Type 2 error.
By a type 2 error, everywhere below we mean a distortion in the encoded sequence of exactly one value at an even position and the absence of other distortions within the dependency distance.
A type 2 error results in at least one non-zero value in the decoded sequence at the position where 0 should be.
Indeed, let k be even and δk ≠ 0. Then e’k = ek + δk ≠ ek. From (3.3.4) it follows
b'k = e'k - (π(e'k-2 + e'k-1) - π(e'k-1)) => π(e'k-2 + e'k-1) - π(e'k-1) = e'k - b'k.
In the same time
bk = ek - (π(ek-2 + ek-1) - π(ek-1)) = 0.
Considering that, assuming that there are no other distortions within the dependency distance, we have: e'k-2 = ek-2 and e'k-1 = ek-1. Then
e'k - b'k = ek => e'k - ek = δk = b'k. (3.3.2.1)
Thus, the value of b'k is certainly non-zero. Consider the value b'k+2.
b'k+2 = e'k+2 - (π(e'k + e'k+1) - π(e'k+1)) => π(e'k + e'k+1) - π(e'k+1) = e'k+2 - b'k+2 (3.3.2.2)
bk+2 = ek+2 - (π(ek + ek+1) - π(ek+1)) => π(ek + ek+1) - π(ek+1) = ek+2 - bk+2 . (3.3.2.3)
We have: bk+2 = 0, e'i = ei for all i ϵ {k+1, k+2}, e'k - ek = δk = b'k ≠ 0. Subtract (3.3.2.3) from (3.3 .2.2), we get
b'k+2 = π(ek + ek+1) - π(e'k + ek+1) (3.3.2.4)
Since e'k - ek = δk = b'k ≠ 0, then π(ek + ek+1) ≠ π(e'k + ek+1), and hence b'k+2 ≠ 0.
Let's summarize all of the above about the type 2 error.
1. A type 2 error is a corruption of exactly one value at an even position and no other corruption within the dependency distance.
2. A sign of a type 2 error is the appearance during decoding of exactly two non-zero values at positions where 0 should be. This is the even position at which the distortion occurred, and the next even position.
3. Type 2 error is unequivocally correctable and does not require resources to correct it.
Experimental results show that type 1 and type 2 errors and their detection and correction algorithms have a decisive impact on the efficiency of the convolutional MCS code. An analysis of a communication channel in which distortions occur bit by bit, randomly and equiprobably with a probability p of distortion of a bit transmitted over the communication channel at the level p ≈ 0.012, showed that the use of a convolutional MCS code, in which only errors of types 1 and 2 are corrected, makes it possible to reduce the number incorrectly received bytes by about 4 times compared with the transmission of information without using the convolutional MCS code. A similar comparison at the error level p ≈ 0.0012 shows that the number of errors is reduced by about 38 times.
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