Questions tagged [information-theory]

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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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14 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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41 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 ...
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1answer
39 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
88 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
76 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/...
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26 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}\...
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17 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 ...
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21 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 ...
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29 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
140 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
293 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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39 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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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 ...
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2answers
35 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 ...
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1answer
31 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
845 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
258 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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157 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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167 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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37 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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513 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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99 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
329 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
241 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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1answer
209 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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173 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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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 ...
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89 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
633 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 ...
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1answer
140 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
146 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
488 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
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 ...
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1answer
206 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
220 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 $\{1,2,...,8\}$....
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1answer
898 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. ...
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1answer
314 views

How to prove relationship between mutual information and differential entropy?

I need to prove that mutual information given by $$I(X;Y)=\int_{x,y}f(x,y) \log_2 \left( \frac{\left (f(x,y)\right)}{f(x) f(y)}\right) \, dx \, dy$$ is equivalent to $I(X;Y)=H(Y) - H(Y|X)$ I am ...
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1answer
315 views

How to solve this entropy integral?

I am having the entropy integral below where $\mathbf x$ is a $N$ dimensional Gaussian vector having variance as $\mathbf P$ and mean zero, $$ -\int\frac {\exp\left(\frac{1}{2}\mathbf x^T\mathbf P^{-...
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1answer
70 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 ...
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1answer
1k views

How to explain this BER vs SNR behaviour?

I wrote a script in MATLAB to simulate an LDPC created using an algorithm of a colleague of mine. The parity check-matrix is regular and has dimensions $1012 \times 1518$ and the code rate is $R=1/3$. ...
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1answer
572 views

What is the overall capacity of two cascaded BSC channel?

Is it true:$C = C_1 * C_2$ where $C_1$ and $C_2$ are the two cascaded BSC which makes $C$.
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347 views

Differences between $\tt wentropy$ in MATLAB and entropy definition

MATLAB offer's a Shannon entropy calculation in its wavelet package: $$ H(X) = -\sum_{i=0}^{N-1} x_i^2\log(x_i^2) $$ I'm wondering what this formula means, since it has no relation with the ...
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1answer
291 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 ...
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1answer
173 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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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{...
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1answer
53 views

Entropy of a dynamical system and source code length

The entropy of a source $H(S)$, gives you 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 ...
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1answer
196 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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72 views

What are bits in the context of channel capacity units?

'bits' are used with 2 different meanings. One can use 'bits' to mean the binary digits i.e. 1's and 0's. Bits are also the units of information in a event of discrete source. I think when channel ...