- node [near end] (afterDemParity2) {} ($(demultiplexer.south)+(0,-.4)$);
\begin{scope}[on background layer] \node [draw, fit=(decoder1) (decoder2) (demultiplexer) (interleaver1) (interleaver2) (interleaver3) (interleaver4) (finalCalculation)] (background) {}; \end{scope}
\visible<1-4>{ \node [below =4mm of decoder2] {Iteration 1}; }
multipl.color <- character() vec <- head(round(params$code, decimal.digits), node.short) for (i in c(0:((length(vec) / 3) - 1))) { temp <- paste0( "\\textcolor{", colorOrig, "}{", vec[i * 3 + 1], "}, ", "\\textcolor{", colorParity1, "}{", vec[i * 3 + 2], "}, ", "\\textcolor{", colorParity2, "}{", vec[i * 3 + 3], "}", collapse = "" ) if (i == ((length(vec) / 3) - 1)) { multipl.color <- paste0(multipl.color, temp, collapse = "") } else { multipl.color <- paste0(multipl.color, temp, ", ", collapse = "") } }
% AfterDemultiplexer
\visible<2>{
\node [showStyle] (showAboveCenterTop) [above=9mm of background] {r multipl.color``r dots(params$code, node.short)};
\draw [showDrawStyle] (showAboveCenterTop) -- (afterInput.center);
\node [showStyle] (showAboveCenter) [above=3mm of background, text=`r colorOrig`] {`r orig`};
\draw [showDrawStyle] (showAboveCenter) -- (afterDemOrig.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background, text=`r colorParity1`] {`r parity1`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemParity1.center);
\node [showStyle] (showBelowCenter) [below=3mm of background, text=`r colorParity2`] {`r parity2`};
\draw [showDrawStyle] (showBelowCenter) -- (afterDemParity2.center);
}
% AfterDemulitplexer, AfterInterleaver2 - AfterDecoder1
\visible<3>{
\node [showStyle] (showAboveCenterTop) [above=9mm of background] {r decode1[[1]]};
\draw [showDrawStyle] (showAboveCenterTop) -- (afterDecoder1.center);
\node [showStyle] (showAboveCenter) [above=3mm of background] {`r orig`};
\draw [showDrawStyle] ($(showAboveCenter.south)+(-.5,0)$) -- (afterDemOrig.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {`r parity1`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemParity1.center);
}
% AfterDecoder1, AfterDemultiplexer - AfterInterleaver1, 2
\visible<4>{
\node [showStyle] (showAboveCenterTop) [above=9mm of background] {r decode1[[1]]};
\draw [showDrawStyle] (showAboveCenterTop) -- (afterDecoder1.center);
\node [showStyle] (showAboveCenter) [above=3mm of background] {`r decode1I[[1]]`};
\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver1.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {`r orig`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemOrigInterl.center);
\node [showStyle] (showBelowCenter) [below=3mm of background] {`r origI`};
\draw [showDrawStyle] (showBelowCenter) -- (afterInterleaver3.center);
}
tikz.string <- character() if (params$iterations > 1) { for (i in c(1:(params$iterations - 1))) { #AfterInterleaver1, 2, AfterDemultiplexer - AfterDecoder2Back slide1 <- paste0( "\\visible<", 5 + 4 * (i - 1), ">{ \\node [showStyle] (showAboveCenterTop) [above=9mm of background] {", parity2, "}; \\draw [showDrawStyle] (showAboveCenterTop) -- (afterDemParity2.center); \\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {", decode2Back[[i]], "}; \\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDecoder2Back.center); \\node [showStyle] (showAboveCenter) [above=3mm of background] {", decode1I[[i]], "}; \\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver1.center); \\node [showStyle] (showBelowCenter) [below=3mm of background] {", origI, "}; \\draw [showDrawStyle] (showBelowCenter) -- (afterInterleaver3.center);}", collapse = "" ) # AfterDecoder2Back - AfterInterleaver2 slide2 <- paste0( "\\visible<", 6 + 4 * (i - 1), ">{ \\node [showStyle] (showAboveCenterTop) [above=9mm of background] {", decode2IBack[[i]], "}; \\draw [showDrawStyle] (showAboveCenterTop) -- (afterInterleaver2.center); \\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {", decode2Back[[i]], "}; \\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDecoder2Back.center);}", collapse = "" ) # AfterDemulitplexer, AfterInterleaver2 - AfterDecoder1 slide3 <- paste0( "\\visible<", 7 + 4 * (i - 1), ">{ \\node [showStyle] (showAboveCenterTop) [above=9mm of background] {", decode2IBack[[i]], "}; \\draw [showDrawStyle] (showAboveCenterTop) -- (afterInterleaver2.center); \\node [showStyle] (showAboveCenter) [above=3mm of background] {", orig, "}; \\draw [showDrawStyle] (showAboveCenter) -- (afterDemOrig.center); \\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {", parity1, "}; \\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemParity1.center); \\node [showStyle] (showBelowCenter) [below=3mm of background] {", decode1[[i + 1]], "}; \\draw [showDrawStyle] (showBelowCenter) -- (afterDecoder1.center);}", collapse = "" ) # AfterDecoder1, AfterDemultiplexer - AfterInterleaver1, 2 slide4 <- paste0( "\\visible<", 8 + 4 * (i - 1), ">{ \\node [showStyle] (showAboveCenterTop) [above=9mm of background] {", decode1[[i + 1]], "}; \\draw [showDrawStyle] (showAboveCenterTop) -- (afterDecoder1.center); \\node [showStyle] (showAboveCenter) [above=3mm of background] {", decode1I[[i + 1]], "}; \\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver1.center); \\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {", orig, "}; \\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDemOrigInterl.center); \\node [showStyle] (showBelowCenter) [below=3mm of background] {", origI, "}; \\draw [showDrawStyle] (showBelowCenter) -- (afterInterleaver3.center);}", collapse = "" ) counter <- paste0( "\\visible<", 5 + 4 * (i - 1), "-", 8 + 4 * (i - 1), ">{\\node [below =4mm of decoder2] {Iteration ", i + 1 ,"};}" ) output <- paste0( "\\visible<", 5 + 4 * (i - 1), "-", 8 + 4 * (i - 1), ">{\\node [below =15mm of background, font=\\small, overlay] {Output : (", resultHard[[i]],")};}" ) tikz.string <- paste0(tikz.string, slide1, slide2, slide3, slide4, counter, output, collapse = "") } }
r tikz.string
%END
\visible<r params$iterations * 4 + 1-r params$iterations * 4 + 3>{
\node [below =4mm of decoder2] {Iteration r params$iterations};
}
\visible<r params$iterations * 4 + 1-r params$iterations * 4 + 3>{
\node [below =15mm of background, font=\small, overlay] {Output : (r resultHard[[params$iterations]])};
}
% AfterInterleaver1, 2, AfterDemultiplexer - AfterDecoder2
\visible<r params$iterations * 4 + 1>{
\node [showStyle] (showAboveCenterTop) [above=9mm of background] {r parity2};
\draw [showDrawStyle] (showAboveCenterTop) -- (afterDemParity2.center);
\node [showStyle] (showAboveCenter) [above=3mm of background] {`r decode1I[[params$iterations]]`};
\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver1.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {`r decode2`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDecoder2.center);
\node [showStyle] (showBelowCenter) [below=3mm of background] {`r origI`};
\draw [showDrawStyle] (showBelowCenter) -- (afterInterleaver3.center);
}
% AfterDecoder2 - AfterInterleaver4
\visible<r params$iterations * 4 + 2>{
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {r decode2};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterDecoder2.center);
\node [showStyle] (showAboveCenter) [above=3mm of background] {`r decode2I`};
\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver4.center);
}
% AfterInterleaver4 - AfterFinalCalculation
\visible<r params$iterations * 4 + 3>{
\node [showStyle] (showAboveCenter) [above=3mm of background] {r decode2I};
\draw [showDrawStyle] (showAboveCenter) -- (afterInterleaver4.center);
\node [showStyle] (showBelowCenterBottom) [below=9mm of background] {`r resultSoft[[params$iterations]]`};
\draw [showDrawStyle] (showBelowCenterBottom) -- (afterFinalCalculation.center);
}
\end{tikzpicture} \end{center}
Terminierung
term.string <- paste0( "- Output mit Terminierung : (", paste0(head(params$tempResultHard[[params$iterations]], length(params$tempResultHard[[params$iterations]]) - params$encoder$M), collapse = ", "), "\\textcolor{orange}{, ", paste0(tail(params$tempResultHard[[params$iterations]], params$encoder$M), collapse = ", "), "})", "\\vspace*{6mm}", "\n- Output ohne Terminierung : (", paste0(params$result$output.hard, collapse = ", "), ")" ) if (length(params$result$output.hard) > node.long) { term.string <- "Da der Output zu lang ist, kann die Terminierung leider nicht angezeigt werden!" }
r term.string
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