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Theoretical and experimental aspects of information theory and coding theory. This tag covers but is not limited to following branches: information theory, information geometry, optimal transportation theory, coding theory.

2 votes

Another formulation of error-correcting coding problem

Here's a long comment that can't be put in the comment section: If you know the location of errors in a binary system, and if errors are just bit flips, you can just flip those erroneous guys again. …
Yuichiro Fujiwara's user avatar
1 vote

Doing column permutation under row overlap constraint

I doubt there is a particular algorithm worth mentioning for avoiding $2 \times 2$ all-one submatrices (or better known as $4$-cycles in the context of LDPC codes) in parity-check matrices which is sp …
Yuichiro Fujiwara's user avatar
5 votes

Cyclic Hamming Code

Before answering your question, not every Hamming code is equivalent to some cyclic code. For instance, the ternary $[4,2,3]_3$ Hamming code (aka the tetracode) is not equivalent to any cyclic code. …
Yuichiro Fujiwara's user avatar
4 votes

Probability of false decoding with LDPC codes

Generally speaking, understanding the decoding error probability of an LDPC code is a very difficult problem. Among major channels that have extensively been studied, as far as I know, binary erasure …
Yuichiro Fujiwara's user avatar
3 votes

Good codes in practice for correcting combination of errors and erasures

Since you asked a reference, the early access pre-edit version of a paper that addresses exactly this problem you're considering just appeared in the IEEE Transactions on Information Theory: K. A. S. …
Yuichiro Fujiwara's user avatar
9 votes

Best upper bound on rate for q-ary codes

So, the supposedly the sharpest one among all known bounds is somehow poorer than the bound you learn in Coding Theory 101 if the alphabet size $q$ approaches infinity. I think the reason you find it …
Yuichiro Fujiwara's user avatar
5 votes

Hot-topics in error correcting coding related to interesting math. ?

Edit: since I only implicitly answered your question in the title (i.e., hot topics in error coding codes related to interesting math), I think one of the current hottest ones is quantum error-correct …