A systematic bit-wise decomposition of M -ary symbol metric

Chia Wei Chang*, Po-Ning Chen, Yunghsiang S. Man

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this paper, we present a systematic recursive formula for bit-wise decomposition of M-ary symbol metric. The decomposed bit metrics can be applied to improve the performance of a system where the information sequence is binarycoded and interleaved before M-ary modulated. A traditional receiver designed for certain system is to de-map the received M-ary symbol into its binary isomorphism so as to facilitate the subsequent bit-based manipulation, such as hard-decision decoding. With a bit-wise decomposition of M-ary symbol metric, a soft-decision decoder can be used to achieve a better system performance. The idea behind the systematic formula is to decompose the symbol-based maximum-likelihood (ML) metric by equating a number of specific equations that are drawn from squarederror criterion. It interestingly yields a systematic recursive formula that can be applied to some previous work derived from different standpoint. Simulation results based on IEEE 802.11a/g standard show that at bit-error-rate of 10 -5, the proposed bit-wise decomposed metric can provide 3.0 dB, 3.9 dB and 5.1 dB improvement over the concatenation of binarydemapper, deinterleaver and hard-decision decoder respectively for 16QAM, 64QAM and 256QAM symbols, in which the inphase and quadrature components in a complex M 2-QAM symbol are independently treated as two real M-PAM symbols. Further empirical study on system imperfection implies that the proposed bit-wise decomposed metric also improves the system robustness against gain mismatch and phase imperfection. In the end, a realization structure that avails the recursive nature of the proposed bit-decomposed metric formula is addressed.

Original languageEnglish
Article number1705936
Pages (from-to)2742-2750
Number of pages9
JournalIEEE Transactions on Wireless Communications
Issue number10
StatePublished - 1 Oct 2006


  • Maximum-likelihood decoding
  • QAM modulation
  • Soft-decision decoding
  • Viterbi decoder


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