# Tagged Questions

The study of data representations that enable error detection, error correction and/or compression.

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### Efficiency of arithmetic coding

I think I know how the arithmetic coding works but what I don't understand is the reasoning about efficiency. I have read in this pdf that the number of bits required to specify a range is greater ...
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### How to pick Hamming distance

Wikipedia's article Cyclic redundancy check states that for the same n (bits) there are multiple CRCs possible with different polynomial. Then it lists this Best CRC Polynomials article that gives ...
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### Encoding the clock signal in ldpc codes

I am aware that with convolutional coding, it is possible to encode the clock signal into the packet. However, is the same possible for linear block codes such as LDPC? I am not so sure it is, because ...
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### Relation between covering radius and columns of parity check matrix

Let $C$ be a $[n,k]$ linear Code over $\mathbb{F}_q$ . I want to show that each vector of $\mathbb{F}_q^{n-k}$ is written as a linear combination of $m$ columns of $H$ iff $\rho \leq m$. I have ...
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Let $C$ be a $[n, k]$ linear code over $\mathbb{F}_q$. I want to calculate the covering radius of the Hamming codes. I have thought the following: Since the Hamming distance is $3$, the coverig ...
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### Lower bound on the covering radius of a code

Let $C$ be a $[n,k]$ linear code over $\mathbb{F}_q$. Suppose that $\rho$ is the covering radius . I want to show that $\rho \geq \frac{n-k}{1+ \log_q{(n)}}$. Could you give me a hint how we could ...
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### Upper bound on the covering radius of a code

Let $C$ be a $[n,k]$ linear code over $\mathbb{F}_q$. Suppose that $\rho$ is the covering radius . I want to show that $\rho \leq n-k$. Could you give me a hint how we could show this? The ...
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### Existence of Hamming code

We are given a number $n \geq 3$ and we know that the Hamming bound is satisfied. Does this imply that there is a Hamming code with length $\frac{q^r-1}{q-1}$, dimension $\frac{q^r-1}{q-1}-r$ and ...
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### Why are long block lengths commonly assumed/used in channel coding proofs?

As the title states, why are long block lengths commonly assumed or used in channel coding proofs?
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### Is Morse code without spaces uniquely decipherable?

Are all Morse code strings uniquely decipherable? Without the spaces, ......-...-..---.-----.-..-..-.. could be Hello World ...
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### Is the Source Coding Theorem straightforward for uniformly distributed random variables?

Shannon's source coding theorem states the following: $n$ i.i.d. random variables $X_1,\dots,X_n$ each with entropy H(x) can be compressed into more than n⋅H(x) bits with negligible risk of ...
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### Compute the Hamming code with odd parity for the memory word 1101 1001 0001 1011

This is the problem I have: Compute the Hamming code with odd parity for the memory word 1101 1001 0001 1011 (2 pts.). In your solution, mark the parity bits as in the following example, where ...
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### Hamming distance required for error detection and correction

I have already asked a pair of questions on the hamming distance, hamming code, valid and invalid codewords on this website, because I cannot understand those concepts fully, and in a few weeks or ...
I was following the textbook by David Mackay: Information theory inference and learning algorithms. I have question on asymptotic equiparition' principle: For an ensemble of $N$ $i.i.d$ random ...