2 Bit Error
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Hamming Code 2 Bit Error Detection
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article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (March 2013) (Learn how and when to remove this template message) This article may be single bit error correction using hamming code too technical for most readers to understand. Please help improve this article to make it understandable secded example to non-experts, without removing the technical details. The talk page may contain suggestions. (February 2016) (Learn how and when to remove this template message) hamming code 2 bit error correction (Learn how and when to remove this template message) Binary Hamming Codes The Hamming(7,4)-code (with r = 3) Named after Richard W. Hamming Classification Type Linear block code Block length 2r − 1 where r ≥ 2 Message length 2r http://www.computerworld.com/article/2567411/networking/sidebar--finding-a-2-bit-error.html − r − 1 Rate 1 − r/(2r − 1) Distance 3 Alphabet size 2 Notation [2r − 1, 2r − r − 1, 3]2-code Properties perfect code v t e In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming(7,4)-code, and were invented by Richard Hamming in 1950. Hamming codes can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, https://en.wikipedia.org/wiki/Hamming_code and can detect only an odd number of bits in error. Hamming codes are perfect codes, that is, they achieve the highest possible rate for codes with their block length and minimum distance of three.[1] In mathematical terms, Hamming codes are a class of binary linear codes. For each integer r ≥ 2 there is a code with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other code word is three) and block length 2r − 1. The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code of the Hamming code is the punctured Hadamard code. The parity-check matrix has the property that any two columns are pairwise linearly independent. Due to the limited redundancy that Hamming codes add to the data, they can only detect and correct errors when the error rate is low. This is the case in computer memory (ECC memory), where bit errors are extremely rare and Hamming codes are widely used. In this context, an extended Hamming code having one extra pari
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring http://stackoverflow.com/questions/5631871/what-is-the-minimum-number-of-bits-needed-to-correct-all-2-bit-errors developers or posting ads with us Stack Overflow Questions Jobs Documentation Tags Users Badges Ask Question x Dismiss Join the Stack Overflow Community Stack Overflow is a community of 4.7 million programmers, just like you, helping each other. Join them; it only takes a minute: Sign up What is the minimum number of bits needed to correct all 2 bit errors? up vote 4 down vote favorite I learned about hamming codes and how to use them to correct bit error 1 bit errors and detect all 2 bit errors, but how extend this to correcting 2 bits, and maybe more? What is the minimum number of bits needed to correct all 2 bit errors? error-correction error-code hamming-code share|improve this question asked Apr 12 '11 at 7:35 user623879 1,83452343 add a comment| 1 Answer 1 active oldest votes up vote 4 down vote accepted I think I figured it out. N=number of data bits, k=number error correcting bits(eg parity for 2 bit error hamming) In any ECC scheme, you have 2^(N+k) possible bit strings. For single bit error: You must find k such that the total number of possible bit strings is larger than the possible number of strings with at most 1 bit error for a given string. The total possible strings with at most 1 bit error is 2^N(n+k+1) 1 string with no error, N+k strings with 1 bit error 2^(N+k)>=(2^N)*(N+k+1) You simply have to plugin values of k until you find the one that satisfies the above(or however you wish to solve it) Similarly for 2 bit error, it is 1 string with no error, N+k strings with 1 bit error, N+k choose 2 strings with 2 bit error. 2^(N+k)>=(2^N)*(N+k+1 + (N+k choose 2)) share|improve this answer edited Apr 12 '11 at 8:03 answered Apr 12 '11 at 7:58 user623879 1,83452343 add a comment| Your Answer draft saved draft discarded Sign up or log in Sign up using Google Sign up using Facebook Sign up using Email and Password Post as a guest Name Email Post as a guest Name Email discard By posting your answer, you agree to the privacy policy and terms of service. Not the answer you're looking for? Browse other questions tagged error-correction error-code hamming-code or ask your own question. asked 5 years ago viewed 5136 times active 5 years ago Related 1How to correct a message using Hamming Code1Hamming c