Сидельников В.М. Теория кодирования. Справочник по принципам и методам кодирования
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τ
q
(N, w, r) (w, r)−
q−
K q
τ
q
(w, r) = lim
N→∞
τ
q
(N, w, r).
q− (w, r)− n
q, w, r = const, n → ∞
(w, r)−
K = K(C
1
), K(C
2
), . . . ,
(2, r)− N
j
K
2− 3
C = C
1
, C
2
, . . . , (2, r)− C
j
n
j
n
j
→ ∞, j → ∞ R
2
(C) = lim
j→∞
log
2
|C
j
|
n
j
C
(2, r)−
τ(K) = lim
j→∞
log
2
|K(C
j
)|
N
j
K
τ(K) =
1
3
R
2
(C).
C
j
(2, r)−
τ
2
(2, r) ≥
1
3
R
2
(2, r) ≥
1
3
Y (2, r).
Y (w, r)
(2, r)− 2−
¤
q > 2
τ(2, 1) τ(2, 1) ≥ τ(2, 1) = 0, 149
τ(2, 1) τ(2, 1)
R
2
(2,1)
3
=
Y (2,1)
3
=
0.2075
3
= 0.0691667
τ(2, 1)
(2, 1)−
2− K 3
(2, 1)−
w = 2
(2, r)−
T, |T| = T,
Q = [T ] = {1, . . . , T }
Q j ∈ Q T
j
K = {k
1
, . . . , k
N
}
K
A = {A
1
, . . . , A
T
} (2, r)−
[N] T (2, r)− N
T
j ∈ Q
K
j
= {k
s
|s ∈ A
j
} ⊂ K.
K
j
j
K
i,j
i, j ∈ Q
K
i,j
= .K
i
∩ K
j
.
(2, r)− S ⊂ Q, |S| ≤ r,
K
i,j
i, j 6∈ S
i, j K
i
∩K
j
S
r
K
i
∩K
j
i j
a = max
j∈Q
|K
j
|,
|K
j
| a
T
a
2− Q
q,2
a(Q
q,2
) = B(q, 2) =
¡
q−1
0
¢
+
¡
q−1
1
¢
= q
(2, r)− Q
n
(C) a(Q
n
(C)) = qn n
q− (w, r)− C
(w, r)−
(d−1)
2
(w, r)−
n−
gf(4)
l s
