Questions tagged [information-theory]

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1answer
225 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 ...
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1answer
66 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 ...
4
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3answers
143 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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1answer
385 views

Relation between SER and the channel capacity

Is there a relation between Symbol Error Rate (SER) and the channel capacity? What is {Modulation Order x (1-SER) / symbol duration [bps]} called?
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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 ...
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3answers
90 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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0answers
15 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
22 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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0answers
20 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}{||...
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1answer
48 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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0answers
35 views

Information entropy of Poisson noise

I would like to calculate the information entropy of the channel with additive Poisson noise. The model consists of an input signal, an optical image, an image acquisition device, and the output ...
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1answer
53 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
38 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
316 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 = ...
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1answer
33 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 ...
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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 ...
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1answer
32 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 $\frac{1}{2}\text{log}_2(1+\text{SNR})$, ...
0
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1answer
619 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 ...
1
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1answer
48 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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1answer
46 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 ...
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2answers
55 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 $\varepsilon$...
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2answers
53 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 ...
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1answer
35 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
28 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 ...
2
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1answer
668 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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2answers
464 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
48 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 ...
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1answer
19 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
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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2answers
316 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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1answer
141 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 ...
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1answer
50 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
156 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 ...
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1answer
698 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
29 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 ...
4
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1answer
270 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: ...
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2answers
42 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 ...
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,...
3
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1answer
433 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 ...
4
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3answers
378 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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2answers
487 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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1answer
281 views

Mechanics of a matrix Interleaver

I am having trouble understanding exactly how the matrix interleaver. I have read the following page from MathWorks. In it, it gives the following example where "123456" is interleaved as "142536." ...
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0answers
40 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
711 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
168 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 ...
3
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2answers
634 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)...
1
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1answer
341 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 ...
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{...