Signal Processing for Communication Systems
Keywords: maximum likelihood estimation, statistical method, probability distribution, MLE, models, practical applications, finance, economics, natural sciences. Introduction Maximum Likelihood Estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution by finding the set of values that maximize the likelihood function of the observed data. In other words, MLE is … Read more
Detection path: ML estimation → ML decoding → Hard vs soft decision → Hamming codes In one sentence: Maximum-likelihood decoding picks the codeword that maximizes the channel likelihood of the received word — on a BSC that reduces to nearest Hamming neighbor when the crossover probability is below one half. Introduction Maximum likelihood decoding … Read more
Hard decision keeps 0/1; soft decision keeps reliability (LLRs). Why soft decoding gains ~2 dB and how it ties to ML decoding.
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.
Shannon–Hartley channel capacity C = B log2(1+SNR): plot bits/s vs SNR in Matlab or Python, and verify with the on-site capacity calculator.
Introduction to Probability: The Foundation of Random Signals In the world of communication engineering, “certainty” is a luxury we don’t have. From the thermal noise in your smartphone’s receiver to the fading of a satellite signal, every process we analyze is governed by uncertainty. Probability is the mathematical language that allows us to model … Read more