- Compute the SNR ceiling for an 8-bit ADC. dB. So if your full-scale input is 1 V peak-to-peak, the quantization noise on a sinusoid is roughly 3 mV RMS. That sets the floor for any signal-processing chain that uses an 8-bit converter; no amount of downstream filtering can recover finer detail.
- Compute the Hamming distance between codewords 1011010 and 1100110: differ in positions 2, 3, 4, 7 (1-indexed from left), so distance 4. A code with this distance can correct up to error per codeword.
- Simulate a BPSK BER curve. The Python snippet in Section 4.6 takes a few seconds. Plot simulated and theoretical curves on log axes; they will overlay.
- Compute the Shannon capacity of a Wi-Fi 6 channel. 80 MHz at 25 dB SNR: Mbps per spatial stream. Real Wi-Fi 6 hits 600+ Mbps per stream in good conditions, leaving very little headroom.
- Try a CRC by hand. Take the message 11010011, polynomial (1011), and compute the CRC. Append it. Verify division gives zero remainder. Then flip a bit and repeat; remainder is non-zero.
- Get an RTL-SDR. Twenty dollars on Amazon. With GNU Radio you can receive AM, FM, ADS-B (aircraft transponders), POCSAG (pagers), AIS (ships), weather satellites, and more. ADS-B is digital comms in the wild: PPM-modulated 1090 MHz pulses, 24-bit CRC, simple frame format. Decoding it from bare IQ samples is the easiest way to feel a real digital receiver in action.
- Read Hamming, "Error Detecting and Error Correcting Codes" (1950). Eight pages, beautiful. The whole field of channel coding starts here.
section 13 of 142 min read