A Proof of Convergence of the MAP Turbo-Detector to the AWGN Case
In this paper, we consider a coded transmission over a frequency-selective channel. We propose to study analytically the convergence of the turbo-detector using a maximum a posteriori (MAP) equalizer and a MAP decoder. We show that the densities of the extrinsic log likelihood ratios (LLRs) exchange...
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| Veröffentlicht in: | IEEE transactions on signal processing 2008-04, Vol.56 (4), p.1548-1561 |
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| container_title | IEEE transactions on signal processing |
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| creator | Sellami, N. Roumy, A. Fijalkow, I. |
| description | In this paper, we consider a coded transmission over a frequency-selective channel. We propose to study analytically the convergence of the turbo-detector using a maximum a posteriori (MAP) equalizer and a MAP decoder. We show that the densities of the extrinsic log likelihood ratios (LLRs) exchanged during the iterations are e-symmetric and output-symmetric. Under the Gaussian approximation, this property allows to perform a one-dimensional (1-D) analysis of the turbo-detector. By deriving the analytical expressions of the extrinsic LLR distributions under the Gaussian approximation, we prove that the bit error rate (BER) performance of the turbo-detector converges to the BER performance of the coded additive white Gaussian noise (AWGN) channel at high signal to noise ratio (SNR), for any frequency-selective channel. |
| doi_str_mv | 10.1109/TSP.2007.910467 |
| format | Article |
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By deriving the analytical expressions of the extrinsic LLR distributions under the Gaussian approximation, we prove that the bit error rate (BER) performance of the turbo-detector converges to the BER performance of the coded additive white Gaussian noise (AWGN) channel at high signal to noise ratio (SNR), for any frequency-selective channel.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/TSP.2007.910467</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Approximation ; AWGN ; Bit error rate ; Channels ; Coding, codes ; Convergence ; Convergence analysis ; Density ; density evolution ; Detection, estimation, filtering, equalization, prediction ; Equalizers ; Exact sciences and technology ; Exact solutions ; Frequency ; Gaussian ; Gaussian approximation ; Gaussian densities ; Information, signal and communications theory ; Iterative decoding ; Likelihood ratio ; MAP detection ; Mathematical analysis ; Performance analysis ; Signal analysis ; Signal and communications theory ; Signal to noise ratio ; Signal, noise ; symmetric densities ; Telecommunications and information theory ; turbo- detection</subject><ispartof>IEEE transactions on signal processing, 2008-04, Vol.56 (4), p.1548-1561</ispartof><rights>2008 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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We propose to study analytically the convergence of the turbo-detector using a maximum a posteriori (MAP) equalizer and a MAP decoder. We show that the densities of the extrinsic log likelihood ratios (LLRs) exchanged during the iterations are e-symmetric and output-symmetric. Under the Gaussian approximation, this property allows to perform a one-dimensional (1-D) analysis of the turbo-detector. By deriving the analytical expressions of the extrinsic LLR distributions under the Gaussian approximation, we prove that the bit error rate (BER) performance of the turbo-detector converges to the BER performance of the coded additive white Gaussian noise (AWGN) channel at high signal to noise ratio (SNR), for any frequency-selective channel.</description><subject>Applied sciences</subject><subject>Approximation</subject><subject>AWGN</subject><subject>Bit error rate</subject><subject>Channels</subject><subject>Coding, codes</subject><subject>Convergence</subject><subject>Convergence analysis</subject><subject>Density</subject><subject>density evolution</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Equalizers</subject><subject>Exact sciences and technology</subject><subject>Exact solutions</subject><subject>Frequency</subject><subject>Gaussian</subject><subject>Gaussian approximation</subject><subject>Gaussian densities</subject><subject>Information, signal and communications theory</subject><subject>Iterative decoding</subject><subject>Likelihood ratio</subject><subject>MAP detection</subject><subject>Mathematical analysis</subject><subject>Performance analysis</subject><subject>Signal analysis</subject><subject>Signal and communications theory</subject><subject>Signal to noise ratio</subject><subject>Signal, noise</subject><subject>symmetric densities</subject><subject>Telecommunications and information theory</subject><subject>turbo- detection</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kEtLAzEQgBdR8Hn24GURFC9bM3lujkt9go-CFb2FbJxopW5qshX896ZWPHgQBmaG-WZgvqLYBTIAIPp4fDcaUELUQAPhUq0UG6A5VIQruZprIlglavW4Xmym9EoIcK7lRtE05SiG4Mscw9B9YHzGzuGi7V-wvG5G5Xge21CdYI-uD7Hsw_ekeTi_KYc24Xax5u004c5P3iruz07Hw4vq6vb8cthcVY5T1leKaRTuCREF5bJVVnHWOu8F163QTIG10osaKfet1QrIk6S1ayWpvZVWAtsqDpd3ZzG8zzH15m2SHE6ntsMwT4ZxTTjVC_DoXxCkAioZr3lG9_-gr2Eeu_yGqSWjhDEQGTpeQi6GlCJ6M4uTNxs_DRCzUG-yerNQb5bq88bBz1mbnJ36aDs3Sb9rlEBdg5aZ21tyk6zld8y5kIoA-wJTK4jf</recordid><startdate>20080401</startdate><enddate>20080401</enddate><creator>Sellami, N.</creator><creator>Roumy, A.</creator><creator>Fijalkow, I.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Applied sciences Approximation AWGN Bit error rate Channels Coding, codes Convergence Convergence analysis Density density evolution Detection, estimation, filtering, equalization, prediction Equalizers Exact sciences and technology Exact solutions Frequency Gaussian Gaussian approximation Gaussian densities Information, signal and communications theory Iterative decoding Likelihood ratio MAP detection Mathematical analysis Performance analysis Signal analysis Signal and communications theory Signal to noise ratio Signal, noise symmetric densities Telecommunications and information theory turbo- detection |
| title | A Proof of Convergence of the MAP Turbo-Detector to the AWGN Case |
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