2006
DOI: 10.4218/etrij.06.0105.0161
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General Log-Likelihood Ratio Expression and Its Implementation Algorithm for Gray-Coded QAM Signals

Abstract: A simple and general bit log‐likelihood ratio (LLR) expression is provided for Gray‐coded rectangular quadrature amplitude modulation (R‐QAM) signals. The characteristics of Gray code mapping such as symmetries and repeated formats of the bit assignment in a symbol among bit groups are applied effectively for the simplification of the LLR expression. In order to reduce the complexity of the max‐log‐MAP algorithm for LLR calculation, we replace the mathematical max or min function of the conventional LLR expres… Show more

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Cited by 17 publications
(3 citation statements)
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“…Without loss of generality, we consider a scheme with one relay node only ; thus, we remove the subscripts of the node relation for simplicity. Since calculating the exact bit LLR by using the conventional MLD is excessively exorbitant, there are a few ways proposed to approximate bit LLR values like in [14,15] whose aim is to avoid the high computation from the exact bit LLR expression. Although by using the conventional MLD the optimum performance can be achieved, the approach requires computation which grows exponentially with the constellation size of the modulation schemes.…”
Section: Derivation Of Symbol Llr Based On Mld and Expected Value Of mentioning
confidence: 99%
“…Without loss of generality, we consider a scheme with one relay node only ; thus, we remove the subscripts of the node relation for simplicity. Since calculating the exact bit LLR by using the conventional MLD is excessively exorbitant, there are a few ways proposed to approximate bit LLR values like in [14,15] whose aim is to avoid the high computation from the exact bit LLR expression. Although by using the conventional MLD the optimum performance can be achieved, the approach requires computation which grows exponentially with the constellation size of the modulation schemes.…”
Section: Derivation Of Symbol Llr Based On Mld and Expected Value Of mentioning
confidence: 99%
“…Based on the results of a thorough literature search and deep analysis, we find the following algorithms having remarkable reduced complexity without compromising on quality of communications performance: (1) the algorithm reported in Lin et al (2010) identifies the two required constellation points to compute one LLR in a very simple way and (2) The algorithms reported in Tosato and Bisaglia (2002); Ryoo et al (2003); Kim et al (2006); Arar et al (2007); and Sun and Zeng (2011) are quite similar to each other and provide a very simple approach to compute LLR. We call this approach as decision threshold algorithm in this sequel.…”
Section: Introductionmentioning
confidence: 99%
“…Since the computation of the LLRs can be pricey [27], good approximations of the LLRs are used. For the Gray coded Mj-QAM schemes described by (4.13), the LLR can be well approximated by the following recursive expression [27][28][29] Si,jKi+k d M Jl{a*r%}, k = 0…”
Section: Soft-bit Maximum Likelihood Detector (Sbmld)mentioning
confidence: 99%