Questions tagged [information-theory]
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91
questions
3
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1answer
210 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 ...
1
vote
1answer
31 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, ...,...
0
votes
1answer
30 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 ...
0
votes
1answer
45 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 ...
0
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2answers
38 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
votes
2answers
41 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
votes
1answer
28 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 ...
1
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0answers
11 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
votes
1answer
244 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/...
1
vote
2answers
107 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 ...
0
votes
0answers
34 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
16 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
0
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1answer
145 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
vote
1answer
89 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
$$p^{(s)}...
1
vote
2answers
230 views
Channel Capacity - is this only for discrete/digital signals?
The units of channel capacity is bits/second. Does this mean this only refers to discrete/digital signals? Is channel capacity analogous to bandwidth in case of an analog signal transmission?
0
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0answers
36 views
Symmetric Capacity of a Binary Discrete Memoryless Channel
While reading this paper https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5075875, I found that the the symmetric capacity of BDMC $W$ is given by
$$I(W) = \sum_{y\in Y}\sum_{x\in X}\...
0
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0answers
20 views
Punctured Turbo Code Decoding: Convergence Issue
I have been trying to create a basic BCJR decoder for a rate (1/2) punctured turbo code. The puncturing is simple, the encoder alternatively selects between the parity bits generated by the two ...
1
vote
1answer
135 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 ...
0
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0answers
23 views
Two inputs channel capacity
Assume that we have an AWGN channel with two inputs (A,B) and the o/p is written as Y = A + g B + Z where Z is an independent Gaussian noise with zero mean and unit variance and g is a constant ...
0
votes
1answer
35 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 ...
1
vote
1answer
143 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
votes
1answer
414 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 ...
1
vote
1answer
42 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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0answers
22 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
votes
1answer
265 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:
...
0
votes
2answers
36 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
votes
1answer
32 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
votes
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
votes
1answer
341 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
votes
3answers
298 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 ...
1
vote
2answers
239 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
230 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 = ...
0
votes
1answer
206 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." ...
1
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0answers
39 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 "...
4
votes
2answers
583 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 ...
1
vote
0answers
116 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 ...
2
votes
2answers
393 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
vote
1answer
290 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
vote
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{...
0
votes
1answer
237 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 ...
1
vote
0answers
206 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 ...
2
votes
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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0answers
94 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 ...
8
votes
3answers
715 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
votes
1answer
234 views
Shannon's entropy for non-equiprobable symbols
I am trying to understand the concept of Shannon's entropy and deciding the codelength. In first case, b is an array of 5 symbols. The symbol set is $\{1,2,...,8\}$....
1
vote
2answers
155 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?
0
votes
1answer
152 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 ...
1
vote
1answer
533 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 ...
0
votes
1answer
70 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 ...
0
votes
1answer
1k views
Entropy : do we prefer higher or lower entropy?
The entropy of a source $H(S)$ gives the average codeword length to encode a given source alphabet. i.e. it is the average number of bits per symbol required to encode the information in the source. ...
