Today, we are going to talk about: Another class of linear codes, known as Convolutional codes. Structures of the encoder and different ways for representing it.: state diagram and trellis representation of the code. What is a Maximum likelihood decoder? How the decoding is performed for Convolutional codes (the Viterbi algorithm) ? | Convolutional Coding Modulation, Demodulation and Coding Today, we are going to talk about: Another class of linear codes, known as Convolutional codes. Structures of the encoder and different ways for representing it.: state diagram and trellis representation of the code. What is a Maximum likelihood decoder? How the decoding is performed for Convolutional codes (the Viterbi algorithm) ? Soft decisions vs. hard decisions Convolutional codes Convolutional codes offer an approach to error control coding 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 a different nature to the design and evaluation of the code. Block codes are based on algebraic/combinatorial techniques. . | Convolutional Coding Modulation, Demodulation and Coding Today, we are going to talk about: Another class of linear codes, known as Convolutional codes. Structures of the encoder and different ways for representing it.: state diagram and trellis representation of the code. What is a Maximum likelihood decoder? How the decoding is performed for Convolutional codes (the Viterbi algorithm) ? Soft decisions vs. hard decisions Convolutional codes Convolutional codes offer an approach to error control coding 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 a different nature to the design and evaluation of the code. Block codes are based on algebraic/combinatorial techniques. Convolutional codes are based on construction techniques. Convolutional codes-cont’d A Convolutional code is specified by three parameters or where is the coding rate, determining the number of data bits per coded bit. In practice, typically 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. Block diagram of the DCS Information source Rate 1/n Conv. encoder Modulator Information sink Rate 1/n Conv. decoder Demodulator Channel A Rate ½ Convolutional encoder Convolutional 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. Input data bits Output coded bits First coded bit Second coded bit (Branch word) A Rate ½ Convolutional encoder 1 0 0 0 1 0 1 0 1 0 1 0 Time Output Output Time Message sequence: (Branch word) (Branch word) A .
