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){
        "1"
      }else{
        ""
      }
    }
  }
  return (paste0(sapply(vec, fun_factory(vec)),collapse=""))
}

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

nextColor = function(x){
  if(x == 'red')
    return('green')
  else if(x == 'green')
    return('blue')
  else if(x == 'blue')
    return('orange')
  else if(x == 'orange')
    return('red')
}


block.encoder = params$block.encoder

enc <- params$enc
enc.corrected <- params$enc.corrected
dec <- params$dec
coderate <- block.encoder$data.length / block.encoder$code.length

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


art.coder <- paste0("Hamming (",block.encoder$code.length,",",block.encoder$data.length,")")


check.matrix <- apply(block.encoder$check.matrix, 1, function(x) paste0(x, collapse ="&"))
check.matrix <-  paste0(check.matrix, collapse = "\\\\")
check.matrix <- paste0("\\begin{pmatrix}",check.matrix, "\\end{pmatrix}", collapse="")

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

dec.print <- apply(dec.matrix, 1, function(x) paste0(x, collapse =","))

corrected.output = c()

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

  corrected.vec = enc.corrected.matrix[i,]

  error.positions = c()
  errors = enc.matrix[i,] - enc.corrected.matrix[i,]
  for(j in 1:length(errors)){
    if(errors[j] != 0){
      corrected.vec[j] = toColor(corrected.vec[j],'green')
      error.positions = c(error.positions,j)
    }
  }

  enc.vec <- paste0(enc.matrix[i,], collapse="\\\\")
  enc.vec <- paste0("\\begin{pmatrix}",enc.vec, "\\\\ \\end{pmatrix}^T", collapse="")

  if(length(error.positions)>0){
    res.vec <- block.encoder$check.matrix[,error.positions[1]]
    res.vec <- sapply(res.vec, function(x) toColor(x,'red'))
    check.matrix.print <- block.encoder$check.matrix
    check.matrix.print[,error.positions[1]] = sapply(check.matrix.print[,error.positions[1]], function(x) toColor(x,'red'))
    check.matrix.print <- apply(check.matrix.print, 1, function(x) paste0(x, collapse ="&"))
    check.matrix.print <-  paste0(check.matrix.print, collapse = "\\\\")
    check.matrix.print <- paste0("\\begin{pmatrix}",check.matrix.print, "\\end{pmatrix}", collapse="")
  }else{
    res.vec <- rep(0,nrow(block.encoder$check.matrix))
    res.vec <- sapply(res.vec, function(x) toColor(x,'green'))
    check.matrix.print <- check.matrix
  }
  res.vec <- paste0(res.vec, collapse="\\\\")
  res.vec <- paste0("\\begin{pmatrix}",res.vec, "\\\\ \\end{pmatrix}^T", collapse="")

  encoding <- paste0(encoding, "$$",enc.vec,". ",check.matrix.print," = ",res.vec,"$$\n\n")

  encoding <- paste0(encoding,"Kodewort: (",paste0(enc.matrix[i,],collapse = ","),") \n\n")
    encoding <- paste0(encoding,"Fehlerindex: ",paste0(error.positions,collapse = " | ")," \n\n")
    encoding <- paste0(encoding,"Korrigiertes Kodewort: (",paste0(corrected.vec,collapse = ","),") \n\n")
    corrected.output = c(corrected.output,corrected.vec)
    if(length(error.positions)>0)
      dec.print[i] = toColor(dec.print[i],'green')


}

enc.corrected.matrix.print <- apply(matrix(corrected.output,ncol=block.encoder$code.length, byrow=T), 1, function(x) paste0(x, collapse ="&"))
enc.corrected.matrix.print <-  paste0(enc.corrected.matrix.print, collapse = "\\\\")
enc.corrected.matrix.print <- paste0("\\begin{pmatrix}",enc.corrected.matrix.print, "\\end{pmatrix}", collapse="")

dec.print = paste0(dec.print,collapse = ",")

Blockcodierer Informationen

• r art.coder Kodierer
• Parity-Check Matrix : $$H = r check.matrix$$
• Kode-Rate : $$\frac{r block.encoder$data.length}{r block.encoder$code.length} \approx r round(coderate,2)$$

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

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

r encoding

Output

• Korrigierte Kodematrix: $$r enc.corrected.matrix.print$$
• Output:(\textcolor{green}{grün = Fehler korrigiert}, schwarz = Keine Fehler) \begin{center}(r dec.print)\end{center}

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