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
threedigit data to be transmitted. These paths are mapped to 8PSK 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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 Spring '11
 Dr.PaoLoLiu
 Information Theory, Error detection and correction, Most significant bit, Least significant bit

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