From: Nils Forssén Date: Thu, 12 Dec 2024 02:33:52 +0000 (+0100) Subject: report wip X-Git-Url: https://gitweb.forssennils.se/?a=commitdiff_plain;h=340dc9d0d314a3bc60a264cbfe858b3fc7d1c839;p=TSKS35.git report wip --- diff --git a/lab3.ipynb b/lab3.ipynb index 902cf93..523d83f 100644 --- a/lab3.ipynb +++ b/lab3.ipynb @@ -2,31 +2,34 @@ "cells": [ { "cell_type": "code", - "execution_count": 22, + "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "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" ] } @@ -42,20 +45,15 @@ "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", @@ -96,10 +94,15 @@ "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)" ] }, { diff --git a/report/main.aux b/report/main.aux index 9865f88..f8a895f 100644 --- a/report/main.aux +++ b/report/main.aux @@ -16,39 +16,64 @@ \gdef\HyperFirstAtBeginDocument#1{#1} \providecommand\HyField@AuxAddToFields[1]{} \providecommand\HyField@AuxAddToCoFields[2]{} -\@writefile{toc}{\contentsline {section}{\numberline {0.1}Laboratory Exercise 2}{1}{section.0.1}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {0.2}Laboratory Exercise 3}{1}{section.0.2}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {0.3}Laboratory Exercise 4}{1}{section.0.3}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline 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@@ \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} @@ -86,7 +200,7 @@ The generated constellations with gray codes are shown in figures~\ref{fig:pam8} \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 @@ -166,16 +280,17 @@ of 2 dB and the plot displays a logarithmic scale for the y-axis to better show \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?} @@ -184,15 +299,92 @@ Answers for the report-questions of Laboratory Exercise 4. \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 diff --git a/report/main.toc b/report/main.toc new file mode 100644 index 0000000..8384791 --- /dev/null +++ b/report/main.toc @@ -0,0 +1,15 @@ +\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}%