Questions tagged [information-theory]

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14
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2answers
4k 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 ...
9
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3answers
931 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 ...
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 ...
8
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2answers
7k 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 ...
7
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3answers
671 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, ...
7
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1answer
181 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 ...
6
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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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2answers
704 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 ...
5
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1answer
170 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
160 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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3answers
369 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
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3answers
133 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: $...
4
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1answer
47 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 ...
4
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1answer
266 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
514 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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2answers
597 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)...
3
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1answer
213 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
265 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 ...
3
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1answer
115 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
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1answer
221 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
421 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
460 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
81 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 ...
2
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3answers
3k 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{...
2
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3answers
288 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
254 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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1answer
678 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 ...
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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1answer
559 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/...
2
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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,...
2
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1answer
307 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 ...
2
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1answer
252 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
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 ...
1
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2answers
379 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 ...
1
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1answer
44 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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2answers
301 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?
1
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2answers
632 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
153 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
91 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
47 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
138 views

How to Detect a Inhomogeneity Region in Image

I have an image that includes object and background. However, the object appears some inhomogeneity region due to illumination. My work is that how to detect inhomogeneity region. Which is feature can ...
1
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1answer
21 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 ...
1
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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)}...
1
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2answers
425 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
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1answer
334 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 ...
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2answers
207 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?
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1answer
343 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'...
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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
303 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 = ...