Modulation and coding course- lecture 10

Another class of linear codes, known as Convolutional codes.-We study the structure of the encoder.-We study different ways for representing the encoder.
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Modulation and coding course- lecture 10 Digital Communications I:Modulation and Coding Course Period 3 - 2007 Catharina Logothetis Lecture 10 Last time, we talked about:Channel codingLinear block codes The error detection and correction capability Encoding and decoding Hamming codes Cyclic codes Lecture 10 2Today, we are going to talk about:Another class of linear codes, known asConvolutional codes.We study the structure of the encoder.We study different ways for representingthe encoder. Lecture 10 3 Convolutional codesConvolutional codes offer an approach to error controlcoding substantially different from that of block codes. A convolutional encoder: encodes the entire data stream, into a single codeword. does not need to segment the data stream into blocks of fixed size (Convolutional codes are often forced to block structure by periodic truncation). is a machine with memory.This fundamental difference in approach imparts adifferent nature to the design and evaluation of the code. Block codes are based on algebraic/combinatorial techniques. Convolutional codes are based on construction techniques. Lecture 10 4 Convolutional codes-cont’dA Convolutional code is specified bythree parameters (n, k , K ) or (k / n, K )where Rc = k / n is the coding rate, determining the number of data bits per coded bit. In practice, usually k=1 is chosen and we assume that from now on. K is the constraint length of the encoder a where the encoder has K-1 memory elements. There is different definitions in literatures for constraint length. Lecture 10 5 Block diagram of the DCSInformation Rate 1/n Modulator source Conv. encoder m = (m1 , m2 ,..., mi ,...) U = G(m) 144 44 2 3 = (U1 , U 2 , U 3 ,..., U i ,...) Channel Input sequence 144 2444 4 3 Codeword sequence U i = u1i ,...,u ji ,...,u ni 14 2444 3 Branch word ( n coded bits)Information Rate 1/n Demodulator sink Conv. decoder m = (m1 , m2 ,..., mi ,...) ˆ ˆ ˆ ˆ Z = ( Z1 , Z 2 , Z 3 ,..., Z i ,...) 144 2444 4 3 received sequence Zi = z1i ,...,z ji ,...,z ni { 14 2444 3 Demodulator outputs n outputs per Branch word for Branch word i Lecture 10 6 A Rate ½ Convolutional encoderConvolutional encoder (rate ½, K=3) 3 shift-registers where the first one takes the incoming data bit and the rest, form the memory of the encoder. u1 First coded bit (Branch word)Input data bits Output coded bits m u1 ,u2 u2 Second coded bit Lecture 10 7 A Rate ½ Convolutional encoder Message sequence: m = (101)Time Output Time Output (Branch word) (Branch word) u1 u1 u1 u 2 u1 u 2 t1 1 0 0 t2 0 1 0 1 1 1 0 u2 u2 u1 u1 u1 u 2 u1 u 2 t3 1 0 1 t4 0 1 0 0 0 1 0 u2 u2 Lecture 10 8 A Rate ½ Convolutional encoderTime Output Time Output (Branch word) (Branch word) u1 u1 u1 u 2 u1 u 2 t5 0 0 1 t6 0 0 0 1 1 0 0 u2 u2 m = (101) Encoder U = (11 10 00 10 11) ...