Maximum Window Size in Selective Reject (Selective Repeat) with $n$-Bit Sequence Numbers

The selective reject protocol (commonly treated in textbooks as Selective Repeat ARQ) uses an $n$-bit sequence number field, giving a total of $2^n$ distinct frame sequence values. The core constraint is that the sender’s window size must be small enough to avoid ambiguity caused by sequence number wrap-around: at any time, the receiver must be able to clearly distinguish “new” frames from “old” (previously used) frames whose sequence numbers have wrapped.

For Selective Repeat, the maximum window size is:

$W_{\max} = 2^{n-1}$

Thus the correct option is (ii) $2^{n-1}$.

Key idea: if the window were larger than half the sequence space, then a frame with a wrapped sequence number could fall inside the receiver’s acceptance set and be misinterpreted as a current-frame duplicate or vice versa, breaking correctness.

Mermaid intuition (wrap-around hazard if window is too large):

Keyword links: selective repeat ARQ selective reject window size sequence number wrap-around.

Selective Repeat (Selective Reject) operates with sliding windows at both sender and receiver. The receiver can store out-of-order frames and acknowledge individually. To ensure correct operation, the window must be limited so that no two different frames within the receiver’s window share the same sequence number meaning across time.

In particular, when the sequence space is $2^n$, the sender window must satisfy:

$W \le 2^{n-1}$

Because:

• The sequence number space is modulo $2^n$.
• The receiver’s “acceptance range” must not include frames that are actually from the previous cycle with the same sequence number values.
• Therefore, the effective distance between “current” and “previous-cycle” meanings of sequence numbers must be at least one window length, which yields the half-space restriction.

So the maximum permissible window is $2^{n-1}$, i.e., option (ii).