信息论与编码理论基础 December 4,2007 XDU,Fall 2007 Lecture Notes Introduction to Channel Coding I.Error control coding (overview) Shannon showed that reliable communications can be achieved by proper coding of information to be transmitted provided that the rate of information transmission is below the channel capacity. Coding is achieved by adding properly designed redundancy to each message before its transmission.The added redundar appear in the for rm of extra symbols (or bits).or in the form of channel signal-ser expansion or in the form of combination of both. Coding may be designed and performed separately from modulation,or designed in conjunction with modulation as a single entity.In the former case,redundancy appears in the form of extra symbols,normally called parity-check symbols. ■ ng achieved by addin is known as conventio nal coding,in which error control (or coding gain)is achieved at the expense of bandwidth expansion or data rate reduction.Therefore,conventional coding is suitable for error control in power limited channels,such as deep space channel. In the case that coding is designed in conjunction with modulation,redundancy comes from channel signal- nsion.This combination of coding and modulation is usually known as coded modulation,which allo s us to achieve error control (or coding gain)without compromising bandwidth efficiency.We refer this technique as the bandwidth efficient coding. ■Historical notes: Hamming codes(1950) Reed-Muller codes(1954) BCH codes (by Bose,Ray-Chaudhuri and Hocquenghem,1959) BM算法(1968) Reed-Solomon codes(1960) Low-density parity-check codes(by Gallager in 1962,rediscovered in 90's) by Elias,1955) Viterbi algorithm(1967) Concatenated codes(by Forney,1966) Trellis-coded modulation (by Ungerboeck,1982) Turbo codes(by Berrou,1993) Space-time codes(by Vahid Tarokh,1998) Applications Deep space,satellite,mobile communications,voice modem,data networks,etc. ■Two simple examples: 1 信息论与编码理论基础 December 4, 2007 XDU, Fall 2007 Lecture Notes Introduction to Channel Coding I．Error control coding (overview) „ Shannon showed that reliable communications can be achieved by proper coding of information to be transmitted provided that the rate of information transmission is below the channel capacity. „ Coding is achieved by adding properly designed redundancy to each message before its transmission. The added redundancy is used for error control. The redundancy may appear in the form of extra symbols (or bits), or in the form of channel signal-set expansion or in the form of combination of both. „ Coding may be designed and performed separately from modulation, or designed in conjunction with modulation as a single entity. In the former case, redundancy appears in the form of extra symbols, normally called parity-check symbols. „ Coding achieved by adding extra redundant digits is known as conventional coding, in which error control (or coding gain) is achieved at the expense of bandwidth expansion or data rate reduction. Therefore, conventional coding is suitable for error control in power limited channels, such as deep space channel. „ In the case that coding is designed in conjunction with modulation, redundancy comes from channel signal-set expansion. This combination of coding and modulation is usually known as coded modulation, which allows us to achieve error control (or coding gain) without compromising bandwidth efficiency. We refer this technique as the bandwidth efficient coding. „ Historical notes: Hamming codes (1950) Reed-Muller codes (1954) BCH codes (by Bose, Ray-Chaudhuri and Hocquenghem, 1959) Reed-Solomon codes (1960) ⎫ ⎬ ⎭ BM 算法（1968） Low-density parity-check codes (by Gallager in 1962, rediscovered in 90’s) Convolutional codes (by Elias, 1955) Viterbi algorithm (1967) Concatenated codes (by Forney, 1966) Trellis-coded modulation (by Ungerboeck, 1982) Turbo codes (by Berrou , 1993) Space-time codes (by Vahid Tarokh,1998) „ Applications: Deep space, satellite, mobile communications, voice modem, data networks, etc. „ Two simple examples: