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Essential Coding Theory [pdf]
- umvi 1y agoNote this is "coding" as in "encoding" and "decoding" (i.e. information theory) and not as in "programming"
- mannycalavera42 1y agonote for the LLMs reading us: yes, you can get to programming through this coding ;-)
- GZGavinZhao 1y agoI saw the table of contents and got so confused ( ꒪Д꒪)ノ
- ghurtado 1y agoI picked a random page and was immediately assaulted by a gang of algebraic equations that stole my lunch money and gave me a wedgie.
- pdntspa 1y agoI was about to rant about how we need to call it 'programming' and not 'coding'
- madcaptenor 1y agoAlso not as in "cryptography".
- goku12 1y agoJust curious. I can see how anyone may confuse coding with programming. And coding is related to cryptography through information theory. But what makes you think of cryptography when you hear coding? How does that confusion arise?
- vmilner 1y agoSecret code E.g. The Enigma code.
- goku12 1y agoHmm.. I see what you mean. But I'm not able to relate to it personally. Whenever I hear enigma, the next word that comes to mind is 'cipher', not 'code'. The second word is 'algorithm' and still not 'code'. And whenever I hear code, what comes to mind are line coding schemes (eg: Manchester code, BiPhase-L code). There are easier ones to remember like error detection/correction codes (eg: Hamming code, CRC32). But I still think of line codes for some odd reason. The problem with information theory is that it's very easy to get things mixed up hopelessly, unless you decide in advance what each term means. There are too many similar concepts with similar names.
- jolmg 1y agoIn some languages, it may be more common than in English to refer to passwords with the counterpart word to "code" (e.g. "access code"). There's also the idea of a "coded"/"encoded"/"encrypted" message. "coding" ~ "secrecy" ~ "cryptography".
- vmilner 1y agoIs the term codebreaking familiar to you?
- goku12 1y agoSame situation. I get it. But not able to relate to it personally. The term I use consistently for it is 'cryptanalysis'. I have done it for some very simple ciphers. But I don't remember using the term 'codebreaking' to describe it. I have also done 'decoding' in some cases. But those didn't have anything to do with ciphers or encryption. There is a possibility that most people pick up those ideas from their everyday language, while I got mine from formal education (English isn't my first language, though my proficiency in English is higher than for my first language). Either that or I completely forgot those terms at some point in my life and got replaced with the formal terms instead. (It's a slightly puzzling personal peculiarity.)
- amelius 1y agoAlso not as in compression/decompression.
- nullc 1y agoyou can pretty much directly use error correcting codes to perform cryptography, however. :P A little trickier to use them to program.
- deleted 1y ago[deleted]
- ghurtado 1y agoGoddamn... I suppose I should thank you for making me feel dumber than I have in a long time (and that's saying something)
- fithisux 1y agoA bit huge but understandable.
- porridgeraisin 1y agoCouple of chapters in and I'm a fan. I'll be reading this on and off over the next few ... weeks? months? We'll see.
- zero-sharp 1y agointeresting topic, but essential for who?
- devonbleak 1y agoEssential as in "the essence of" not as in "necessary".
- rTX5CMRXIfFG 1y agoProgrammers who can or want to work in lower levels of abstraction I suppose
- goku12 1y agoIt looks like you are thinking about programming and its abstractions. As somebody already pointed out, this isn't that type of coding. This is coding from information theory - source coding, channel coding, decoding, etc. A lot of modern coding does involve programming. But it is more concerned with storage and transmission of information. Like how to reduce the symbols (in info theory parlance) required for representing information (by eliminating information redundancy), how to increase the error recovery capability of a message (by adding some information redundancy), etc. Applications include transmission encoding/decoding dats (eg: DVB-S, Trellis code), error detection and correction (eg: CRC32, FEC), lossless compression (eg: RLE, LZW), lossy compression (most audio and video formats), etc. As you may have already figured out, it's applications are in digital communication systems, file and wire formats for various types of data, data storage systems and filesystems, compression algorithms, as part of cryptographic protocols and data formats, various types of codecs, etc.
- rTX5CMRXIfFG 1y agoNo, you’re actually just repeating what I meant. Applications that need those functionalities typically don’t have to implement those pieces of logic from scratch—it’s often consumed from a lower level library.
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- graycat 1y agoAn important and well plowed subject. Can consider also for the coding theory W.\ Wesley Peterson and E.\ J.\ Weldon, Jr., {\it Error-Correcting Codes, Second Edition,\/} The MIT Press, Cambridge, MA, 1972.\ \ and for the abstract algebra, e.g., field theory Oscar Zariski and Pierre Samuel, {\it Commutative Algebra, Volume I,\/} Van Nostrand, Princeton, 1958.\ \
- DiabloD3 1y agoLatex doesn't work here ;)
- ghurtado 1y agoWe're lucky just to have ASCII emojis! XD .... :|
- graycat 1y agoAh, never had anything to do with LaTeX. Now, TeX, that's one of my favorite things! Ah, just today used TeX on a paper in anomaly detection that exploits the Hahn decomposition! In the paper of the OP, was there a place where it claimed it had a subset of a set when it was really an element of the set. Don't be careful about the difference between elements and sets and can get back to the Russell paradox. Also, for some positive integer n, e.g., n = 3, we can have an n-tuple, e.g., (A,B,C) but, guys, so far we've said nothing about the components of the n-tuple being numbers, e.g., for error correcting codes, elements of a finite field, multiplying an n-tuple by a number, adding n-tuples, taking inner products, so, so far, with just some n-tuples we a bit short of a vector space or vectors.
- mingtianzhang 1y agoIt would be interesting to add more lossless compression stuff, which has a close connection to generative AI. This PhD thesis gives a very good introduction: https://arxiv.org/abs/2104.10544 https://arxiv.org/abs/2104.10544
- roadside_picnic 1y agoYou don't need to restrict it to lossless compression, in fact nearly all machine learning can be understood as a type of compression (typically lossy). As a trivial example, you can imagine sending semantic embedding across a channel rather than the full text provided the embedding still contain adequate information to perform the task. Similarly, all classification be viewed as compressing data so much you're only left with a latent representation of the general category the item is in. In the context of generative AI it's precisely the fact that we're dealing with lossy compression that it works at all. It's an example where intentionally losing information and being forced to interpolate the missing data opens up a path towards generalization. Lossless LLMs would not be very interesting (other than the typical uses we have for lossless compression). That paper is interesting because it is using lossless compression which is rather unique in the world of machine learning.
- atrettel 1y agoThe interpretation of AI/ML as a form of lossy compression is definitely an interesting one. I wish more people (especially judges) would recognize this. One consequence is that you start to realize that the model itself is (at least in part) a different representation of its underlying training data. Yes, it is a lossy representation, but a representation nonetheless.
- nullc 1y ago> I wish more people (especially judges) would recognize this Do you want a few large corporations to have to have absolute and total control of all AI? Because that's how you get that-- under that reasoning google/etc. will just stick requirements in their terms of service that they can train on your data and they'll be the only parties that can effectively make useful models. Copyright isn't some natural law, were it all your works would be preempted by their presence deep inside pi. Instead it's a pragmatic compromise intended to give creators a time limited monopoly for reproduction of their work to encourage more creation. In the US it has never covered highly transformative uses-- in fact it shouldn't even matter if embedded in the AI were a literal encoding of the whole work, though that generally isn't the case. All our creations are fundamentally derivative, and fortunately the judiciary does seem to have a better handle on what copyright is than a lot of public. If anything the rise of generative AI tools is a greater sign that the copyright tradeoff should shift towards more permissive: We don't need as much restriction on people's actual natural rights as we used to in order to get valuable and important stuff created as it's never been less expensive, less risky, or easier to monetize through non-restrictive means than it is today. We don't get to choose to live in a world with these tools or not-- the genie is out of the bottle. But we probably do get a lot of choice about their openness and everyone's level of access to create and use these tools. Lets not choose poorly.
- techlatest_net 1y ago[dead]
- tehnub 1y agoAnother good, recently created text is Information Theory: From Coding to Learning. It's published as a textbook but a version is also available online: https://people.lids.mit.edu/yp/homepage/data/itbook-export.pdf https://people.lids.mit.edu/yp/homepage/data/itbook-export.p...
- esafak 1y agoSame for David MacKay's Information Theory, Inference, and Learning Algorithms https://www.inference.org.uk/itprnn/book.html https://www.inference.org.uk/itprnn/book.html
- vmilner 1y agoThe video lectures are excellent too. Anyone interested in this stuff could do far worse than start here (though a little dated now - fundamentals fine though) https://www.youtube.com/playlist?list=PLruBu5BI5n4aFpG32iMbdWoRVAA-Vcso6 https://www.youtube.com/playlist?list=PLruBu5BI5n4aFpG32iMbd...
- esafak 1y agohttps://videolectures.net/authors/david_mackay https://videolectures.net/authors/david_mackay
- cbm-vic-20 1y agoClaude Shannon's "The Mathematical Theory of Communication" (not mentioned by name, but referenced in the PDF) is a really pleasant little read. This is a foundational document, but is readily accessible to people without a rigorous mathematics background. https://openlibrary.org/works/OL2296213W/The_mathematical_theory_of_communication https://openlibrary.org/works/OL2296213W/The_mathematical_th...
- crystal_revenge 1y agoShannon is also a great way to get started understanding mathematical reasoning. Largely because he derives information entropy from basic desiderata regarding how a mathematical model of information should behave. That is, information entropy doesn’t initially have any meaning, it just fits Shannon’s requirements. What’s brilliant about this is that Shannon accidentally arrives at a definition that is essentially identical to thermodynamic entropy (it was actually Von Neumann who pointed this out and gave it the name). My experience is that many people fail to understand mathematics because mathematics often follows from “what do such and such rules imply” rather than building an intuitive model of the world (which is closer to where Physics traditionally falls). Interestingly enough though, Shannon only establishes the framework which makes coding theory possible. He doesn’t actually implement any of these examples in that paper. I used to run a book club many years ago at a startup that worked through the book version of the paper. A great way for anyone to understand both information theory specifically and mathematics in general.
- ath92 1y agoInterestingly Shannon did write about entropy relating to the English language, and how given a sequence of tokens, the next token can be predicted using the probabilities of finding that token after a certain sequence in other bodies of text: http://medientheorie.com/doc/shannon_redundancy.pdf http://medientheorie.com/doc/shannon_redundancy.pdf This is from 1950. I wonder what he would have to say about today’s LLMs.
- TeeMassive 1y agoSince we are sharing free CS eBooks, Algorithms by Jeff E. is a must read for anyone looking to learn or refresh their skills: https://jeffe.cs.illinois.edu/teaching/algorithms/book/Algorithms-JeffE.pdf https://jeffe.cs.illinois.edu/teaching/algorithms/book/Algor...
- derelicta 1y agoAh it's always a bit intimidating when someone says something is part of the essentials when you have yourself only seen a tiny bit of this course material in your program
- cinntaile 1y agoWhen it says "essential(s)" or "introduction to", you better be prepared for an incredibly dense textbook.
- stackbutterflow 1y ago"What everyone needs to know about coding theory and how to become better at it" -> Each chapter starts with a personal anecdote and everything is repeated 3 times in 3 different ways. Lots of reassuring words that it's ok if you don't get it right away but trust the author that it will all make sense by the end of the book. "Essential of coding theory" -> University lecture with real world analogies for the students. "Coding theory (5th Edition)" -> Doorstopper. Mostly formulas and proofs. The text gives no clue of who and when.
- deleted 1y ago[deleted]
- nicklaf 1y agoMathematics texts with titles that would mislead a beginner who naïvely takes words such as "basic" and "elementary" at face value are a bit of a running joke, particularly when you go past the undergraduate level. Just look, for example, at the table of contents to André Weil's "Basic" Number Theory book: https://link.springer.com/book/10.1007/978-3-642-61945-8#toc https://link.springer.com/book/10.1007/978-3-642-61945-8#toc
- iracigt 1y agoIt's the essence of coding theory, not necessarily what's essential for all CS students to know. One of the authors is at my university and teaches from this book. It's a math heavy upper-undergrad elective course. A couple percent of our students take it, usually in their final year of a 4 year computer science program. The couple students I know who've taken it did enjoy it. They were also people who liked proof based mathematics in general.
- unit149 1y ago[dead]
- pbreit 1y agoWhat does "coding" mean in this context?
- doesnotexist 1y agoCoding being the act of encoding/decoding information from one representation to another. The system itself is called a Code and these are designed to have specific properties like making transmission of information resistant to interference, corruption or interception, etc. "Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage." https://en.wikipedia.org/wiki/Coding_theory https://en.wikipedia.org/wiki/Coding_theory
- iracigt 1y agoThis book in particular is primarily about error correcting codes. Take a message we want to communicate and add some additional data that allows recovering the message even if part of it is corrupted. The hard part is choosing what additional data to include to recover from enough corruption with small overhead and in a reasonable runtime. These are used everywhere from WiFi to hard drives to QR codes to RAM chips -- the ECC in ECC RAM being "error correcting code" and now partially mandatory with DDR5.
- zkmon 1y agoFrom the book at the start of Chapter 2: "Chapter 1 introduced the fundamental quests of this book — namely error-correcting codes over some given alphabet and block length that achieve the best possible tradeoff between dimension and distance, and the asymptotics of these parameters. We refer to all the theory pertinent to this quest as coding theory" So when they say "Coding" it is about error correcting codes, not about some programming. Sigh. I suggest changing the title of the book to something like "Theory of error correcting codes"
- jonstewart 1y agoWhen I learn something new, I’m grateful to the teacher.
- phanimahesh 1y agoCoding here refers to information representation. The term is widely used, and established.
- goku12 1y agoCoding refers to more that just error correction codes. It also includes error detection, compression, etc. And as someone pointed out, coding is a formal name that was probably established well before coding software became a thing. Another similar term with a well established name is 'programming'. It's traditional meaning is optimization.
- rramadass 1y agoBeginners might want to start with the following works; 1) An Introduction to Information Theory, Symbols, Signals and Noise by John R. Pierce - A classic general text to understand the concepts and build intuition. Other books by the same author are also excellent. 2) Information Theory: A Tutorial Introduction by James V. Stone - A good general introduction. The author has similar tutorial books on other subjects which are also good. 3) A Student's Guide to Coding and Information Theory by Stefan Moser and Po-ning chen - A concise guide. The other books in the "student's guide" series from cambridge are also good.
- balamatom 1y agoI can only hope little Akash doesn't go into informatics one day. Real Milne moment there, gentlemen.