"cells": [
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 8,
"metadata": {},
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"text": [
- "Source entropy: 3.752113900074267\n",
- "A 100 0.11124094587747317\n",
- "G 011 0.10871437801707752\n",
- "J 010 0.10387210756270529\n",
- "N 000 0.10117027679041204\n",
- "D 0011 0.05197115173264662\n",
- "H 1011 0.06917828453811696\n",
- "I 0010 0.05068162249832686\n",
- "K 1100 0.06944726813123069\n",
- "L 1111 0.09883293392076788\n",
- "O 1101 0.08712441679935146\n",
- "F 10101 0.03078339099377846\n",
- "P 11101 0.04731352894459562\n",
- "B 101000 0.013013334609193211\n",
- "C 101001 0.014536815467673516\n",
- "E 111001 0.022193047647813914\n",
- "M 111000 0.019926496468836808\n",
- "decoded: JGGAKLPM\n",
+ "A 010 0.10889628583541382\n",
+ "C 001 0.09152888714794946\n",
+ "G 000 0.08903984849793534\n",
+ "B 1011 0.07059353601667875\n",
+ "E 1001 0.07001353988551143\n",
+ "H 1111 0.08826797559046656\n",
+ "J 1101 0.07422403331445343\n",
+ "K 0111 0.05648000917065521\n",
+ "L 1110 0.08784093309263273\n",
+ "N 0110 0.05289972255448987\n",
+ "O 1100 0.07110861095979067\n",
+ "P 1010 0.07018129978231921\n",
+ "F 10000 0.024254244476492406\n",
+ "D 100011 0.022376076316506087\n",
+ "I 1000100 0.006899547136273925\n",
+ "M 1000101 0.015395450222431209\n",
+ "\n",
+ "encoded: 01001101110011001111111011110000\n",
+ "decoded: ANLNKHKF\n",
+ "\n",
+ "Source entropy: 3.802902958392826\n",
"Average codeword length: 4.375\n"
]
}
"letters = [chr(i+65) for i in range(num_of_letters)]\n",
"random_probs = [random.random() for _ in range(num_of_letters)]\n",
"total_prob = sum(random_probs)\n",
- "# cannot be 1 / 256\n",
"probabilities = {letters[i]: random_probs[i] / total_prob for i in range(16)}\n",
"\n",
+ "# Probability cannot be 1 / 256\n",
"while True:\n",
" for i in range(16):\n",
" if list(probabilities.values())[i] <= (1 / 256):\n",
- " print(\"false\")\n",
" continue\n",
" break\n",
"\n",
- "\n",
- "source_entropy = -1*sum([p * math.log2(p) for l, p in probabilities.items()])\n",
- "print(\"Source entropy: \", source_entropy)\n",
- "\n",
"def huffman_coding(probabilities):\n",
" heap = [[weight, [symbol, \"\"]] for symbol, weight in probabilities.items()]\n",
" heapify(heap)\n",
"encoded_string=\"01001101110011001111111011110000\"\n",
"decoded_symbols = huffman_decoding(encoded_string, code_dict)\n",
"\n",
- "print(f\"decoded: {decoded_symbols}\")\n",
+ "print()\n",
+ "print(f\"encoded: {encoded_string}\\ndecoded: {decoded_symbols}\")\n",
+ "print()\n",
+ "\n",
+ "source_entropy = -1*sum([p * math.log2(p) for l, p in probabilities.items()])\n",
+ "print(\"Source entropy: \", source_entropy)\n",
"\n",
"average_len = sum([len(code) for l, code in code_dict.items()]) / len(code_dict)\n",
- "print(\"Average codeword length: \", average_len)\n"
+ "print(\"Average codeword length: \", average_len)"
]
},
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-\documentclass[11pt]{report}
+\documentclass[11pt]{article}
\usepackage{graphicx}
\usepackage{listings}
\begin{document}
\maketitle
-\section{Laboratory Exercise 2}
-\section{Laboratory Exercise 3}
-\section{Laboratory Exercise 4}
+\newpage
+\tableofcontents
+\section{Introduction}
+
+This lab report covers the student tasks and report questions from the laboratory exercises
+2, 3 and 4 in the course TSKS35, Information and Communications
+Engineering. The tasks and results from laboratory 1 is not included in this report.
+
+\section{Laboratory exercise 2}
+
+\subsection{Student tasks}
+
+Exercise 2 is made up of three student tasks covering the following topics:
+\todo{}.
+\begin{itemize}
+ \item This is a topic
+
+ \item This is another topic
+\end{itemize}
+
+\subsection{Report questions}
+
+Answers for the report questions of Laboratory Exercise 2.
+
+\begin{enumerate}
+ \item \textbf{Explain what is an energy- and power-type signal and their
+ characteristics. Is the signal from Student Task 1 a power- or energy-type signal?
+ Why is it called time-average autocorrelation function, and what is the power
+ spectrum?}
+
+ This is my answer \todo
+
+ \item \textbf{What happen at different sampling rates in Student Task 2?
+ What is the aliasing distortion?}
+
+ This is my answer
+
+ \item \textbf{3. What is the lowpass representation of a
+ bandpass signal?}
+
+ This is my answer
+
+\end{enumerate}
+
+\section{Laboratory exercise 3}
+
+Exercise 3 is also made up of three student tasks, although the results are better summarized in a single section.
+
+\subsection{Student tasks}
+
+The first task was to create an alphabet of 16 symbols, each encoded using at most 8 bits for Huffman coding.
+After the alphabet was generated the given, incomplete, Huffman encoding algorithm was to be finalized.
+The final task was similarly to finish a Huffman decoding algorithm and verify the functionality of the algorithms created.
+
+The resulting Python-code is included in the appendix\nobreakspace\ref{app:code_lab3} and the resulting output (an example) from the code is shown below:
+
+\begin{lstlisting}
+ A 010 0.10889628583541382
+ C 001 0.09152888714794946
+ G 000 0.08903984849793534
+ B 1011 0.07059353601667875
+ E 1001 0.07001353988551143
+ H 1111 0.08826797559046656
+ J 1101 0.07422403331445343
+ K 0111 0.05648000917065521
+ L 1110 0.08784093309263273
+ N 0110 0.05289972255448987
+ O 1100 0.07110861095979067
+ P 1010 0.07018129978231921
+ F 10000 0.024254244476492406
+ D 100011 0.022376076316506087
+ I 1000100 0.006899547136273925
+ M 1000101 0.015395450222431209
+
+ encoded: 01001101110011001111111011110000
+ decoded: ANLNKHKF
+
+ Source entropy: 3.802902958392826
+ Average codeword length: 4.375
+\end{lstlisting}
+
+In the output the alphabet is first listed in the format: \textit{symbol Huffman-code probability}.
+The probabilities are all randomly generated. Shown below the alphabet is the bitstring to be decoded and
+the resulting string of symbols obtained when decoding the bitstring using the generated alphabet. Finally
+the entropy and the average codeword length of the source, the generated alphabet, is calculated and displayed.
+
+\subsection{Report questions}
+
+Answers for the report questions of Laboratory Exercise 3.
+
+\begin{enumerate}
+ \item \textbf{What is the difference between lossless and lossy compression? What type of compression is done with Huffman coding?}
+
+ This is my answer \todo
+
+ \item \textbf{Why Huffman source code is called fixed to variable-length coding?}
+
+ This is my answer
+
+ \item \textbf{What is the prefix condition?}
+
+ This is my answer
+
+ \item \textbf{Why Huffman codes are said to be instantaneous?}
+
+ This is my answer
+
+ \item \textbf{Calculate the entropy of the source in Student task 1 and
+ the average length of the corresponding Huffman code in Student task 2.
+ Comment on your results and relate it to the source-coding theorem.}
+
+ This is my answer
+
+\end{enumerate}
+
+\section{Laboratory exercise 4}
+
+Exercise 4 is also made up of three student tasks covering the following topics:
-Exercise 4 is made up of 3 parts, student tasks, covering the following topics:
\begin{itemize}
\item Generation of different constellations representing symbols to be used by a transmitter.
\item Assigning gray codes to the symbols.
\item Transmission and reception of the symbols through an AWGN (Additive White Gaussian Noise) channel.
\item Comparison of the symbol/bit error rates of the different constellations.
- \item Transmission and reception of encoded data using the Hamming code (7, 4) and comparison
- of the symbol/bit error rates of the different constellations.
+ \item Transmission and reception of encoded data across an AWGN channel using the Hamming code (7, 4) and
+ comparison of the symbol/bit error rate of a channel using this code to a channel without any coding.
\end{itemize}
-The code used to solve the tasks and generate all figures is included in the appendix\nobreakspace\ref{app:code_lab4}
+The python-code used to solve the tasks and generate all figures is included in the appendix\nobreakspace\ref{app:code_lab4}
\subsection{Student task 1: Generation of constellations}
\caption{16-QAM constellation}\label{fig:qam16}
\end{figure}
-\subsection{Student task 2: Signal transmission through AWGN channel}
+\subsection{Student task 2: Signal transmission through an AWGN channel}
The second task was to generate $10^6$ randomized symbols using the constellations from
student task 1 and transmit them through an AWGN channel. The received symbols were then
\caption{Bit error rate of QPSK modulated symbols with and without Hamming code (7, 4) across different SNR values. }\label{fig:qpsk_hamming}
\end{figure}
-\subsection{Report Questions}
+\subsection{Report questions}
-Answers for the report-questions of Laboratory Exercise 4.
+Answers for the report questions of Laboratory Exercise 4.
-\begin{itemize}
+\begin{enumerate}
\item \textbf{What are the difference between one- and two-dimensional constellations?
What is the difference between amplitude and phase modulations?
Observe and describe the constellations.}
- This is my answer
+ This is my answer \todo
+
\item \textbf{What is the purpose of Gray encoding? What is the difference between symbol
error rate and bit error rate after applying Gray coding?}
\item \textbf{Comment on the difference on the symbol error rate for different modulation
schemes, what are the advantages and disadvantages of those?}
- This is my answer
+ This is my answer
\item \textbf{What is the purpose of channel coding?}
This is my answer
-\end{itemize}
+
+\end{enumerate}
\appendix
-\section{Code for Laboratory Exercise 4}\label{app:code_lab4}
+\section{Python-code: Laboratory exercise 2}\label{app:code_lab2}
+\begin{lstlisting}[language=Python]
+
+\end{lstlisting}
+\section{Python-code: Laboratory exercise 3}\label{app:code_lab3}
+\begin{lstlisting}[language=Python]
+ # %%
+ import random
+ from heapq import heappush, heappop, heapify
+ from collections import defaultdict
+ import math
+
+ num_of_letters = 16
+
+ letters = [chr(i+65) for i in range(num_of_letters)]
+ random_probs = [random.random() for _ in range(num_of_letters)]
+ total_prob = sum(random_probs)
+ probabilities = {letters[i]: random_probs[i] / total_prob for i in range(16)}
+
+ # Probability cannot be 1 / 256
+ while True:
+ for i in range(16):
+ if list(probabilities.values())[i] <= (1 / 256):
+ continue
+ break
+
+ def huffman_coding(probabilities):
+ heap = [[weight, [symbol, ""]] for symbol, weight in probabilities.items()]
+ heapify(heap)
+
+ while len(heap) > 1:
+ lo = heappop(heap)
+ hi = heappop(heap)
+ for elm in lo[1:]:
+ elm[1] = "0" + elm[1]
+ for elm in hi[1:]:
+ elm[1] = "1" + elm[1]
+
+ heappush(heap, [lo[0] + hi[0]] + lo[1:] + hi[1:])
+
+ return sorted(heappop(heap)[1:], key=lambda p: (len(p[1]), p))
+
+ def huffman_decoding(encoded_string, codes):
+ reverse_codes = {v: k for k, v in codes.items()}
+
+ acc = ""
+ output = ""
+
+ for bit in encoded_string:
+ acc += bit
+ if acc in reverse_codes.keys():
+ output += reverse_codes[acc]
+ acc = ""
+
+ return output
+
+ codes = huffman_coding(probabilities)
+
+ code_dict = {item[0]: item[1] for item in codes}
+
+ for letter, code in code_dict.items():
+ print(letter, code, probabilities[letter])
+
+ encoded_string="01001101110011001111111011110000"
+ decoded_symbols = huffman_decoding(encoded_string, code_dict)
+
+ print()
+ print(f"encoded: {encoded_string}\ndecoded: {decoded_symbols}")
+ print()
+
+ source_entropy = -1*sum([p * math.log2(p) for l, p in probabilities.items()])
+ print("Source entropy: ", source_entropy)
+
+ average_len = sum([len(code) for l, code in code_dict.items()]) / len(code_dict)
+ print("Average codeword length: ", average_len)
+\end{lstlisting}
+\section{Python-code: Laboratory exercise 4}\label{app:code_lab4}
\begin{lstlisting}[language=Python]
# %%
import numpy as np
--- /dev/null
+\contentsline {section}{\numberline {1}Introduction}{2}{section.1}%
+\contentsline {section}{\numberline {2}Laboratory exercise 2}{3}{section.2}%
+\contentsline {subsection}{\numberline {2.1}Student tasks}{3}{subsection.2.1}%
+\contentsline {subsection}{\numberline {2.2}Report questions}{3}{subsection.2.2}%
+\contentsline {section}{\numberline {3}Laboratory exercise 3}{3}{section.3}%
+\contentsline {subsection}{\numberline {3.1}Student tasks}{3}{subsection.3.1}%
+\contentsline {subsection}{\numberline {3.2}Report questions}{4}{subsection.3.2}%
+\contentsline {section}{\numberline {4}Laboratory exercise 4}{5}{section.4}%
+\contentsline {subsection}{\numberline {4.1}Student task 1: Generation of constellations}{6}{subsection.4.1}%
+\contentsline {subsection}{\numberline {4.2}Student task 2: Signal transmission through an AWGN channel}{6}{subsection.4.2}%
+\contentsline {subsection}{\numberline {4.3}Student task 3: Channel coding}{12}{subsection.4.3}%
+\contentsline {subsection}{\numberline {4.4}Report questions}{12}{subsection.4.4}%
+\contentsline {section}{\numberline {A}Python-code: Laboratory exercise 2}{14}{appendix.A}%
+\contentsline {section}{\numberline {B}Python-code: Laboratory exercise 3}{14}{appendix.B}%
+\contentsline {section}{\numberline {C}Python-code: Laboratory exercise 4}{15}{appendix.C}%
projects / TSKS35.git / commitdiff