 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-2/3i/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

m

letters of the blocked source contain exactly the first

m N

letters of the original source, so

H (Y_{1}, \dots, Y_{m}) = H (X_{1}, \dots, X_{m N}) .

If the original information rate is

h

, then

lim_{m \to \infty} \frac{1}{m} H (Y_{1}, \dots, Y_{m}) = N lim_{m \to \infty} \frac{1}{m N} H (X_{1}, \dots, X_{m N}) = N h .

Thus fixed-length blocking multiplies information rate by $N$ , exactly as recorded by information rate under fixed-length blocking.

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