Question E8C10:
How can data rate be increased without increasing bandwidth?  

Choices:  
A: It is impossible  
B: Increasing analog-to-digital conversion resolution  
C: Using a more efficient digital code  
D: Using forward error correction    

Correct Answer is  C: Using a more efficient digital code  

Correct answer: C — Using a more efficient digital code

Why C is correct:
- You can increase throughput at the same occupied bandwidth by increasing spectral efficiency—i.e., sending more information per symbol on average.
- A “more efficient digital code” (e.g., source coding, compression, or variable-length codes like Varicode in PSK31) reduces the average number of bits per character, so the same symbol rate (and thus bandwidth) carries more information.

Key ideas and formulas:
- Spectral efficiency: $$\eta = \frac{R}{B}\quad \text{[bits/s/Hz]}$$
  Increase $\eta$ to raise data rate $R$ without increasing bandwidth $B$.
- For $M$-ary modulation: $$R = R_s \log_2 M$$
  With bandwidth roughly proportional to symbol rate $R_s$, making coding more efficient (or using higher-order modulation) increases $R$ at the same $B$.
- Shannon limit: $$C = B \log_2(1+\text{SNR})$$
  Better coding helps approach this limit, increasing usable data rate without changing $B$.

Why the other choices are incorrect:
- A: It is impossible  
  Incorrect. Spectral efficiency can be improved through better coding/encoding, so data rate can increase without widening bandwidth.
- B: Increasing analog-to-digital conversion resolution  
  Higher ADC resolution improves dynamic range/quantization noise but does not, by itself, increase data throughput at a given bandwidth.
- D: Using forward error correction  
  FEC adds redundancy to improve reliability or allow lower SNR operation. At the same symbol rate and bandwidth, the net user data rate usually decreases due to parity/overhead bits.

Rule of thumb:
- To increase data rate at fixed bandwidth, improve spectral efficiency via smarter encoding/compression or higher bits-per-symbol modulation, while staying within channel capacity.