Convolution Code and Error Correcting Capability

In summary, calculating the error correcting capability for a convolution code involves determining the fixed number of errors that the code can correct based on its rate, as well as considering the location of the errors. The number of errors that can be corrected may vary depending on the distance between them. It is recommended to read up on error correcting codes for a better understanding.
  • #1
chingkui
181
2
Anyone know how to calculate the error correcting capability for a convolution code? My boss basically is giving me pressure to come up some answer by the end of this week... I won't have time to read things deep...
My first question is: For a particular convolution code with a rate k/n, is there a fixed number e of errors that the code can correct and that when the number of errors exceed e, the code cannot be corrected? Does the number of error correctable depend on the location the error occurs? (e.g. will it be the case that a convolution code can correct 3 errors that occur far apart from each other, but cannot correct 3 errors that are next to each other?)

Please let me know asap, thanks. It will be a frustrating week... :frown:
 
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  • #3
For a quick crash course on Error Correcting Codes,

try this: A Commonsense Approach to the Theory of Error Correcting Codes by Benjamin Arazi (MIT press 1988 England)

This might get you through the difficulty of trying to learn in a few days what normally takes a lot longer!
 

1. What is a convolution code?

A convolution code is a type of error-correcting code used in digital communication systems to detect and correct errors that may occur during data transmission. It is a linear code that operates on blocks of data, breaking them into smaller pieces and adding redundancy bits to the data to allow for error correction.

2. How does a convolution code work?

In a convolution code, the input data is divided into equal-sized blocks and each block is encoded using a convolutional encoder. This encoder adds redundant bits to the data based on a predefined code rate. The encoded data is then transmitted over a noisy channel. At the receiver end, a decoder uses the same code rate and algorithm to correct any errors that may have occurred during transmission.

3. What is the difference between convolution code and block code?

The main difference between convolution code and block code is that convolution code operates on a continuous stream of data, whereas block code operates on discrete blocks of data. Convolution codes are also more complex and have higher error-correcting capabilities compared to block codes.

4. What is the error-correcting capability of a convolution code?

The error-correcting capability of a convolution code is determined by its code rate and constraint length. A higher code rate and longer constraint length result in a higher error-correcting capability. For example, a convolution code with a code rate of 1/2 and constraint length of 7 can correct up to 3 errors in a data block.

5. What are some applications of convolution codes?

Convolution codes are widely used in various digital communication systems such as satellite and wireless communication, digital television, and internet protocols. They are also used in storage systems, such as hard disk drives, to ensure the integrity of stored data. Convolution codes are also used in deep space communication, where the signal is subject to high levels of noise and interference.

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