An Iterative Decoding Scheme for Serially Concatenated
`Convolutional Codes
`
`Mohamed Siala, Eckhard Papprothl, Kais Haj Taieb, and Ghassan Kawas Kaleh
`Ecole Nationale Supérieure des Telecommunications,
`46 rue Barrault, 75634 Paris 13, France
`
`softoutputs for the sequence received from the inner decoder
`Ty") associated with the new estimated symbols 1321",). This al-
`gorithm is referred to as the outer SOVA. The metric adopted
`by this stage is the simple correlation metric
`
`— Zen — wit“) — org"),
`1‘
`
`where ,3,- E {“D”, “1”} is an arbitrary path symbol with the
`same position as 3;") in the outer encoder trellis 7;. Once
`again, the enhanced soft—information Variables f‘g-m) represent,
`up to a multiplicative factor, an approximation of the log-
`likelihood ratios
`
`in Pa = “clutch, {rm .
`Po.- = “1”l{5§-7"’},{f§7"’})
`
`This second stage exploits the fact that the sequence {fig-mu,
`when correct, must be a codeword sequence of the outer en-
`coder. Denote respectively by {ESZ'U} and {Arm} the inter-
`leaved versions of the sequences {55”,} and {f‘g’m}. The in-
`trinsic contribution of the outer SOVA in comparison with the
`inner one is measured by the difference
`
`Ag”) :2 (26%") — my") w (2st”) ~ 1M1”).
`
`For the following iteration, the new soft—information variables
`generated by the inner SOVA and its associated decisions are
`denoted by [\(hml'l) and 51”“), respectively.
`At the final f—th iteration of the iterative decoding process,
`an outer conventional Viterbi decoder delivers the estimated
`
`{0i}
`
`sequence, {iii}, of the information sequence. The metric used
`by this decoder is — 2,-(2fi1 — 0055-” — my).
`
`
`Inner
`{I11}
`{b1}
`{Ck}
`encoder
`
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`flfim {Ar}
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`k
`Interleaver {5”} (25km) _ DA?)-(253") __1) NZ")
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`l{1:jigim~ SOVA
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`{bio}
`..
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`{‘1'}
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`Viterbi
`algorithm
`
`Abstract ~ We present an iterative soft-output de—
`coding algorithm for serially concatenated convolu—
`tional codes which has better performance than the
`conventional noniterative decoding algorithm. The
`proposed decoding scheme can be used whenever
`some form of serial concatenation of encoders and
`
`channels with memory is applied.
`The figure shows the block diagram for a. serially concate—
`nated coding system with iterative soft-output Viterbi decod-
`ing. The binary data sequence {a5} is fed into the outer en-
`coder. The binary sequence {171‘} at the output of this encoder
`is interleaved to result in {ck}. This sequence is then serially
`encoded by the inner encoder into the sequence {dz}. The se-
`quence {rig} is sent over a. Gaussian channel and produces at
`its output the noisy sequence {y}, where y; = d; + n;. The
`{at} denotes an additive white Gaussian noise sequence with
`zero mean and variance 02.
`
`In the first stage of the m-th iteration of the decoding al—
`gorithm, soft information, Aim), k = . . . , —1, 0, 1,. i .
`, associ-
`ated with the estimated symbols 65;"), k = .. .,—-1,0, l,...,
`are computed by the simplified version of the SOVA [1] taking
`into account the intrinsic contributions of the outer decoder
`from the previous iterations. This algorithm is referred to as
`the inner SOVA. Let T; denote the trellis which represents
`the structure of the inner encoder. The metric adopted by
`this stage is the Euclidean metric
`
`ZCyz — 6:)2 — 2(2)“ - 1) Zkhmgnn)
`t
`k
`u
`
`where x}; and f. are respectively the inputs and noiseless out-
`puts in an arbitrary path with the same position as y; in 7;
`and 71. goes over all previous iterations. For a. given SNR, the
`positive parameters 6(7‘) are arbitrary and should be chosen to
`minimize the bit—error-probability of the sequence {rig} at the
`end of the iterative decoding process. A1") are the intrinsic
`contributions of the outer SOVA as defined below. The soft-
`
`information variables Aim) represent, up to a multiplicative
`factor, an approximation of the log-likelihood ratios
`
`in
`
`PM = “0”l{yz})
`PM = “1”l{yz})
`
`'
`
`The sequence of estimated symbols and the associated reliabil—
`ity information are dcinterleaved using the reverse procedure
`of the block interleaver. The resulting sequences are denoted
`by {£37m} and {fgmd}, respectively.
`The outer decoder uses also a simplified SOVA. It applies
`the structure of the outer encoder trellis to the sequence de-
`livered by the inner decoder. Therefore, it provides enhanced
`
`"Author to whom correspondence may be addressed. E. Pep-
`proth was supported by a DAAD-fellowship HSP II financed by the
`Gerri-inn Federal Ministry for Research and Technology (BMFT).
`
`REFERENCES
`
`[1] J. Hagenauer and P. Hoeher, ”A Viterbi Algorithm with Soft-
`Decision Outputs and Its Applications,” GLOBECOMSQ, Dal-
`las, Texas, pp. 47.11—47.17, November 1989.
`
`473
`
`ERICSSON EXHIBIT 1025
`
`