Trellis - Trellis Coded Modulation Trellis coded modulation...

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Trellis Coded Modulation Trellis coded modulation (TCM) involves both channel coding and modulation, i.e., mapping of digital data to physical signals. Channel coding facilitates error detection and correction by adding redundant bits. For two bits of input data, TCM transmits three bits, i.e., 2 from the source message and 1 as the redundant bit. The input data consists of two bits, the least significant bit and the most significant bit. The most significant bit is kept the way it is. TCM generates the redundant bit by keeping track of the two previous least significant data bits. The least significant bit is fed through two shift registers. The current least significant bit and the two previous least significant bits are combined (or hashed in the term of information theory) by XOR gates to generate two bits. Since two previous bits are involved, this is a convolution encoder. The two bits and the most significant bit constitute the current encoded data to be transmitted. The two previous bits in the shift registers determine the state of the encoder. Since there are two shift registers, there are four states, 00, 01, 10, and 11. At any given moment, there are four possible states. When data transmission occurs, the initial state evolves to the next state. The transitions are not random. Only specific paths exist in the trellis or state diagram because of the convolution encoding. For example the starting state of 00 can only reach ending states 00 and 01. Likewise, the starting state of 11 can only reach 11 or 10. Each path represents a specific three-digit data to be transmitted. These paths are mapped to 8-PSK constellation points. Each constellation point represents a distinctive physical signal. How to map these encoded data to constellation points is the key to the success of trellis coded modulation. The basic idea is to map paths with least difference in starting and ending states to
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Trellis - Trellis Coded Modulation Trellis coded modulation...

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