課程名稱︰錯誤更正碼 課程性質︰選修 課程教師︰林茂昭 開課學院：電資學院 開課系所︰電機系 電信所 考試日期（年月日）︰2012/01/11 考試時限（分鐘）：1 hr 50 min 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : The Final Error-Correcting Codes January 9 , 2012 1. Please draw the state diagram of the (3,1,2) Convolutional code with generator sequences g_1 ^(1) =(110) , barg_1 ^(2) = (101) , g_1 ^(3) = (111). (10%) 2. Please prove that maximum likelihood decoding is equivalent to nearest neighbor decoding over the binary symmetric channel with transition probability ε < 1/2 .(10%) 3. Consider the (3,2) convolutional code with | D D^2 1 | G(D)=| | | 0 1 D | (a) Please draw an encoder in feedforward form for this code. (5%) (b) Please find a parity check matrix fot this code. (5%) (c) Please draw a systematic encoder for this code. (10%) 4. Use the EXIT chart to explain the behavior of bit error rates of the parallel concatenated turbo code. (10%) 5. (a) Let U ∈ {+1 , -1}. Find the probability P_U (u=+1) in terms of the log likelihood ratio L(u). (5%) (b) Find the soft bit of u ,i.e.,the mean of U. (5%) (c) Find L(u_1⊕u_2) in terms of L(u_1) and L(u_2). (5%) (d) Find the approximation of L(u_1⊕u_2). (5%) 6. Consider the transmission using an (n,k) low-density parity check code over AWGN channel with symbol energy E_s and one-sided power spectral density N_0. Please describe the iterative decoding for this code including the Tanner graph, the message passing from the variable nodes to the check nodes and the message passing from check nodes to the variable nodes. (15%) 7. Consider a (t,s)-regular low density parity check (LDPC) code of code length n. What is its coding rate ? (5%) 8. Please explain the reason that systematic convolutional codes are prefected over the nonsystematic convolutional codes in constructing the parallel turbo code.(10%) --

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