# [SOLVED]Convolutional codes (error correction)

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#### manhattene

##### Newbie level 3 Hi everyone,

I'm thinking about implementing an error-correcting convolutional code.
My question is related to the error correcting capability of these codes. For example how many errors are corrected when using a rate R=1/2 and a constraint length K=3 ? Is there a formula to calculate this number?
If a convolutional code is said to correct 2 errors what does it mean exactly ? Does it mean a maximum number of 2 errors every x bits ? If so, how is x calculated?

Many thanks.

#### lomaxe

##### Member level 1 Hi everyone,

I'm thinking about implementing an error-correcting convolutional code.
My question is related to the error correcting capability of these codes. For example how many errors are corrected when using a rate R=1/2 and a constraint length K=3 ? Is there a formula to calculate this number?
If a convolutional code is said to correct 2 errors what does it mean exactly ? Does it mean a maximum number of 2 errors every x bits ? If so, how is x calculated?

Many thanks.

A convolutional code is described by three integers, n, k, and K, where the ratio k/n has the same code significance that it has for block codes. The integer parameter K is a parameter known as the constraint length; it represents the number of k-tuple stages in the encoding shift register.
With regard to the expression t=(d-1)/2 (where d is the free distance, t - error correcting capability in bits) we can say that the code can, with maximum likelihood decoding, correct t errors within a few constraint lengths, where "few" here means 3 to 5. The exact length depends on how the errors are distributed.

• manhattene

### manhattene

Points: 2

#### andre_luis

##### Super Moderator
Staff member ...If a convolutional code is said to correct 2 errors what does it mean exactly ?...

The amount of detectable bit errors is related to minimum distance d parameter.
For instance, d=2 means that 2 bits can be corrected. +++

#### manhattene

##### Newbie level 3 Thank you very much for the detailed answer lomaxe correct t errors within a few constraint lengths, where "few" here means 3 to 5. The exact length depends on how the errors are distributed.

I searched for this information but I could not find it. All the papers online are talking about encoding and decoding convolutional codes but not about their error correcting capabilities!
It would be really nice if you can give me the source where I can find it !

#### lomaxe

##### Member level 1 You can find it in the book "Digital Communications" by Bernard Sklar. It's a very good book.

• manhattene

### manhattene

Points: 2

#### manhattene

##### Newbie level 3 thank you Status
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