Signal Processing for Communication Systems
Reed-Solomon (RS) codes are powerhouse error-correcting tools, but they have a specific Achilles’ heel: if a burst inside one codeword exceeds the correction radius \(t = \lfloor (n-k)/2 \rfloor\), a bounded-distance decoder fails on that codeword. Block Interleaving is the mathematical bridge that allows RS codes to survive massive, contiguous bursts by spreading the damage … Read more
Convolutional Encoding Unlike block codes (like Reed-Solomon), Convolutional Codes do not have a fixed block size. Instead, they process a continuous stream of bits. The output at any given time depends not only on the current input bit but also on the previous $K-1$ bits, where $K$ is the Constraint Length.+1. Convolutional codes are a … Read more
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.