Questions tagged [information-theory]

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11
votes
1answer
3k views

Relationship between entropy and SNR

In general any form of enropy is defined as uncertainty or randomness. In a noisy environment, with increase in noise, I believe that entropy increases since we are more uncertain about the ...
8
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2answers
4k views

What is the meaning of Mutual Information beyond the numerical calculation?

Beyond the raw equation for calculating mutual information, what does it mean in physical terms? For example: From Information Theory, we know that entropy is the smallest loss-less compression scheme ...
7
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3answers
601 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 ...
6
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2answers
6k views

What are some typical lossless compression ratios?

A client was trying to send me 250 GB worth of files. After attempting various ways of sharing the data, he sent me a zipped folder only 4 GB in size. That sounds like too much compression to me--I ...
6
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3answers
600 views

Is concept of “bit” in computer programming similar to the concept of “bit” in information theory?

until today I knew that one bit is a variable, or a space in memory that can hold a value of either One (high) or Zero (low). This is the concept I learned from studying computer programming, ...
6
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1answer
166 views

Issues related to entropy

I have long been faced with the confusion regarding entropy and would be obliged if the following are answered in less technical jargon. Following the link Different kinds of entropy raises the ...
5
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1answer
138 views

Does any error correction code still work in such situation?

I'm looking for a kind of error correction code or solution that can correct my codeword in this case: My message holds $k$ bits, and $2k$ bits codeword (rate is $1/2$) is produced by the generator ...
5
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1answer
2k views

Why is mutual information symmetric but conditional entropy isn't?

Conditional entropy $H(X|Y)$ tells us how much the average uncertainty about a channel input $X$ is after observing channel output $Y$, and mutual information $I(X,Y)$ measures how much information ...
5
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1answer
148 views

Mutual Information, is this calculation correct or should I contact the author about fixing it?

Background information According to Cover's text book on information theory Mutual Information is calculated as: $$(1) I(W;C) = \Sigma_k\Sigma_i P(C_k,W_i)log(\frac{P(C_k,W_i)}{P(C_k)P(W_i)}) $$ ...
4
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2answers
479 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 ...
4
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3answers
236 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 ...
4
votes
1answer
262 views

Image registration / fusion optimal similarity metrics

I have a theoretical question about optimal similarity metrics for comparing data sets. In reading this linked paper, pp. 488-489 [1], I read the following 2 interesting statements. On page 488: ...
3
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2answers
1k views

Meaning of channel capacity in the AWGN channel

I understand the concept of channel capacity as the maximal rate of the channel code I can apply without making a mistake in the receiver, in that sense the capacity is between 0 and 1. What I don't ...
3
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2answers
445 views

What is the entropy for these cases?

This question stems from an article, "Entropy estimation of symbol sequences" download link where the abstract mentions the need for using symbols in information theory. Random chains of ...
3
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1answer
178 views

Difficulties in understanding mutual information concept

What does mutual information (MI) convey? If 2 signals are independent then MI is zero; What does this imply and mean in the case of mutual information of error, and in general definition of MI and ...
3
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1answer
110 views

Conceptual question on entropy and its relation to information

Learning Informative Statistics: A Nonparametric Approach paper presents an approach to parameter estimation by entropy minimization. There are other related works "Minimum-entropy estimation in semi-...
3
votes
1answer
203 views

Conceptual problem : numberof symbols for nonuniform distribution using entropy : how to determine block size?

A sequence of data of length $N$ can be subdivided into equal sixed blocks each of length (size) $l$. For each block, $w$, we can calculate the entropy known as the block entropy. Considering, entropy ...
3
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1answer
300 views

Mathematical model of equivalent-time sampling, the resulting unevenly spaced periodic signal, and its interpretation

I sample a continuous signal $s(T)$ over time. This leads to $s[t]$, which depends on several factors of which some are (pseudo-) periodic. I am interested in the effect of one such periodic factors ...
2
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2answers
367 views

Conceptual definition of entropy

What is the conceptual difference between Kolmogorov-Sinai entropy, Shannon entropy and Boltzmann entropy? Are they interchangeable and mean the same? Where can I find a good lucid explanation about ...
2
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3answers
252 views

Is there a proof that equal bandwidths have equal information-carrying capacity?

Consider a continuous channel, band-limited to the $[f_{\text{min}},\,f_{\text{max}}]$ frequency window. A well-known statement says that, as far as the dependence on the frequencies, the information-...
2
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2answers
215 views

Entropy Of A Symbol

Does the entropy of a symbol represent the most optimal average number of bits that can be used to represent a symbol? For example take the example of tossing a coin: $$ H_{source} = -p_{head} ...
2
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2answers
300 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)...
2
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1answer
1k views

What is Shannon's source entropy

Suppose that ${X_n; Y_n}$ is a random process with a discrete alphabet, that is, taking on values in a discrete set for $n$ data length. They correspond to the input and output of a communication ...
2
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2answers
662 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,...
2
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1answer
220 views

Mutual information of $ \infty $-PAM

I'm trying to compute using matlab the mutual information for an $ \infty $-PAM input (the limit of a very dense PAM constellation) for a range of snr and I got stuck. I'm working with a real-valued ...
2
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1answer
217 views

Effect of noise and entropy

Relation of Entropy and SNR : Based on this question and answer, I had another question that struck me and I am curious to know, if somebody can shed some light, on the following situation: $y= ...
2
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0answers
53 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 ...
1
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3answers
2k views

What is the theoretical probability of error for OOK transmission?

I am trying to simulate an optical wireless communication channel which uses OOK modulation. Looking at equation 14 in this literature, I found that: For electrical SNR at the receiver $$\textrm{...
1
vote
1answer
38 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, &...
1
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2answers
134 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
469 views

Confusion about shannon's entropy of the grayscale image after lossy compression

I have a .pgm format 480 * 640 gray scale image named 'columns.pgm'. Using PCA (principal component analysis), by preserving 40 principal components I compressed original image with 1218 KB to 301 KB ...
1
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1answer
137 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 ...
1
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1answer
455 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 ...
1
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1answer
65 views

Why are some LDPC codes more immune to noise than others?

When one analyzes an LDPC code, it is usual to plot the BER versus the $E_b / N_0$. My questions are: Why are some LDPC codes better than others in terms of noise immunity? After all, they are just ...
1
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1answer
45 views

Can channel capcity be explained in simple terms? [closed]

Can channel capacity be explained in simple terms - without mutual information and such probabilistic concepts? In its most general form, what are all the parameters that it depends on? What is its ...
1
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1answer
79 views
+50

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)}...
1
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2answers
129 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. ...
1
vote
1answer
204 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 ...
1
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2answers
140 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?
1
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1answer
278 views

Source and channel encoding

In information theory, there are two concepts that are widely used: source encoding and channel encoding. I'm afraid I may not be capable of expressing my doubts clearly, but the thing is that I don'...
1
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1answer
59 views

Discrete entropies

I've been given a problem where I need to find the entropy of two random variables. I can find part of the answer, but not all of it. I am given the following: $X$ is a uniformly distributed random ...
1
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1answer
184 views

Why is $x$ not considered a primitive polynomial while being considered an irreducible polynomial?

In "Shu Lin, Daniel J. Costello-Error Control Coding (2nd Edition), Prentice Hall 2004" it is given that in $GF(2)$, if $f(x)$ is an irreducible polynomial of degree $m$ it divides $x^n+1$ where $n = ...
1
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2answers
127 views

What are the fundamental reasons that suggest us to minimise transmission power for energy-efficient radio link design?

My question in short: Under which scenarios minimising transmission power is beneficial in terms of transmitter energy-efficiency? is there any fundamental reason to keep a low-power oriented design ...
1
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1answer
70 views

Can somebody help me with some very basic questions about the fundamentals of information theory?

I just started to study information content of the source and there are some very fundamental topics I am not really clear on. These might be a long question or a series of questions. Please help me. ...
1
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1answer
192 views

Filters performance analysis

I am working on some experimental data which, at some point, need to be time-integrated and then high-pass filtered (to remove low frequency disturbancies introduced by integration and unwanted DC ...
1
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1answer
299 views

Dominant eigenvectors of an unknown matrix

Do you have any idea about how we can find the principal eigenvectors of an unknown matrix ${H}$? The elements of $H$ are unknown in general. If you are familiar with channel estimation procedure in ...
1
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1answer
32 views

Why entropy value can be used as measure of 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/...
1
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0answers
21 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
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0answers
35 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 "...
1
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0answers
94 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 ...