Signal Processing for Communication Systems
Introduction The Hamming codes described in previous articles are suitable for random bit errors. However, if the communication medium is prone to burst errors (contiguous blocks of bits being corrupted), Hamming codes are no longer efficient. For these scenarios, we use a class of Error Correcting Codes called Reed-Solomon (RS) Codes. Applications of RS … Read more
How Hamming codes work: parity-bit placement, syndrome decoding, single-error correction, and why (7,4) Hamming is the classic teaching example.
Information theory path: BPSK AWGN → Shannon capacity → Shannon power-efficiency limit → Capacity calculator In one sentence: Shannon capacity is the highest rate (bits per channel use, or bits per second for a continuous-time bandlimited AWGN channel) at which information can be sent with arbitrarily small error probability. Shannon theorem dictates the maximum … Read more