An Introduction to Coding Theory

A: A higher code rate looks attractive but pushes the operating point out of the waterfall so HARQ churn eats the gain. Reduced trellis depth does cut compute but it doesn't rescue distance properties at fixed Eb/N0. Ideal interleaving doesn't cancel the fundamental parity overhead at a fixed error target. Extra parity reduces payload bits and you're already past the knee so there's no BER headroom to trade.

A: Metric quantization spreads errors more uniformly rather than in bursts. LLR scaling errors raise BER but don't align errors in time. Shortened blocks hurt distance but still randomize error locations. A shallow interleaver lets a fade wipe adjacent coded bits, which the decoder can't decorrelate.

A: Two parity bits can't index all error locations so single error correction fails. Padding to powers of two confuses block length with parity count and overstates distance. Single error correction still requires distance three, not two. Three parity bits satisfy 2^p ≥ n+1, giving a (7,4) code with distance three.

A: CRCs are very effective against random independent errors. Thermal noise is exactly the environment CRCs are designed around. Overhead affects efficiency, not protection. A repeating fault that maps to a multiple of the polynomial can slip through undetected.