课程名称︰错误更正码 课程性质︰选修 课程教师︰林茂昭 开课学院：电资学院 开课系所︰电机系 电信所 考试日期（年月日）︰2012/01/11 考试时限（分钟）：1 hr 50 min 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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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