In DaniWi/Channelcoding: channelcoding

vecToPoly = function(vec){
  fun_factory = function(vec){
    i = length(vec)
    function(x){
      i <<- i-1
      if(x>0 && i>0){
        paste0("x^{",i, "}")
      }else if(i == 0 && x>0){
        "1"
      }else{
        ""
      }
    }
  }
  vec = sapply(vec, fun_factory(vec))
  return (paste0(vec[vec != ""],collapse=" + "))
}

toColor = function(x, color){
  return(paste0("\\textcolor{",color,"}{",x,"}"))
}


block.encoder = params$block.encoder

message <- params$message
code <- params$code
coderate = block.encoder$data.length / block.encoder$code.length

message.matrix <- matrix(message, ncol=block.encoder$data.length, byrow = TRUE)
code.matrix <- matrix(code, ncol=block.encoder$code.length, byrow = TRUE)

art.coder <- paste0("BCH (",block.encoder$code.length,",",block.encoder$data.length,",",block.encoder$code.t*2+1,")")


gen.poly.print <- vecToPoly(rev(block.encoder$gen.poly))

message.matrix.print <- apply(message.matrix, 1, function(x) paste0(x, collapse ="&"))
message.matrix.print <-  paste0(message.matrix.print, collapse = "\\\\")
message.matrix.print <- paste0("\\begin{pmatrix}",message.matrix.print, "\\end{pmatrix}", collapse="")

code.matrix.print <- apply(code.matrix, 1, function(x) paste0(x, collapse ="&"))
code.matrix.print <-  paste0(code.matrix.print, collapse = "\\\\")
code.matrix.print <- paste0("\\begin{pmatrix}",code.matrix.print, "\\end{pmatrix}", collapse="")



rest.length <- block.encoder$code.length-block.encoder$data.length

encoding <- ""
for(i in 1:nrow(message.matrix)){
  encoding <- paste0(encoding, "## Kodieren des ",i,". Blocks \n")

  data.poly <- vecToPoly(rev(message.matrix[i,]))
  datastar.poly <- vecToPoly(c(rev(message.matrix[i,]),rep(0,rest.length)))
  rest.poly <- vecToPoly(rev(code.matrix[i,][1:rest.length]))
  code.poly <- vecToPoly(rev(code.matrix[i,]))

  encoding <- paste0(encoding,"Input: (",toColor(paste0(message.matrix[i,],collapse = ","),'green'),") \n\n")
  encoding <- paste0(encoding,"Daten Polynom: $$d(x) = ",data.poly,"$$\n")
  encoding <- paste0(encoding,"Generator Polynom: $$g(x) = ",gen.poly.print,"$$\n")
  encoding <- paste0(encoding,"$$ d^*(x) = d(x)*x^{",rest.length,"} = ",datastar.poly,"$$\n")
  encoding <- paste0(encoding,"Rest Polynom: $$r(x) = d^*(x)\\mod g(x) = ",rest.poly,"$$\n")
  encoding <- paste0(encoding,"Kode Polynom: $$c(x) = c( r(x)|d(x) ) = ",code.poly,"$$\n")
  encoding <- paste0(encoding,"Output: (\\textcolor{red}{",paste0(code.matrix[i,][1:rest.length],collapse = ","),",}\\textcolor{green}{",paste0(code.matrix[i,][(rest.length+1):block.encoder$code.length],collapse = ","),"})\n\n")
  encoding <- paste0(encoding," (\\textcolor{red}{Redundanzbits},\\textcolor{green}{Datenbits})\n\n")
}

Blockcodierer Informationen

• r art.coder Kodierer
• Generatorpolynom : $$g(x) = r gen.poly.print$$
• Verbesserbare Fehler pro Block: $$r block.encoder$code.t$$
• Kode-Rate : $$\frac{r block.encoder$data.length}{r block.encoder$code.length} \approx r round(coderate,2)$$

Nachricht in Blöcke der Länge r block.encoder$data.length aufteilen

• Nachricht: \begin{center}(r message)\end{center}
• Nachrichtsmatrix: $$r message.matrix.print$$

r encoding

Output

• Kodematrix: $$r code.matrix.print$$
• Kode: \begin{center}(r code)\end{center}

DaniWi/Channelcoding documentation built on May 6, 2019, 1:23 p.m.