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Ly Thuyet TCM+TCM Encoder

Apr 05, 2018

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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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