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Results tagged with coding-theory
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user 19885
The theory of error-correcting codes stems from Shannon's 1948 _A mathematical theory of communication_, and from Hamming's 1950 "Error detecting and error correcting codes".
5
votes
How to quantify the error correction capacity of LDPC code?
As @John mentioned, there is not general way and nice formula for computing the minimum distance of codes. The problem remain difficult for LDPC codes as like as other codes. But, there are several wa …
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5
votes
Accepted
Effects of many degree-2 variable nodes in the Tanner graph during the decoding of LDPC codes
As maybe you know, the most good decoding algorithm for LDPC codes, for example iterative decoding, has not provable efficiency, except in special cases. But, it is believed that variable nodes with d …
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2
votes
Accepted
The generator polynomial of cyclic code
The generator polynomial of $\bar{C}$ is $\overline{g(x)}$. Because the conjugation operation is distributive over summation and multiplication.
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2
votes
0
answers
110
views
Mutual benefits of coding theory and the reconstruction conjecture
Let $G_n$ denotes all graphs with $n$ nodes. For any graph $G$ in $G_n$, the adjacency matrix $A(G)$ can be viewed as a codeword of length $n^2$. Also, the codes arises from $G_n$ is a linear binary c …
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1
vote
Self-dual binary codes of Hamming weight divisible by 8?
We say the Code $C$ is formally self-dual (f.s.d) if the codes $C$ and $C^\perp$ have identical weight distribution. So, a self dual code is f.s.d. Also, f.s.d, code is divisible if there exists an i …
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6
votes
1
answer
394
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Binary weight of shifted integers
Suppose $n_2$ denotes the binary representation of the integer number $n$. Let $X_2(n)=[1_22_2\ldots n_2]$,$n\geq3$, be a binary vector which is obtained by concatenating of binary representation of t …
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