Questions tagged [information-theory]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
4
votes
2answers
184 views

Shannon capacity limit & FEC comparisons

In this figure from Fundamentals of Digital Communications by Madhow , pp 328 there is a comparison of a rate 1/3 turbo code with the shannon limit for rate 1/3 BPSK: Trying to understand the limit ...
1
vote
0answers
104 views

Soft-output decoder

I am trying to implement the soft-output for my soft-decoder, however, the resulting log-likelihood ratios are not corresponding to the corrected hard bits. The soft-output regards the LLR-values for ...
0
votes
2answers
165 views

value of 0 log0 in entropy formula

Why is the value of $p_i\log(p_i)$ in entropy formula considered $0$ when $p_i =0$? I get that it is the limiting value, but does that mean $p$ is never equals to zero, but only tends to?
0
votes
0answers
26 views

Is there a way to describe the pattern of a signal as a numeric value?

I've been digging a little into signal processing and I just started a networks and telecommunications class at college. We saw there are different encode techniques Amplitude, Frequency and Phase ...
1
vote
0answers
49 views

Secret Sharing & Information Theory

I'm reading a paper -- Common Randomness in Information Theory and Cryptograph-secret. And I do have trouble in understanding formula (2.6): $$ \frac {1}{n} H(K)> H-\epsilon \tag{2.6}\label{2.6}, $$...
4
votes
3answers
230 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: $...
2
votes
3answers
172 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 ...
0
votes
0answers
30 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 $...
1
vote
1answer
33 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 ...
0
votes
0answers
26 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}{||...
4
votes
1answer
59 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 ...
-1
votes
1answer
69 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
votes
1answer
42 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 ...
0
votes
1answer
39 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
votes
1answer
58 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 ...
2
votes
1answer
71 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
2answers
133 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
266 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
48 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
vote
0answers
42 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 ...
1
vote
2answers
1k 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
vote
0answers
67 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
votes
1answer
24 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
votes
2answers
1k 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 ...
0
votes
1answer
151 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 ...
1
vote
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)}...
2
votes
1answer
1k 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
1answer
62 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
68 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
169 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
1k 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
50 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
vote
0answers
31 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 ...
0
votes
2answers
50 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
35 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
2k 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,...
4
votes
3answers
442 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 ...
2
votes
2answers
428 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
vote
2answers
739 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
0answers
44 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 "...
6
votes
2answers
868 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
237 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
votes
2answers
1k 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
375 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 ...
0
votes
1answer
310 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
329 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
57 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
vote
0answers
114 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 ...
10
votes
3answers
1k 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
213 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 ...