# The art of error correcting coding - Moreloz R.H.

ISBN 0471-49581-6

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COMBINING CODES AND DIGITAL MODULATION

193

Figure 125 The encoder structure of a turbo TCM scheme with symbol interleaving.

Figure 126 An iterative decoder for turbo TCM with symbol interleaving.

block diagram of the encoder structure is shown in Figure 127, for the case of two component codes.

MAP decoding and bit metrics

The decoder structure for turbo TCM with bit interleaving is similar to that of binary turbo codes. The main difference is that conversion of LLRs from bits to symbols, and from symbols to bits, needs to be performed between decoders [BDMP2, Vuc]. For decoding of turbo TCM with bit interleaving, the LLRs that are computed per bit need to be converted to a symbol level a-priori probability. Also, the a priori probabilities per symbol need to be converted to a bit level extrinsic LLR’s.

This is done in the following way. Let X denote the 2*'-ary modulation signal set. For a symbol x(b) <E X with label b = (l>i,b-2, ? ? ? .bv), the extrinsic information of bit bi, i = 1, 2, • • ?, v, is computed as

A e{bi) = log

x(b),bi~ 1

eAe(x(6))

\x(b),bi— 0 /

(9.16)

194

THE ART OF ERROR CORRECTING CODING

(v - 1 - k )/2 bits

(v - 1 - k )/2 bits

v

bits

Figure 127 Encoder for turbo TCM with bit interleaving.

Similarly, the a-priori symbol probability can be computed from the extrinsic LLR at the bit level through the expression,

>biAe(bi

i=l

_f_ gAe(&i)

(9.17)

The Art of Error Correcting Coding Robert H. Morelos-Zaragoza Copyright © 2002 John Wiley & Sons Ltd ISBNs: 0-471-49581-6 (Hardback); 0-470-84782-4 (Electronic)

References

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196

REFERENCES

[Bos] M. Bossert, Channel Coding for Telecommunications, John Wiley & Sons, 1999.

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[CCG] J. B. Cain, G. C Clark and J. M. Geist, “Punctured Convolutional Codes of Rate (n— 1 )/n and Simplified Maximum Likelihood Decoding,” IEEE Trans. Info. Theory, vol. IT-25, pp. 97100, Jan. 1979.

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