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Digital Communication I: Modulation and Coding Course-Lecture 12

How decoding is performed for Convolutional codes? What is a Maximum likelihood decoder? What are soft decisions and hard decisions? How does the Viterbi algorithm work?The demodulator makes a firm or hard decision whether one or zero was transmitted and provides no other information for the decoder such as how reliable the decision is. | Digital Communications I: Modulation and Coding Course Term 3 - 2008 Catharina Logothetis Lecture 12 Lecture 12 Last time, we talked about: How decoding is performed for Convolutional codes? What is a Maximum likelihood decoder? What are soft decisions and hard decisions? How does the Viterbi algorithm work? Lecture 12 Trellis of an example ½ Conv. code 1 0 1 0 0 11 10 00 10 11 Input bits Output bits Tail bits 1/11 0/00 0/10 1/11 1/01 0/00 0/11 0/10 0/01 1/11 1/01 1/00 0/00 0/11 0/10 0/01 0/00 0/11 0/00 1/01 Lecture 12 Block diagram of the DCS Information source Rate 1/n Conv. encoder Modulator Information sink Rate 1/n Conv. decoder Demodulator Channel Lecture 12 Soft and hard decision decoding In hard decision: The demodulator makes a firm or hard decision whether one or zero was transmitted and provides no other information for the decoder such as how reliable the decision is. In Soft decision: The demodulator provides the decoder with some side information together with the . | Digital Communications I: Modulation and Coding Course Term 3 - 2008 Catharina Logothetis Lecture 12 Lecture 12 Last time, we talked about: How decoding is performed for Convolutional codes? What is a Maximum likelihood decoder? What are soft decisions and hard decisions? How does the Viterbi algorithm work? Lecture 12 Trellis of an example ½ Conv. code 1 0 1 0 0 11 10 00 10 11 Input bits Output bits Tail bits 1/11 0/00 0/10 1/11 1/01 0/00 0/11 0/10 0/01 1/11 1/01 1/00 0/00 0/11 0/10 0/01 0/00 0/11 0/00 1/01 Lecture 12 Block diagram of the DCS Information source Rate 1/n Conv. encoder Modulator Information sink Rate 1/n Conv. decoder Demodulator Channel Lecture 12 Soft and hard decision decoding In hard decision: The demodulator makes a firm or hard decision whether one or zero was transmitted and provides no other information for the decoder such as how reliable the decision is. In Soft decision: The demodulator provides the decoder with some side information together with the decision. The side information provides the decoder with a measure of confidence for the decision. Lecture 12 Soft and hard decision decoding ML soft-decisions decoding rule: Choose the path in the trellis with minimum Euclidean distance from the received sequence ML hard-decisions decoding rule: Choose the path in the trellis with minimum Hamming distance from the received sequence Lecture 12 The Viterbi algorithm The Viterbi algorithm performs Maximum likelihood decoding. It finds a path through trellis with the largest metric (maximum correlation or minimum distance). At each step in the trellis, it compares the partial metric of all paths entering each state, and keeps only the path with the largest metric, called the survivor, together with its metric. Lecture 12 Example of hard-decision Viterbi decoding 0 2 0 1 2 1 0 1 1 0 1 2 2 1 0 2 1 1 1 1 0 2 3 0 1 2 3 2 3 2 0 2 3 0 Branch metric Partial metric Lecture 12 Example of soft-decision Viterbi decoding 5/3 -5/3 4/3 0 0 1/3 1/3 -1/3 .