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Source-Channel Fixed-Length Code

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Definition

Given a discrete source {Vi}i=1āˆž\{V_{i}\}^\infty_{i=1} with alphabet V\mathcal{V} and a discrete channel (X,Y,{PYn∣Xn}i=1āˆž)(\mathcal{X},\mathcal{Y},\{P_{Y^{n}|X^{n}}\}^\infty_{i=1}) an mm-to-nn source-channel fixed-length code Cm,n\mathcal{C}_{m,n} with rate mn\frac{m}{n} source symbol/channel symbol is a pair of maps (fsc,gsc)(f_{sc},g_{sc}): fsc:Vm→Xn\mbox(encoder)f_{sc}:\mathcal{V}^{m}\to\mathcal{X}^{n}\mbox{ (encoder)}and gsc:Xm→Vn\mbox(decoder)g_{sc}:\mathcal{X}^{m}\to\mathcal{V}^{n}\mbox{ (decoder)}

Average Probability of Error (Source-Channel Code)

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