In DaniWi/Channelcoding: channelcoding
# transforms an integer value n to a at least min.length bit binary vector
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(tail(result,min.length))
}
# returns an ordering of the state numbers for a nice state diagram
ordering <- function(num.states, next.state) {
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)
}
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)
}
conv.encoder <- params$conv.encoder
message <- c(params$message)
M <- conv.encoder$M
N <- conv.encoder$N
generators <- conv.encoder$generators
output <- conv.encoder$output
next.state <- conv.encoder$next.state
prev.state <- conv.encoder$prev.state
termination <- conv.encoder$termination
rsc.flag <- conv.encoder$rsc
terminate <- params$terminate
num.states <- 2^M
# add termination bits to message if termination is TRUE
s <- 0
for (bit in message) {
s <- next.state[s+1, bit+1]
}
if (terminate) {
for (i in 1:M) {
bit <- if(rsc.flag) termination[s+1] else 0
message <- c(message, bit)
s <- next.state[s+1,bit+1]
}
}
state.color.vector <- rep(NA, length(message))
arrow.color.vector.0 <- rep(NA, length(message))
arrow.color.vector.1 <- rep(NA, length(message))
s <- 0
for (i in 1:length(message)) {
state.color.vector[i] <- s
if (message[i] == 0) {
arrow.color.vector.0[i] <- s
} else {
arrow.color.vector.1[i] <- s
}
s <- next.state[s+1,message[i]+1]
}
state.order <- ordering(num.states, next.state)
## STATE DIAGRAM
tikz.diagram <- ""
# state diagram nodes
for (s in 0:(num.states-1)) {
color.frames <- paste(which(state.color.vector == state.order[s+1])+1, collapse = ",")
color.frames <- if(color.frames == "") 0 else color.frames
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],M),collapse = "")
black.state <- paste0("\\node[state] (state",state.order[s+1],") at (",position,") {",name,"};")
color.state <- paste0("\\node[state, orange] (state",state.order[s+1],") at (",position,") {",name,"};")
state <- paste0("\\alt<",color.frames,"> {",color.state,"}{",black.state,"};")
tikz.diagram <- paste(tikz.diagram, state)
}
# state diagram connections
for (s in 0:(num.states-1)) {
color.frames.0 <- paste(which(arrow.color.vector.0 == s) + 1, collapse = ",")
color.frames.0 <- if(color.frames.0 == "") 0 else color.frames.0
color.frames.1 <- paste(which(arrow.color.vector.1 == s) + 1, collapse = ",")
color.frames.1 <- if(color.frames.1 == "") 0 else color.frames.1
this.state <- paste0("(state",s,")")
n_next.state.0 <- next.state[s+1,1]
n_next.state.1 <- 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(output[s+1,1],N),collapse = "")
label.value.1 <- paste(binVector(output[s+1,2],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,";")
color.edge.0 <- paste("\\draw[->, orange]",this.state,"to",loop,label.0,this.state,";")
}
else {
# 'normal' edge to other node
bend <- ""
if (next.state[n_next.state.0+1,1] == s || 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,";")
color.edge.0 <- paste("\\draw[->, orange]",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,";")
color.edge.1 <- paste("\\draw[->, dashed, orange]",this.state,"to",loop,label.1,this.state,";")
}
else {
# 'normal' edge to other node
bend <- ""
if (next.state[n_next.state.1+1,1] == s || 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,";")
color.edge.1 <- paste("\\draw[->, dashed, orange]",this.state,"to",bend,label.1,str_next.state.1,";")
}
edge.0 <- paste0("\\alt<",color.frames.0,"> {",color.edge.0,"}{",edge.0,"};")
edge.1 <- paste0("\\alt<",color.frames.1,"> {",color.edge.1,"}{",edge.1,"};")
tikz.diagram <- paste(tikz.diagram, edge.0, edge.1)
}
# Legend of bit transitions (--- Bit 0, - - - Bit 1)
mid.state.num <- state.order[num.states / 2 + 1]
legend.bit.0 <- paste0("\\draw [->] ($(state",mid.state.num,")+(-.5,-2)$) node (bit0) {} -- ++(1,0) node [right] {Bit 0};")
legend.bit.1 <- paste0("\\draw [->, dashed] ($(bit0)+(0,-.5)$) -- ++(1,0) node [right] {Bit 1};")
tikz.diagram <- paste(tikz.diagram, legend.bit.0, legend.bit.1)
## ENCODE TABLE
encode.table <- ""
visible.output <- ""
index <- 2
state <- 0
for (i in message) {
visibility <- paste0("\\visible<",index,"->")
thisState <- paste(binVector(state,M),collapse = "")
code.output <- paste(binVector(output[state+1,i+1],N),collapse = "")
nextState <- paste(binVector(next.state[state+1,i+1],M),collapse = "")
hline <- ""
if (terminate && index == length(message) + 1 - M) {
hline <- "\\hline"
}
table.row <- paste(visibility,"{",i,"&",thisState,"&",nextState,"&",code.output,"\\\\",hline,"}")
encode.table <- paste(encode.table, table.row)
## step for step output is displayed
# first iteration: "(" else: ","
first.char <- if(index - 2 == 0) "(" else ", "
output.bits <- paste(binVector(output[state+1,i+1],N) , collapse = ", ")
output.bits <- paste0(first.char, output.bits)
if (index - 1 == length(message)) {
output.bits <- paste0(output.bits, ")")
}
visible.def <- paste0("\\visible<",index,"->")
visible.part <- paste0(visible.def,"{",output.bits,"}")
visible.output <- paste0(visible.output, visible.part)
index <- index + 1
state <- next.state[state+1,i+1]
}
# Kodierer Informationen
if (rsc.flag == TRUE) {
art.coder <- "Rekursiver"
} else {
art.coder <- "Nicht-Rekursiver"
}
if (rsc.flag == FALSE) {
generator.matrix <- paste0(decToBin(octalToDec(generators)), " \\\\ ", collapse = "")
generator.print <-
paste0("(", paste(generators, collapse="_8,"), "_8) = \\begin{pmatrix}", generator.matrix, "\\end{pmatrix}")
} else {
generator.print <- paste0("\\left(1,", paste0("\\frac{", head(generators, length(generators) - 1), "_8}{", tail(generators, 1), "_8}", collapse = ","), "\\right)")
}
Faltungskodierer Informationen
r art.coder Kodierer- Anzahl von Ausgängen : $$N=
r N$$
- Länge des Schieberegisters : $$M=
r M$$
- Generatoren : $$
r generator.print$$
- Koderate : $$\frac{1}{
r N}$$
Faltungskodierer Matrix : Nächster Zustand
\begin{center}
next.table <- 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 <- 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}
Faltungskodierung
Input : (r message)
\begin{center}
\begin{minipage}{.45\textwidth}
\begin{center}
\begin{tabular}{c c c c}
\visible<1-> {Input & Zustand & Folgezustand & Output\ \hline}
r encode.table
\end{tabular}
\end{center}
Output : r visible.output
\end{minipage}
\hfill
\begin{minipage}{.45\textwidth}
\begin{center}
\begin{tikzpicture}[scale=.70, >=stealth, font=\tiny]
\tikzstyle{state} = [draw, circle, inner sep=1mm, minimum size=6mm, font=\scriptsize]
r if (M < 4) tikz.diagram
\end{tikzpicture}
\end{center}
\end{minipage}
\end{center}
Output : Kode zu Signal
- Kode : (
r ifelse(params$code >= 0, 0, 1))
\vspace{10mm}
\begin{equation}
\text{Signal(bit)} =
\begin{cases}
+1 & \quad \text{wenn bit} = 0\
-1 & \quad \text{wenn bit} = 1\
\end{cases}
\end{equation}
\vspace{10mm}
- Signal : (
r params$code)
DaniWi/Channelcoding documentation built on May 6, 2019, 1:23 p.m.
R Package Documentation
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# transforms an integer value n to a at least min.length bit binary vector 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(tail(result,min.length)) } # returns an ordering of the state numbers for a nice state diagram ordering <- function(num.states, next.state) { 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) } 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) }
conv.encoder <- params$conv.encoder message <- c(params$message) M <- conv.encoder$M N <- conv.encoder$N generators <- conv.encoder$generators output <- conv.encoder$output next.state <- conv.encoder$next.state prev.state <- conv.encoder$prev.state termination <- conv.encoder$termination rsc.flag <- conv.encoder$rsc terminate <- params$terminate num.states <- 2^M # add termination bits to message if termination is TRUE s <- 0 for (bit in message) { s <- next.state[s+1, bit+1] } if (terminate) { for (i in 1:M) { bit <- if(rsc.flag) termination[s+1] else 0 message <- c(message, bit) s <- next.state[s+1,bit+1] } } state.color.vector <- rep(NA, length(message)) arrow.color.vector.0 <- rep(NA, length(message)) arrow.color.vector.1 <- rep(NA, length(message)) s <- 0 for (i in 1:length(message)) { state.color.vector[i] <- s if (message[i] == 0) { arrow.color.vector.0[i] <- s } else { arrow.color.vector.1[i] <- s } s <- next.state[s+1,message[i]+1] } state.order <- ordering(num.states, next.state) ## STATE DIAGRAM tikz.diagram <- "" # state diagram nodes for (s in 0:(num.states-1)) { color.frames <- paste(which(state.color.vector == state.order[s+1])+1, collapse = ",") color.frames <- if(color.frames == "") 0 else color.frames 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],M),collapse = "") black.state <- paste0("\\node[state] (state",state.order[s+1],") at (",position,") {",name,"};") color.state <- paste0("\\node[state, orange] (state",state.order[s+1],") at (",position,") {",name,"};") state <- paste0("\\alt<",color.frames,"> {",color.state,"}{",black.state,"};") tikz.diagram <- paste(tikz.diagram, state) } # state diagram connections for (s in 0:(num.states-1)) { color.frames.0 <- paste(which(arrow.color.vector.0 == s) + 1, collapse = ",") color.frames.0 <- if(color.frames.0 == "") 0 else color.frames.0 color.frames.1 <- paste(which(arrow.color.vector.1 == s) + 1, collapse = ",") color.frames.1 <- if(color.frames.1 == "") 0 else color.frames.1 this.state <- paste0("(state",s,")") n_next.state.0 <- next.state[s+1,1] n_next.state.1 <- 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(output[s+1,1],N),collapse = "") label.value.1 <- paste(binVector(output[s+1,2],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,";") color.edge.0 <- paste("\\draw[->, orange]",this.state,"to",loop,label.0,this.state,";") } else { # 'normal' edge to other node bend <- "" if (next.state[n_next.state.0+1,1] == s || 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,";") color.edge.0 <- paste("\\draw[->, orange]",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,";") color.edge.1 <- paste("\\draw[->, dashed, orange]",this.state,"to",loop,label.1,this.state,";") } else { # 'normal' edge to other node bend <- "" if (next.state[n_next.state.1+1,1] == s || 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,";") color.edge.1 <- paste("\\draw[->, dashed, orange]",this.state,"to",bend,label.1,str_next.state.1,";") } edge.0 <- paste0("\\alt<",color.frames.0,"> {",color.edge.0,"}{",edge.0,"};") edge.1 <- paste0("\\alt<",color.frames.1,"> {",color.edge.1,"}{",edge.1,"};") tikz.diagram <- paste(tikz.diagram, edge.0, edge.1) } # Legend of bit transitions (--- Bit 0, - - - Bit 1) mid.state.num <- state.order[num.states / 2 + 1] legend.bit.0 <- paste0("\\draw [->] ($(state",mid.state.num,")+(-.5,-2)$) node (bit0) {} -- ++(1,0) node [right] {Bit 0};") legend.bit.1 <- paste0("\\draw [->, dashed] ($(bit0)+(0,-.5)$) -- ++(1,0) node [right] {Bit 1};") tikz.diagram <- paste(tikz.diagram, legend.bit.0, legend.bit.1) ## ENCODE TABLE encode.table <- "" visible.output <- "" index <- 2 state <- 0 for (i in message) { visibility <- paste0("\\visible<",index,"->") thisState <- paste(binVector(state,M),collapse = "") code.output <- paste(binVector(output[state+1,i+1],N),collapse = "") nextState <- paste(binVector(next.state[state+1,i+1],M),collapse = "") hline <- "" if (terminate && index == length(message) + 1 - M) { hline <- "\\hline" } table.row <- paste(visibility,"{",i,"&",thisState,"&",nextState,"&",code.output,"\\\\",hline,"}") encode.table <- paste(encode.table, table.row) ## step for step output is displayed # first iteration: "(" else: "," first.char <- if(index - 2 == 0) "(" else ", " output.bits <- paste(binVector(output[state+1,i+1],N) , collapse = ", ") output.bits <- paste0(first.char, output.bits) if (index - 1 == length(message)) { output.bits <- paste0(output.bits, ")") } visible.def <- paste0("\\visible<",index,"->") visible.part <- paste0(visible.def,"{",output.bits,"}") visible.output <- paste0(visible.output, visible.part) index <- index + 1 state <- next.state[state+1,i+1] }
# Kodierer Informationen if (rsc.flag == TRUE) { art.coder <- "Rekursiver" } else { art.coder <- "Nicht-Rekursiver" } if (rsc.flag == FALSE) { generator.matrix <- paste0(decToBin(octalToDec(generators)), " \\\\ ", collapse = "") generator.print <- paste0("(", paste(generators, collapse="_8,"), "_8) = \\begin{pmatrix}", generator.matrix, "\\end{pmatrix}") } else { generator.print <- paste0("\\left(1,", paste0("\\frac{", head(generators, length(generators) - 1), "_8}{", tail(generators, 1), "_8}", collapse = ","), "\\right)") }
Faltungskodierer Informationen
r art.coderKodierer- Anzahl von Ausgängen : $$N=
r N$$ - Länge des Schieberegisters : $$M=
r M$$ - Generatoren : $$
r generator.print$$ - Koderate : $$\frac{1}{
r N}$$
Faltungskodierer Matrix : Nächster Zustand
\begin{center}
next.table <- 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 <- 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}
Faltungskodierung
Input : (r message)
\begin{center}
\begin{minipage}{.45\textwidth}
\begin{center}
\begin{tabular}{c c c c}
\visible<1-> {Input & Zustand & Folgezustand & Output\ \hline}
r encode.table
\end{tabular}
\end{center}
Output : r visible.output
\end{minipage}
\hfill
\begin{minipage}{.45\textwidth}
\begin{center}
\begin{tikzpicture}[scale=.70, >=stealth, font=\tiny]
\tikzstyle{state} = [draw, circle, inner sep=1mm, minimum size=6mm, font=\scriptsize]
r if (M < 4) tikz.diagram
\end{tikzpicture}
\end{center}
\end{minipage}
\end{center}
Output : Kode zu Signal
- Kode : (
r ifelse(params$code >= 0, 0, 1)) \vspace{10mm} \begin{equation} \text{Signal(bit)} = \begin{cases} +1 & \quad \text{wenn bit} = 0\ -1 & \quad \text{wenn bit} = 1\ \end{cases} \end{equation} \vspace{10mm} - Signal : (
r params$code)
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