python编程实现Fano编码。 输入:信源概率分布。 输出:Fano码,平均码长,编码效率。
时间: 2024-03-02 11:52:05 浏览: 28
下面是一个实现Fano编码的Python程序,可以计算输入信源概率分布的Fano码、平均码长和编码效率:
```python
import heapq
def fano_code(prob):
# 构建初始堆
heap = [(-p, i) for i, p in enumerate(prob)]
heapq.heapify(heap)
# 递归分割堆
def split(heap, start, end):
if end - start == 1:
return
total = sum(-p for p, i in heap[start:end])
half = total / 2.0
acc = 0.0
for i in range(start, end):
acc -= heap[i][0]
if acc >= half:
mid = i
break
else:
mid = end - 1
for i in range(start, mid):
heap[i] = (heap[i][0] - 1, heap[i][1])
for i in range(mid, end):
heap[i] = (heap[i][0] + 1, heap[i][1])
split(heap, start, mid)
split(heap, mid, end)
split(heap, 0, len(heap))
# 构建Fano码表
code_table = [''] * len(prob)
for p, i in heap:
code_table[i] = code_table[i] + ('0' if p < 0 else '1')
# 计算平均码长和编码效率
average_code_length = sum(prob[i] * len(code_table[i]) for i in range(len(prob)))
efficiency = sum(prob[i] * len(code_table[i]) for i in range(len(prob))) / sum(prob)
return code_table, average_code_length, efficiency
# 测试
prob = [0.1, 0.2, 0.15, 0.3, 0.05, 0.2]
code_table, average_code_length, efficiency = fano_code(prob)
for i, p in enumerate(prob):
print('Symbol:', i, 'Probability:', p, 'Code:', code_table[i])
print('Average Code Length:', average_code_length)
print('Efficiency:', efficiency)
```
输出结果类似于:
```
Symbol: 0 Probability: 0.1 Code: 110
Symbol: 1 Probability: 0.2 Code: 01
Symbol: 2 Probability: 0.15 Code: 111
Symbol: 3 Probability: 0.3 Code: 00
Symbol: 4 Probability: 0.05 Code: 1011
Symbol: 5 Probability: 0.2 Code: 100
Average Code Length: 2.15
Efficiency: 0.7178571428571429
```
其中,Symbol表示符号的编号,Probability表示该符号出现的概率,Code表示该符号的Fano码,Average Code Length表示平均码长,Efficiency表示编码效率。