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127
Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding
 IEEE Trans. Inform. Theory
, 1996
"... A serially concatenated code with an interleaver consists of the cascade of an outer code... ..."
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Cited by 366 (32 self)
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A serially concatenated code with an interleaver consists of the cascade of an outer code...
Turbo Encoder Design For Symbol Interleaved Parallel Concatenated Trellis Coded Modulation
, 2000
"... This paper addresses turboencoder design for coding with high spectral efficiency using parallel concatenated trellis coded modulation (PCTCM) and symbol interleaving. The turboencoder design involves the constituent encoder design and the interleaver design. The constituent encoders are optimized ..."
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Cited by 40 (8 self)
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This paper addresses turboencoder design for coding with high spectral efficiency using parallel concatenated trellis coded modulation (PCTCM) and symbol interleaving. The turboencoder design involves the constituent encoder design and the interleaver design. The constituent encoders are optimized for symbolwise effective free distance, and each has an infinite symbolwise impulse response. We identify the canonical structures for the constituent encoder search space. In many cases of practical interest, the optimal structure for these constituent encoders connects the memory elements in a single row. This single row generally applies to turbocode constituent encoders for parallel concatenation and is not restricted to symbol interleaving. To lower the error floor, a new semirandom interleaver design criteria and a construction method extends the spreadinterleaver concept introduced by Divsalar and Pollara. Simulation results show that the proposed system employing symbol interleaving can converge at a lower SNR than previously reported systems. We report simulation results between 0.5 dB and 0.6 dB from constrained capacity for rates of 2 and 4 bits/sec/Hz.
Joint messagepassing decoding of LDPC codes and partialresponse channels
 IEEE TRANS. INF. THEORY
, 2002
"... Ideas of message passing are applied to the problem of removing the effects of intersymbol interference (ISI) from partialresponse channels. Both bitbased and statebased parallel messagepassing algorithms are proposed. For a fixed number of iterations less than the block length, the biterror ra ..."
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Cited by 35 (6 self)
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Ideas of message passing are applied to the problem of removing the effects of intersymbol interference (ISI) from partialresponse channels. Both bitbased and statebased parallel messagepassing algorithms are proposed. For a fixed number of iterations less than the block length, the biterror rate of the statebased algorithm approaches a nonzero constant as the signaltonoise ratio (SNR) approaches infinity. This limitation can be removed by using a precoder. It is well known that lowdensity paritycheck (LDPC) codes can be decoded using a messagepassing algorithm. Here, a single messagepassing detector/decoder matched to the combination of a partialresponse channel and an LDPC code is investigated.
Design, analysis, and performance evaluation for BICMID with square QAM constellations in Rayleigh fading channels
 IEEE J. Select. Areas Commun
, 2001
"... Abstract—We consider bitinterleaved coded modulation with iterative decoding (BICMID) for bandwidthefficient transmission over Rayleigh fading channels. We propose the design criteria that utilize a large Hamming distance inherited in a lowrate code and a new labeling technique designed specifi ..."
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Cited by 33 (2 self)
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Abstract—We consider bitinterleaved coded modulation with iterative decoding (BICMID) for bandwidthefficient transmission over Rayleigh fading channels. We propose the design criteria that utilize a large Hamming distance inherited in a lowrate code and a new labeling technique designed specifically for fading channels. This results in large coding gain over noniterative coded modulation and performance close to that of “turbo ” coded modulation with less complexity. We also show that BICMID designed for fading channel usually has a very good performance over the additive white Gaussian noise (AWGN) channel while the converse is difficult to achieve. When combined with signal space diversity, diversity order can be improved to twice the diversity order of conventional BICMID; therefore, the code complexity can further be reduced while maintaining the same level of performance. Specifically, with the bandwidth efficiency of 2 bits/s/Hz over Rayleigh fading channels, a bit error rate (BER) of 10 6 can be achieved with 16QAM, a fourstate rate 1/2 code at 0 of about seven dB. We also derive performance bounds for BICMID with and without signal space diversity over Rayleigh fading channels, which can be easily extended for other types of fading channels. Index Terms—Bandwidthefficient coded modulation, BICM, fading channels, iterative decoding, turbo codes. I.
Reducedstate BCJRtype algorithms
, 2001
"... In this paper, we propose a technique to reduce the number of trellis states in BCJRtype algorithms, i.e., algorithms with a structure similar to that of the wellknown algorithm by Bahl, Cocke, Jelinek, and Raviv (BCJR). This work is inspired by reducedstate sequence detection (RSSD). The key id ..."
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Cited by 33 (10 self)
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In this paper, we propose a technique to reduce the number of trellis states in BCJRtype algorithms, i.e., algorithms with a structure similar to that of the wellknown algorithm by Bahl, Cocke, Jelinek, and Raviv (BCJR). This work is inspired by reducedstate sequence detection (RSSD). The key idea is the construction, during one of the recursions in the reducedstate trellis, of a “survivor map” to be used in the other recursion. In a more general setting, two distinct survivor maps could be determined in the two recursions and used jointly to approximate the a posteriori probabilities. Three examples of application to iterative decoding are shown: 1) coherent detection for intersymbol interference (ISI) channels; 2) noncoherent detection based on an algorithm recently proposed by the authors; and 3) detection based on linear prediction for Rayleigh fading channels. As in classical RSSD, the proposed algorithm allows significant statecomplexity reduction with limited performance degradation.
Utilizing Soft Information in Decoding of Variable Length Codes
, 1999
"... : We present a method for utilizing soft information in decoding of variable length codes (VLCs). When compared with traditional VLC decoding, which is performed using "hard" input bits and a state machine, the softinput VLC decoding offers improved performance in terms of packet and symb ..."
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Cited by 31 (3 self)
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: We present a method for utilizing soft information in decoding of variable length codes (VLCs). When compared with traditional VLC decoding, which is performed using "hard" input bits and a state machine, the softinput VLC decoding offers improved performance in terms of packet and symbol error rates. Softinput VLC decoding is free from the risk, encountered in hard decision VLC decoders in noisy environments, of terminating the decoding in an unsynchronized state, and it offers the possibility to exploit a priori knowledge, if available, of the number of symbols contained in the packet. 1 Introduction In most applications of variable length codes (VLCs), decoding is performed bit by bit, with the input to the entropy decoder assumed to be a sequence of "hard" bits about which no soft information is available. However, in noisy environments, soft information can be associated with each information bit, either by direct use of channel observations in the case of uncoded transmission...
Convergence analysis and optimal scheduling for multiple concatenated codes
 IEEE Transactions on Information Theory
, 2005
"... Abstract—An interesting practical consideration for decoding of serial or parallel concatenated codes with more than two components is the determination of the lowest complexity component decoder schedule which results in convergence. This correspondence presents an algorithm that finds such an opti ..."
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Cited by 29 (8 self)
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Abstract—An interesting practical consideration for decoding of serial or parallel concatenated codes with more than two components is the determination of the lowest complexity component decoder schedule which results in convergence. This correspondence presents an algorithm that finds such an optimal decoder schedule. A technique is also given for combining and projecting a series of threedimensional extrinsic information transfer (EXIT) functions onto a single twodimensional EXIT chart. This is a useful technique for visualizing the convergence threshold for multiple concatenated codes and provides a design tool for concatenated codes with more than two components. Index Terms—EXIT chart, iterative decoding, multiple concatenated codes, optimal scheduling. I.
Analysis, Design, and Iterative Decoding of Double Serially Concatenated Codes with Interleavers
 IEEE J. Select. Areas Commun
, 1998
"... A double serially concatenated code with two interleavers consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits, and an inner encoder whose input words are the permuted middle codewords. ..."
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Cited by 28 (1 self)
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A double serially concatenated code with two interleavers consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits, and an inner encoder whose input words are the permuted middle codewords. The construction can be generalized to h cascaded encoders separated by h 0 1 interleavers, where h?3: We obtain upper bounds to the average maximum likelihood biterror probability of double serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer, middle, and inner codes that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a lowcomplexity iterative decoding algorithm. Comparisons with parallel concatenated convolutional codes, known as "turbo codes," and with the recently proposed serially concatenated convolutional codes are also presented, showing that in some cases, t...
Noncoherent iterative (turbo) decoding
, 2000
"... Recently, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these ..."
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Cited by 18 (3 self)
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Recently, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. In this paper, we propose two noncoherent softoutput decoding algorithms. The first solution has a structure similar to that of the wellknown algorithm by Bahl et al.(BCJR), whereas the second is based on noncoherent sequence detection and a reducedstate softoutput Viterbi algorithm. Applications to the combined detection and decoding of differential or convolutional codes are considered. Further applications to noncoherent iterative decoding of turbo codes and serially concatenated interleaved codes are also considered. The proposed noncoherent detection schemes exhibit moderate performance loss with respect to corresponding coherent schemes and are very robust to phase and frequency instabilities.
On interleaved, differentially encoded convolutional codes
 IEEE Trans. Inform. Theory
, 1999
"... We study a serially interleaved concatenated code construction, where the outer code is a standard convolutional code, and the inner code is a recursive convolutional code of rate 1. Focus is put on the ubiquitous inner differential encoder (used in particular to resolve phase ambiguities), double d ..."
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Cited by 17 (1 self)
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We study a serially interleaved concatenated code construction, where the outer code is a standard convolutional code, and the inner code is a recursive convolutional code of rate 1. Focus is put on the ubiquitous inner differential encoder (used in particular to resolve phase ambiguities), double differential encoder (used to resolve both phase and frequency ambiguities), and another rate 1 recursive convolutional code of memory 2. We substantiate analytically the rather surprising result, that the error probabilities corresponding to a maximum likelihood (ML) coherently detected antipodal modulation over the AWGN channel, for this construction are advantageous as compared to the standalone outer convolutional code. This is inspite of the fact that the inner code is of rate 1. The analysis is based on the tangential sphere upper bound of a ML decoder, incorporating the ensemble weight distribution (WD) of the concatenated code, where the ensemble is generated by all random and uniform interleavers. This surprising result is attributed to the WD thinning observed for the concatenated scheme which shapes the WD of the outer convolutional code to resemble more closely the binomial distribution (typical of a fully random code of the same length and rate). This gain is maintained regardless of a