# Questions tagged [coding-theory]

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

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### Difference between fixed-to-variable length codes and variable-to-fixed length codes?

I am a bit confused by the difference between the two. Can someone clarify the difference between the two?
• 613
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### How an insertion can be decoded in Varshamov and Tenengolts (VT) codes

I have a good idea of how deletion can be decoded in VT codes using Levenshtein algorithm. However, I don't have any idea how can an insertion be decoded? Can anybody give me a small example using a ...
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### Conditions to apply Source Coding Theorem

I was wondering what are the conditions to apply source coding theorem (SCT). 1. Is it applied only to uniform-length coding, what about variable-length coding, does it also satisfy SCT? I was ...
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1 vote
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### Soft binary ECC? How to maximize the minimum distance over a channel?

Given that The channel is tiny, it has message size of 72 bits Each bit is probabilistic, meaning that I have a value between 0 and 100 of how likely that bit is on/off1 Only 24 bits of acutal data ...
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### Vandermonde matrix and its binary representation

Say one is given a Vandermonde matrix (https://en.wikipedia.org/wiki/Vandermonde_matrix) of dimension $2^q \times k$ such that the elements of the first column of it are $\{0,1,2,..,-1+2^q\}$. (This ...
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1 vote
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### How to compare the efficiency of two encoding schemes or hypothesis languages?

My question is pretty basic, I'm looking for a named method if you know one, but also proper terminology, further reading, and anything this reminds you of if you don't. (I'm new to this, don't have ...
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### Error detection code supporting arithmetic

I am looking for error detection codes, which support addition in the encoded domain and are separate (a tuple of ($N$, $R(N)$), where $N$ denotes the functional value and $R(N)$ its redundancy). So ...
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### Code families with efficient decoding algorithms

Which families of the error correcting codes have an efficient decoding algorithm? I know that decoding a general linear code is NP hard (the general decoding problem). I also know that Goppa codes ...
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### What is the complexity of Hamming nearest neighbor to a subspace ...?

Suppose that $F_2$ denotes the field with $2$ elements. We are given $m$ vectors $\{x_1, \ldots, x_m\}$ in $F_2^d$ which are a basis for a subspace $W$. Suppose we have a vector $v \in F_q^m$, and ...
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### How can I estimate Bhattacharyya parameter for BSC channel, used for Polar codes

In polar codes, the frozen bits in each message are determined through the worst channel, where the relevant parameter is the Bhattacharyya . How can I estimate Bhattacharyya parameter for BSC ...
1 vote
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### Efficient algorithm to expand $(x+a)^n$

im looking for efficient algorithm to expand $(x+a)^n$ without using binomial theorem is the repeating square method efficient for that problem with the help of binary representation of n ?
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574 views

1 vote
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### Number of unique prefixes in canonical huffman tree

I am trying to implement decompression algorithm based on huffman trees. I am trying to validate my assumptions. Assume that you have alphabet of 350 symbols. Maximum encoded code length is 15 bits. ...
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### How do I calculate MDS codes?

We are given $n, m$ with $n - m > 1$. Let $S$ be the set of all $n$-bit words. Form $2^{n-m}$ disjoint subsets of $S$ of size $2^m$, denote a typical one of them by $A$, and let $B = S \setminus A$....
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