"IT-4B Shannon定理与卷积码简介：现代编码理论与应用"

IT-4B Shannon theorem Convolutional code Introduction 1; Convolutional code introduction (3): Decoding of convolutional code (Viterbi algorithm) (4) The decoding problem of convolutional code is to find the codeword stream = such that the corresponding codeword stream is obtained from the noisy received bit stream r=r(0)r(1)r(2)...; Information theory signaling and the theoretical basis of processing Shannon channel coding theorem (Section 7.7); Convolutional coding and modern coding introduction (additional content) The statement of the theorem (Shannon, 1948) For a BSC channel with capacity C, for any real number 0<R<C, there exists a family of (n,k) block coding schemes with transmission efficiency k/n=R, such that the decoding error probability of this group scheme satisfies Pe(n) = 0 as n→∞. Conversely, if a family of (n,k) block coding schemes has a decoding error probability satisfying Pe(n) = 0 as n→∞, then its transmission efficiency k/n satisfies k/n ≤ C. Shannon's theorem shows that through block redundancy coding, information can be transmitted on the BSC channel with arbitrarily low error probability (as the codeword length increases), provided that the transmission efficiency k/n per bit does not exceed the limit set by the channel capacity C. There are corresponding Shannon theorems on other types of complex channels. Since the capacity C is the limit of the transmission efficiency associated with reliable communication on various channels, the capacity formula on various types of channels is of particular importance. Shannon theorem (1) Key points of Shannon theorem proof (see tutorial for proof of theorem 7.7.1) Group coding scheme (random coding) For a given transmission efficiency R<C, let k = [nR]. Take any binary random variable x∈{;" ...