cdma encoding

cdma.Rmd

@@ -20,21 +20,61 @@ on the receiving side.
 knitr::opts_chunk$set(echo = TRUE)
 ```
 
-## Getting Input
+## Input and binary interpretation
 We first get input by reading a file `input.txt`, where each line (0-3) is one communication channel.
 Because UTF8 maintains compatibility with ASCII, the UTF8 conversion can be used assuming that the input is only ASCII.
 ASCII characters require 7 bits of information per character.
 ```{r input}
-lines <- readLines('./input.txt')
+lines <- readLines('./input.txt',encoding = 'ASCII')
-lines_bin <- unlist(lapply(lines, utf8ToInt))
+strToBin <- function(s){
+  # FIXME for strings longer than 1
+  r <- as.integer(intToBits(utf8ToInt(s)))
+  r <- r[1:7]
+  return(r)
+}
+lines_bin <- do.call(rbind, lapply(lines, strToBin))
 ```
 
 ```{r input-demo, echo=FALSE}
 print(lines)
-print(lines_bin)
+print(lines_bin[1])
+print(lines_bin[2])
+print(lines_bin[3])
+print(lines_bin[4])
+
 ```
 
 ## Orthogonal Code
-For an orthogonal code, we are looking for vectors $(a,b,...n)$ in  that satisfy pairwise orthogonality $a \perp b$.
+For an orthogonal code, we are looking for vectors $(a,b,...n)$ that satisfy pairwise orthogonality $a \perp b$.
+```{r orth}
+o1 <- c( 1, 1, 1, 1, 1)
+o2 <- c(-1,-1, 1, 1, 1)
+o3 <- c( 1,-1, 1,-1,-1)
+o4 <- c(-1, 1, 1,-1,-1)
+orthogonals <- do.call(rbind,list(o1,o2,o3,o4))
+```
+
+```{r orth-demo, include=FALSE}
+perms <- combn(x = orthogonals,m = 2, simplify = FALSE)
+```
+
+## Encode
+
+
+```{r encode}
+output = c()
+for (j in 1:ncol(lines_bin)){
+  col <- lines_bin[,j]
+  output_symbol <- 0
+  for (i in 1:length(col)){
+    symbol <- col[i] # the symbol to be encoded
+    code <- orthogonals[i,] # the code vector
+
+    single_symbol <- (-1)^(1+symbol) * code # the resulting encoded vector
+    output_symbol <- output_symbol + single_symbol # the sum of all encoded vectors
+  }
+  output <-append(output, output_symbol)
+}
+```