## Fundamental concepts in communication |

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algorithm alphabet approach approximation AWGN band-limited bandwidth basis BCH codes Bernoulli trials binary digits bit error calculate central limit theorem channel capacity Chapter code word coder coefficients complex consider coordinates correlation corresponding decoding error defined degrees of freedom detection distribution elements encoding energy contrast ratio ensemble entropy error patterns error probability error-control codes Euclidian example expression finite Fourier transform frequency Gaussian noise GF(q given Hamming information rate information source inner product input integral large number law of large linear code linear vector space M-ary Markov matched filter matched-filter mathematical measure messages metric modulation multiplication mutual information n-tuples noncoherent output performance polynomial possible Prob properties quantity quantization random variables rate-distortion theory received waveform representation represented samples scalars sequence Shannon's shown in Fig signal space signal-to-noise ratio source symbols spectral density statistically independent symbol error total number transmitted uncoded vector space waveform