ly thuyet tcm+tcm encoder
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Lecture 9b ConvolutionalCoding/Decoding and Trellis
Code modulation
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Convolutional Coder Basics
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Coder State Diagram
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Coder Tree
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Viterbi Decoding
For Simplicity assume Binary Sym.Channel Encoder has Constraint length 3, Rate
A trellis represents the decoder
Trellis transitions are labeled with branchmetrics (hamming distance between branch
code word and received codeword If two paths merge the path with larger
metric is eliminated
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Decoder Trellis
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Free Distance
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Free Distance and Coding Gain
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Introduction to TCM
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What is TCM?
TCM schemes achieve coding gains without using additional
bandwidth
The technique employs non-binary modulation in conjunction
with a finite state encoder
The encoder dictates the selection of modulation waveformsfor generating a sequence of coded waveforms
At the receiver the noisy signals are detected/decoded by a soft
decision maximum-likelihood decoder
TCM is another technique in the evolution of coding methods
that contributes toward the fulfillment of shannon;s coding gain
prediction
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Today TCM can be used to privde a coding of 3 dB withrelative ease
6 dB coding gain can be provided with additional
complexity
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Evolution of TCM
First Proposed by Ungerboeck and Csajkain 1976 (IBM Research in Swiss)
A more detailed publication in 1982
received the information theory best paperaward
In 1984 TCM with 4 dB coding gain wasadopted by the CCITT for use in high speedvoice band modem
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Structured Sequence Coding
Channel coding can be partitioned into twostudy areas: Structured sequence coding(parity bit design) and Waveform coding
Waveform coding attempts to find betterwaveforms which provide improveddistance properties
Waveform coding can include redundantwaveforms as in the case of TCM
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Reasons for Disappointing results of
conventional coding methods when thechannel is band-limited
With hard-decision decoding, irreversible errors can be made by the
demodulator prior to decoding With soft decision decoding (using Euclidean distance), the following
problem becomes apparent
For a code, the optimized for hamming distance, the mapping of code
symbols into non-binary modulation waveforms doe not guarantee a
good Euclidean distance structure
Generally one cannot find a monotonic relationship between hamming
and Euclidean distances Squared Euclidean and hamming distances are equivalent only in the
case of binary modulation or 4 phase modulation
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Coding gain when bandwdith
expansion is allowed
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Theory of TCM
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Theory of TCM
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Set Partitioning Rules for 8-PSK
All signals should occur with equal frequency and
with a fair amount of regularity and symmetry
Transitions originating from the same state are
assigned signals either from subset B0 or B1 Transitions joining in the same state are assigned
signals either from subset B0 or B1
Parallel transitions receive signals either from
subset C0 or C1 or C2 or C3
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Partitioning (contd)
Rule 1 follows our intuition that good codes
should have a regular structure
Rules 2,3,4 guarantee that bit sequences are
assigned to waveforms so that the free distancewill exceed the free distance of the uncoded 4
PSK reference modulation by at least 3 dB
Parallel transitions refer to the branch wordsresulting from the transmission of uncoded bits
along with coded bits.
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TCM Code Construction First a suitable trellis structure is selected. This can be
done without any particular encoder in mind If k bits are to be encode per modulation interval then there
must be 2^k possible transitions from each state to a
successor state More than one transition (Parallel transitions) may occur
between pairs of states
Next from an extended set of 2^k+1 modulation signals,assignments of signals to trellis transitions will be made so
as to maximize the free Euclidean distance
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Modulation Signal Sets
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4-TCM Encoder
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TCM Trellis
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4 State Trellis with parallel Paths
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8 state trellis with partitioning
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16 QAM Partitioning
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16-QAM Trellis
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