Questions tagged [information-theory]
The information-theory tag has no usage guidance.
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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):
$$
\frac {1}{n} H(K)> H-\epsilon \tag{2.6}\label{2.6},
$$...
4
votes
3answers
172 views
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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0answers
10 views
Mutual information smaller on data subsets compared to entire data set
I am estimating the mutual information for a continuous data set using the kNN-based mutual information estimator proposed by Kraskov et al [1].
Lets consider two features $X$ and $Y$, and the ...
2
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3answers
111 views
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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17 views
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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1answer
27 views
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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21 views
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}{||...
4
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1answer
50 views
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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1answer
58 views
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.
...
0
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1answer
40 views
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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1answer
33 views
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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1answer
38 views
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 ...
1
vote
1answer
50 views
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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2answers
80 views
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 $\varepsilon$...
0
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2answers
79 views
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 ...
0
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1answer
41 views
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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0answers
30 views
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 ...
1
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2answers
596 views
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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0answers
51 views
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 ...
0
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1answer
21 views
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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1answer
744 views
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 ...
0
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1answer
97 views
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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1answer
91 views
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
$$p^{(s)}...
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1answer
832 views
Can the Entropy Be Used as a Measure of the Contrast of an Image?
I was looking for value that can measure a contrast of an image. And I found a couple of answers like this one https://stackoverflow.com/questions/13397394/how-to-measure-contrast-in-opencv-visual-c/...
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1answer
49 views
What is the Asymptotic Equipartition Property (AEP)?
I am currently studying about Polar Codes in 5G standard and while reading my paper I found something called AEP which is required for channel coding. I surfed the web but didn't found a satisfying ...
1
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1answer
53 views
Relationship between spectral efficiency and PAR
Low PAR means less fluctiations in the magnitude of a signal and hence analog signal processing (e.g., power amplifier) is tremendously reduced. For example, constant envelope modulation schemes like ...
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1answer
168 views
Concatenated Deletion & Sticky Channel Capacity
Suppose you are sending information through a deletion channel with a deletion rate of .5 and then the output of this channel is sent through a sticky channel with a repeat rate of .5 also. No error ...
0
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1answer
793 views
White noise and entropy confusion about concepts
The spectral entropy (SE) of a signal is a measure of its spectral power distribution. The concept is based on the Shannon entropy, or information entropy, in information theory. The SE treats the ...
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1answer
46 views
Why $H(A)=H(C)$ where $C$ is $A$ with an additional parity bit?
Let $A=\{00,01,10,11\}$ with equal probabilities for each symbol, and $B=\{0, 1\}$ be a parity generator such that
$$
b=\begin{cases}
0, & \text{if} \,\, a=00 \quad \text{or} \quad a=11 \\
1, &...
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0answers
30 views
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 ...
1
vote
2answers
45 views
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 ...
0
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1answer
34 views
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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2answers
1k views
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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3answers
401 views
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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vote
2answers
338 views
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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2answers
549 views
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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0answers
43 views
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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2answers
756 views
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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0answers
183 views
What is the difference between entropy and entropy rate and which one is important in information theory? [duplicate]
By entropy I understand the uncertainty or randomness. But if the uncertainty is high then what is its implication and advantage in transmitting information or as an information source or is high ...
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2answers
713 views
Will the capacity of a channel becomes unbounded if i increase its signal-to-noise ratio $S/N$ without limit?
According to the Shannon-Hartley theorem the capacity $C$ of a channel which has a signal-to-noise ratio of $S/N$ and a bandwidth $B$ can be calculated to be $C = B \log_2 \left( 1 + \frac{S}{N}\right)...
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1answer
358 views
How to calculate the entropy of random normally distributed samples?
I have a hardware device that outputs a normal distribution of readings. It's (fitted) parameters are mean = 35 units, std.dev. = 8 units and I read the values as 8 bit integers.
I'm trying to ...
0
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1answer
291 views
coding gain and shaping gain in SCMA
It is said that sparse code multiple access (SCMA) has the advantage of higher shaping and coding gain over LDS-CDMA due to the multidimensional constellation. What exactly is the shaping gain and how ...
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0answers
288 views
SNR for channel after equalization
Suppose I have a channel described by $h[n]$ or $H(z)$ over which I send a simple PAM2 signal. After the channel AWGN is added.
What is the best possible SNR with equalization?
As suggested in the ...
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0answers
54 views
Is there a theoretical limit for how much information hiding can be done through watermarking?
There is a classic channel-capacity notion that exist based on the work of Shannon that gives gives measure of amount of information that can be passed through the channel given its properties.
In ...
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0answers
112 views
Intuitive interpretation of transform coding
I am currently studying source coding of waveform in a course of Information Theory and Coding. More precisely, I am trying to understand, both mathematically and intuitively, transform coding and its ...
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3answers
1k views
Capacity of AWGN channel
I am confused understanding basic concepts of communication over AWGN channels. I know the capacity of a discrete time AWGN channel is:
$$C=\frac{1}{2}\log_2\left(1+\frac{S}{N}\right)$$
and it is ...
0
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1answer
183 views
Given a noise-free channel with limited bandwidth, why is the channel capacity infinite? [duplicate]
In the Shannon Hartley theorem, if N = 0 but B is limited, the theorem tells us that C is infinite. Why is this intuitively true?
If bandwidth is limited, I can only post so many pulses per second ...
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2answers
232 views
Why is bandwidth always limited in a real (physical) channel?
I'm talking about a continuous analog channel.
Why can't it support infinite bandwidth?
Is there a physics reasons for it say for electrical signals?
2
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1answer
762 views
What is the effect of noise on Shannon entropy?
Since entropy is a measure of uncertainty or randomness, intuitively we would suppose that adding noise to an image would increase its entropy since we are now more uncertain about the information of ...
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1answer
76 views
Word length for time series
This question is based on , "A Symbolic Representation of Time Series, with Implications for Streaming Algorithms".
Let, $N = w\cdot l$ where $N$ is the number of data points in a time series ...
