Questions tagged [information-theory]
The information-theory tag has no usage guidance.
112
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Applying Blahut-Arimoto Algorithm for AWGN Channels Capacity Calculation with Cost
I am exploring the Blahut-Arimoto algorithm (or any numerical method) for channel capacity calculations, particularly for continuous channels. I understand its application in discrete scenarios, but I ...
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How to calculate the following mutual infomation between $X$ and $Y$ in matlab or python?
Recently I meet the following question: Let $X\in {\mu_1,\mu_2,\cdots,\mu_m}$, $Y \in {R_1,R_2,\cdots,R_n}$, where $\mu_i, i = 1,2,\cdots,m$ is means of $m$ gauss probablity density function, $Y$ is ...
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Lower bound on information or entropy?
Inspired by this question: Does a simple photograph contain more information than a complex painting?
Say that I have a discrete representation of some physical object - eg an image file. What is the ...
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How to code Rician fading channel gains from k-factor?
I know that MATLAB provides some built-in functions but I am not interested in those. I want to know how can we code to obtain the Rician fading channel gains from normal or Gaussian distributions. ...
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Advantages/disadvantages of impulse excitation vs step excitation
i'm currently working on a circuit transient simulation, and I'm wondering how the type of input excitation can affect the final result. In particular the focus is on impulse input vs step input, to ...
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What is the intuition explaining the Shannon-Hartley theorem?
In the digital domain, the signal to noise ratio (SNR) may be interpreted loosely but usefully as the number of discrete or quantized levels one can transmit reliably. For instance, loosely speaking, ...
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What are the differences between GPS and GLONASS?
I'm studying the localization systems, especially the GPS one. I inquired about other systems and wanted to understand what are the main differences between GPS and GLONASS, why has the first type ...
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Entropy Loss in Linear Filters
I've been trying to figure out the result for the entropy loss/entropy gain in linear systems derived in "The Mathematical Theory of Communication" by Claude Shannon.
Claude Shannon states ...
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Proof that block of independent Gaussian symbols has higher mutual information than correlated Gaussian symbols in band- & power-limited AWGN channel
Given a discrete-time AWGN channel defined by:
$$
Y = X + N
$$
where $N$ is a zero-mean Gaussian RV with $E[N^2] = P_N$ representing additive noise, $X$ is the transmitted symbol with power ...
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Shannon capacity limit & FEC comparisons
In this figure from Fundamentals of Digital Communications by Madhow , pp 328 there is a comparison of a rate 1/3 turbo code with the shannon limit for rate 1/3 BPSK:
Trying to understand the limit ...
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Soft-output decoder
I am trying to implement the soft-output for my soft-decoder, however, the resulting log-likelihood ratios are not corresponding to the corrected hard bits.
The soft-output regards the LLR-values for ...
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value of 0 log0 in entropy formula
Why is the value of $p_i\log(p_i)$ in entropy formula considered $0$ when $p_i =0$? I get that it is the limiting value, but does that mean $p$ is never equals to zero, but only tends to?
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Is there a way to describe the pattern of a signal as a numeric value?
I've been digging a little into signal processing and I just started a networks and telecommunications class at college. We saw there are different encode techniques Amplitude, Frequency and Phase ...
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Secret Sharing & Information Theory
I'm reading a paper -- Common Randomness in Information Theory and Cryptograph-secret.
And I do have trouble in understanding formula (2.6):
$$
\frac {1}{n} H(K)> H-\epsilon \tag{2.6}\label{2.6},
$$...
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Encoding sequence of unfair coin flips
The question: Consider transmitting the results of $1000$ flips of an unfair coin where the probability of heads is given by $p_H$. The information contained in an unfair coin flip can be computed:
$...
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Determining Loss of Information by Taking Average (Mean of Signal)
So basically information is defined by expected value of Shannon's information i.e. Entropy. I am curious how much information is lost if we simply take the average of the sample given to us. I am ...
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About convergence of KL divergence: if the two probability distributions are type, does the law of large number work?
If I pick $N$ samples from $P_X$ and $P_Y$, they are two independent discrete distributions.
$X_1,X_2,\ldots,X_N$ are drawn i.i.d from $P_X$, and $Y_1,\ldots,Y_N$ are drawn i.i.d from $P_Y$.
I got $...
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Why the requirement of the GCD of the lengths of all circuits in the graph being one?
I am reading A Mathematical Theory of Communication. The second requirement of an ergodic process confuses me (emphasis mine):
All the examples of artificial languages given above are ergodic. This
...
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Channel Impulse Response is zero mean Gaussian random variable?
In the Paper "Key Generation From Wireless Channels" the channel estimation is given as:
$\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||S_B||^2}$,
$\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||...
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Can the Nyquist sample rate be extended to stochastic sampling?
It appears there are lots of questions here about Nyquist, and a few questions about stochastic sampling here. But I haven't found any that address quite what I'm after. This is the closest I've ...
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Bandwidth and probability of continuous signal
I'm a little bit confused as to how to calculate the bandwidth of a signal. A question has me believing that it is correlated with the probability distribution. I am however not sure of this.
...
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Information theory vs system theory ( commented in Determining linearity, causality, memory, and time invariability from a picture of the signal)
I have seen this question :
At the comment asked about :
Is this "information theory" or "systems theory"? – The Photon
So i liked to know why this comment asked? Why the system theory vs ...
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Wireless communications outage
For communication systems, there is usually a target minimum rate $R$ bits per second. An outage occurs if the actual rate ever falls below $R$. Since $\frac{1}{2}\text{log}_2(1+\text{SNR})$, ...
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Example of Entropy and Channel Capacity Computation
Can you help me on verifying if this computation of entropy is correct and on understanding its meaning?
I am not sure of the result especially because it is equal to 0: it means that we cannot ...
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Understanding Asymptotic Equipartition Property
I have some problems in understanding the precise meaning of the Asymptotic Equipartition Property, related to a large number n of independent and identically distributed random variables (X1, X2, ...,...
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When channels are in a cascade and are independent is the capacity the sum?
Just wondering if two channels are independent then is the overall capacity, the sum of the individual capacities?
For example suppose I have two BEC where the probability of erasure is $\varepsilon$...
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Definition of Perfect Code (and example of Hamming Code)
Let's consider the following sentences about coding a message before transmitting it in a communication system (here you find the complete pdf)
First question: can you explain me these two ...
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Band-limited signal recovery with finite bit depth
The sampling theorem tells us that a signal with no frequencies above $f$ can be completely described by sampling it a rate of $2f$. However, the theorem makes no reference to quantization, and so I ...
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Pearson correlation coefficient vs mutual information
I recently computed both the pearson coefficient and the mutual information of two time series as well as the corresponding error bars, and what I find out in the end is a significant level of ...
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Nyquist noiseless channel capacity; how can bit-rate be two times the bandwidth?
I'm confused by the Nyquist channel capacity formula. How can channel maximum capacity approach double the bandwidth.
$C = 2\times BW \times log_{2}(L)$ bits/sec
The way it was explained to me ...
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Capacity achieving codes for BPSK at low SNR
I don't know a lot about comm system design.
I have an AWGN channel and low SNR (-3dB). Bandwidth is constrained to some maximum, B. I would like to know good choices of modulation and coding to ...
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How good is the Leech lattice for AWGN coding or MSE quantization of Gaussian sources?
Anyone know where to find graphs showing how well it works vs other schemes? thanks
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How do I measure the amount of information within an image?
I'm trying to find some information threshold that is required for performing detection of objects in images. However, I'm not sure how exactly to quantify the amount of information contained within ...
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Proof that DFT does not require more than N points
I'm trying to show how the discrete Fourier transform (DFT) arises from the equation for the continuous-time Fourier Transform. I've run into an interesting caveat which I can't seem to find an ...
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Maximizing entropy on a channel
In Shannon's paper "A Mathematical Theory of Communication", in Theorem 8 he states:
Theorem 8: Let the system of constraints considered as channel have a capacity $C = \log W$. If we assign
$$p^{(s)}...
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Can the Entropy Be Used as a Measure of the Contrast of an Image?
I was looking for value that can measure a contrast of an image. And I found a couple of answers like this one https://stackoverflow.com/questions/13397394/how-to-measure-contrast-in-opencv-visual-c/...
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What is the Asymptotic Equipartition Property (AEP)?
I am currently studying about Polar Codes in 5G standard and while reading my paper I found something called AEP which is required for channel coding. I surfed the web but didn't found a satisfying ...
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Relationship between spectral efficiency and PAR
Low PAR means less fluctiations in the magnitude of a signal and hence analog signal processing (e.g., power amplifier) is tremendously reduced. For example, constant envelope modulation schemes like ...
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Concatenated Deletion & Sticky Channel Capacity
Suppose you are sending information through a deletion channel with a deletion rate of .5 and then the output of this channel is sent through a sticky channel with a repeat rate of .5 also. No error ...
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White noise and entropy confusion about concepts
The spectral entropy (SE) of a signal is a measure of its spectral power distribution. The concept is based on the Shannon entropy, or information entropy, in information theory. The SE treats the ...
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Why $H(A)=H(C)$ where $C$ is $A$ with an additional parity bit?
Let $A=\{00,01,10,11\}$ with equal probabilities for each symbol, and $B=\{0, 1\}$ be a parity generator such that
$$
b=\begin{cases}
0, & \text{if} \,\, a=00 \quad \text{or} \quad a=11 \\
1, &...
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Does Mutual information utilize spatial information to calculate image similarity?
To calculate images similarity based on Mutual Information (MI), histogram and join histogram is required. In the literature, there are 2 contradict opinions about MI operation. 1. MI does not utilize ...
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Rate in CDMA setup
I am working on a CDMA system with only 4 chips/symbol. I want to use $R=\frac{1}{2}log_2(1+SNR)$ chips/channel use to calculate what $SNR$ I require to successfully receive a given transmission. In ...
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Is there some literature to understand finite state ISI channel?
I am trying to understand channels with memory, where the state of the channel gives the past input information. I want to delve further into capacity for channels with ISI. I came across a ...
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Choosing samples per symbol for modem pulse
One of the parameters in my DSP library for pulse design is "samples per symbol", and I would like to get some advice about choosing this parameter when designing a modem.
The smaller the pulse width,...
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How to reconcile "bandwidth" in the Shannon-Hartley Theorem with a spread-spectrum principle
I'm trying to understand something about channel "bandwidth" $B$ in the Shannon-Hartley Theorem: $$C = B \log_2 \left( 1 + \dfrac{S}{N} \right) $$
Suppose I have a bitstream encoded as a signal that ...
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Channel Capacity - is this only for discrete/digital signals?
The units of channel capacity is bits/second. Does this mean this only refers to discrete/digital signals? Is channel capacity analogous to bandwidth in case of an analog signal transmission?
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Don't understand what is meant by signal dimension
I don't understand the concept of dimension of a signal. I ran into it in an explanation of Shannon Capacity, and in a paper on spread spectrum. I was hoping somebody could explain with an example. ...
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Capacity region of 'symbol asynchronous' Gaussian multiple access channel
I was interested to learn what theoretical limits have been determined so far for the 'multiple access channel' with additive Gaussian noise. This brought me to the 1989 paper by Sergio Verdu, named "...
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What is the meaning of channel capacity?
If the transmitted information signal takes values from a modulation constellation, then is there a way to know what the channel capacity is?
Is there a connection between the modulation kind and ...
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