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1answer
19 views

Conditions that should be satisfied by the Generator Function to detect odd number of bits in error

"Let $G\left ( x \right )$ be the generator polynomial used for CRC checking.What is the condition that should be satisfied by $G\left ( x \right )$ to detect odd number of bits in error? a) ...
1
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2answers
27 views

Why is Hamming Weight (in the CRC context) independent from the data?

I'm designing a communication protocol for 24 to 52 bits (typically 32 bits) data including the CRC-8 for error detection. I'm trying to select the best polynomial for this kind of application. In ...
1
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0answers
50 views

Two dimensional parity check

Firstly, I would like to apologize if I misplaced this topic / i think the theory of coding is close to CS / I am little bit confused right now, in the school we were learning about Hamming's code, ...
2
votes
2answers
109 views

Hamming code — identical parity bits for different errors

(7,4) Hamming Code (HC) detects all 2-bit errors and corrects all 1-bit errors. However, there can be 2-, 3- or 4-bit errors that come with the same parity bits as that of 1-bit errors. Eg.: Let ...
-1
votes
1answer
106 views

use of Hamming Distance in Communication Networks

I am trying to put things in places on the use of Hamming Distance (HD) in error detection and correction in Computer Networks. I'm looking for correction/verification on the following: HD is a ...
1
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0answers
19 views

Can I use a 128b Hsiao decoder to decode a 64b word?

I have implemented a 128b Hsiao decoder on an FPGA. This decoder checks a 9b ECC for each 128b of data received. In order to save on resources, I am time-sharing this decoder between multiple ...
8
votes
1answer
100 views

How do you determine the number of errors in the Welch-Berlekamp algorithm?

In the Welch-Berlekamp algorithm for decoding Reed-Solomon codes, one is given a list of points $(a_i, b_i)$ representing a message with $e$ errors on the $b_i$ in unknown locations (and $e$ is given ...
2
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0answers
28 views

hamming error correction with non-uniform error correction capability

I have a question regarding the hamming codes. If I understood correctly, hamming codes assume the uniform correction among all the bits. It means all the bits have the same weight in terms of ...
2
votes
1answer
52 views

What does feedforward inversion mean in the context of convolution and catastrophic codes?

i'm reading the article of J. L. Massey and M. K. Sain, "Inverses of Linear Sequential Circuits" (Date of Publication - April 1968) (here) and i cannot understand - what is "feedforward inversion"? ...
2
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0answers
23 views

Codes for correcting a single deletion and re-ranking of a permutation

I was struggling with this paper about codes which can correct single deletion and re-ranking in permutations, http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6875337 [Published ...
1
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2answers
104 views

How much bits need to add to 100bit of data in order to correct up to 10bits?

I'm trying to calculate how much minimum bits need to be added to data of 100bits, in order to correct 10 bits that are messed up by: bits that deleted (Erasure Correcting) bits that corrupted ...
3
votes
1answer
33 views

How is the Varshamov-Tenegolts code decoded?

For $0 \leq a \leq n$ the VT code $VT_a(n)$ consists of all tuples $(x_1,x_2,..,x_n) \in \{ 0,1\}^n$ such that $ \sum_{i=1}^{n} ix_i = a (mod (n+1))$ For example $VT_0(4) = \{ 0000,1001,0110,1111 \}$ ...
3
votes
1answer
65 views

About codes over $\mathbb{F}_2$

I was looking through these notes but I am not sure I can locate the answer to these questions of mine - it would be great if someone can just even point out what to look for! So any set of binary ...
1
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0answers
25 views

How many parity syndromes are there?

In RAID 6, there is a parity scheme that allows 2 concurrent disk failures. This requires 2 ‘syndromes’, one of which is simply XOR, as used for RAID 5's only parity. In trying to find out whether ...
0
votes
1answer
50 views

Hamming and BCH codes

Why are Hamming codes the best 1-error-correcting codes? I need references. I know that hamming codes are the best 1-error-correcting codes but I want to know why they are best?
0
votes
2answers
2k views

Hamming distance necessary for detecting d-bit error and for correcting a d-bit error [duplicate]

I am trying to understand what hamming distance of a code is needed to detect a d-bit error, or to correct a d-bit error. This is what I have found around the web: If two codewords are Hamming ...
1
vote
1answer
6k views

Hamming distance required for error detection and correction

I have already asked a pair of questions on the hamming distance, hamming code, valid and invalid codewords on this website, because I cannot understand those concepts fully, and in a few weeks or ...
0
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0answers
28 views

G1, G2, H1, H2 are submatrices of the generator and parity check matrices of a code as described below. Can G1 * H2' and G2 * H1' both be all zeroes?

$ G $ and $ H $ are the generator and parity check matrices respectively of a linear block code. Let $ G_1 = G(:, 1:n-s) $ (Matlab style representation of sub matrices). That is, $ G_1 $ is equal to ...
3
votes
1answer
139 views

Error-correction code for transmission only with bit-flipping from 0 to 1

I am using a transmission system that uses a Bloom filter (this part is out of my control). I want to send a small amount of data (32 bits) using this system. For each bit [0,31], I add its index to ...
1
vote
1answer
85 views

Error detection/correction algorithm

We have 2 stations that communicate with each other, but we need to detect (or even correct) when something is wrong. We use 8 binary words: each consisting of 3 bits and to send it we code it as ...
3
votes
1answer
60 views

Range of CRC-32

What is the range of “the” CRC-32, the one used by Unix, Ethernet, zip, and many other industrial standards? Mathematically, a CRC is defined as follows: let $G$ be the CRC polynomial in ...
3
votes
2answers
43 views

Forward Error Correction for streaming data

I am very familiar with error correcting codes. However, it is not obvious how to apply them to adaptive streaming data. There also doesn't seem to be much literature on the problem. The naive ...
3
votes
2answers
416 views

Commonly used Error Correcting Codes

We know error correcting codes are parameterized as (n,k,d) codes. I wanted to know the values of these parameters for some commonly used error correcting codes in computer memories or in DRAMs, etc. ...
5
votes
4answers
5k views

Is the 2nd parity bit in RAID 6 a simple calculation?

I'm trying to understand how the 2nd parity bit or byte is set in RAID 6. I'm reading a paper by H. Peter Anvin, and it goes into Galois field algebra, which is somewhat new to me. Anyway, a rep from ...