# Tagged Questions

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### Maximizing variance of Hamming distance of a system

I have a system as shown below, where 4 registers have 8 bit input A,B,C,...
56 views

### Fano's inequality and error rate

The Wire-tap channel II (http://link.springer.com/chapter/10.1007%2F3-540-39757-4_5) article in proof of Theorem 1 uses Fano's inequality to estimate the entropy $H(S|\hat{S}) \leq K \cdot h(P_e)$ ...
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### information and coding theory weakly independent problem

$X$ is weakly independent of $Y$ if the rows of the transition matrix $\begin{bmatrix}p(x|y)\end{bmatrix}$ are linearly dependent. Show that if $X$ and $Y$ are independent, then $X$ is weakly ...
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### When is a minimum distance decoder also a maximum likelihood decoder?

It is well known that if we have a binary symmetric channel with crossover probability $\epsilon<0.5$ and we send a word $x$ through it, the most likely word is the one with minimum hamming ...
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### Distributing partially known data between n parties

Assume that $n = 2r+1$. There are $n$ elements $a_1,a_2,\ldots,a_n$ from a finite field $\mathcal{F}$, and $n$ parties. Each party knows the values of at least $r+1$ elements out of those $n$ ...
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### Prove that communication protocol complexity less than $n\epsilon$

Alice and Bob get as an input words $x$ and $y$, which consist of $0$ and $1$. Length of $x$ is $n$ and length of $y$ is $2n$. They want to know if the word $x$ is subword of word $y$. For example, ...
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### Code for specific case [Information Theory]

I have a channel where the probability of sending a $0$ and receiving a $1$ is $P_e$, sending $0$ and receiving $0$ is $1-P_e$, sending $1$ receiving $0$ is $P_e$, sending $1$ receiving $1$ is ...
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### Generator Structure for Hamming and Dual code

To begin with i am not sure again if this is related to this particular forum ot it is an acceptable question.My question to find a (3,1) Hamming (repetition code) and its dual code and then draw the ...
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### 3-bit sensors — A question about Hamming distance in signals

I came across this question on Willy Wu's riddle site You have two 3-bit sensors, A and B, that measure the same thing, whatever it is -- temperature of the room, radioactivity levels, whatever. ...
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### Hamming Code Error Detection

I am learning few things about hamming code and error detection so my question may sound stupid. So i know that lets i ahve (7,4) hamming code and i made transpose of parity check matrix H(t). Now say ...
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### Need help in understanding state transition diagram of a convolutional coder. How are the output bits calculated?

Have a look at the above figure. I am confused in how the output bits are calculated. e.g. according to my understanding a state transition from 00 to 10 (with input bit 1) should produce output 10 ...
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### questions in channel capacity

Q) Suppose we have a set of t coins, all but two of which have uniform weight $0$. and two counterfeit coins have different weights$>0$. If one can only use a spring scale, what is the ...
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### Entropy vs predictability vs encodability

Imagine there's a guessing game where a series of binary symbols are presented and a human must decide quickly if the symbol is the same as the previous or different. There's a property of the ...
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### 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 2*k bits codeword (rate is 1/2) is produced by the generator ...
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### Error correction code handling deletions and insertions

I have data which is expressed in form of fixed-length sequence of decimal digits, typically 10 digits in length. I'm looking for error correction code that would allow me to append one or more ...
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### Huffman code with probabilities $p_1, p_2,\ldots, p_n$

I have solved the first two subsections of an assignment, but I can't solve the last subsection. We have a Huffman code with probabilities $p_1,p_2,\ldots, p_n$ and we know that ...
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### Intuition about the relation of combinations and entropy

It is not difficult to show that $${n \choose \lambda n} \leq 2^{H(\lambda)n}$$ where $H$ is the binary entropy function: $$H(\alpha) = -\alpha \lg \alpha - (1-\alpha)\lg (1-\alpha)$$ I was ...
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### Has error correction been “solved”?

I recently came across Dan Piponi's blog post An End to Coding Theory and it left me very confused. The relevant portion is: But in the sixties Robert Gallager looked at generating random sparse ...
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### Variations of the Hamming code.

What types of basic variations of the Hamming code are there and what are their objectives? I was taught the following version: $$L = n + k$$ $$n \geq \log_2M$$ $$k \ge \log_2(n+k+1)$$ where ...
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### How do i calculate the probability of erroneous transmission?

In information theory, how do I calculate the probability of an erroneous transmission? Let's take for instance a binary symmetric channel with an error probability $1-d=0.25$ and send codewords of ...
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### Do equal distance distributions imply equivalence?

Let $A$ and $B$ be two binary $(n,M,d)$ codes. We define $a_i = \#\{(w_1,w_2) \in A^2:\:d(w_1,w_2) = i\}$, and same for $b_i$. If $a_i = b_i$ for all $i$, can one deduct that $A$ and $B$ are ...