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51
"Turbo equalization": principles and new results
, 2000
"... Since the invention of \turbo codes" by Berrou et al. in 1993, the \turbo principle" has been adapted to several communication problems such as \turbo equalization", \turbo trellis coded modulation", and iterative multi user detection. In this paper we study the \turbo equalizati ..."
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Cited by 274 (25 self)
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Since the invention of \turbo codes" by Berrou et al. in 1993, the \turbo principle" has been adapted to several communication problems such as \turbo equalization", \turbo trellis coded modulation", and iterative multi user detection. In this paper we study the \turbo equalization" approach, which can be applied to coded data transmission over channels with intersymbol interference (ISI). In the original system invented by Douillard et al., the data is protected by a convolutional code and a receiver consisting of two trellis-based detectors are used, one for the channel (the equalizer) and one for the code (the decoder). It has been shown that iterating equalization and decoding tasks can yield tremendous improvements in bit error rate (BER). We introduce new approaches to combining equalization based on linear ltering with the decoding. The result is a receiver that is capable of improving BER performance through iterations of equalization and decoding in a manner similar to turbo ...
Coded cooperation in wireless communications: space-time transmission and iterative decoding
- IEEE Trans. Signal Processing
, 2004
"... Abstract—When mobiles cannot support multiple antennas due to size or other constraints, conventional space-time coding cannot be used to provide uplink transmit diversity. To address this limitation, the concept of cooperation diversity has been introduced, where mobiles achieve uplink transmit div ..."
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Cited by 201 (3 self)
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Abstract—When mobiles cannot support multiple antennas due to size or other constraints, conventional space-time coding cannot be used to provide uplink transmit diversity. To address this limitation, the concept of cooperation diversity has been introduced, where mobiles achieve uplink transmit diversity by relaying each other’s messages. A particularly powerful variation of this principle is coded cooperation. Instead of a simple repetition relay, coded cooperation partitions the codewords of each mobile and transmits portions of each codeword through independent fading channels. This paper presents two extensions to the coded cooperation framework. First, we increase the diversity of coded cooperation in the fast-fading scenario via ideas borrowed from space-time codes. We calculate bounds for the bit- and block-error rates to demonstrate the resulting gains. Second, since cooperative coding contains two code components, it is natural to apply turbo codes to this framework. We investigate the application of turbo codes in coded cooperation and demonstrate the resulting gains via error bounds and simulations. Index Terms—Channel coding, diversity, space-time coding, user cooperation, wireless communications.
Analyzing the Turbo Decoder Using the Gaussian Approximation
- IEEE Trans. Inform. Theory
, 2001
"... In this paper, we introduce a simple technique for analyzing the iterative decoder that is broadly applicable to different classes of codes defined over graphs in certain fading as well as additive white Gaussian noise (AWGN) channels. The technique is based on the observation that the extrinsic inf ..."
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Cited by 91 (0 self)
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In this paper, we introduce a simple technique for analyzing the iterative decoder that is broadly applicable to different classes of codes defined over graphs in certain fading as well as additive white Gaussian noise (AWGN) channels. The technique is based on the observation that the extrinsic information from constituent maximum a posteriori (MAP) decoders is well approximated by Gaussian random variables when the inputs to the decoders are Gaussian. The independent Gaussian model implies the existence of an iterative decoder threshold that statistically characterizes the convergence of the iterative decoder. Specifically, the iterative decoder converges to zero probability of error as the number of iterations increases if and only if the channel 0 exceeds the threshold. Despite the idealization of the model and the simplicity of the analysis technique, the predicted threshold values are in excellent agreement with the waterfall regions observed experimentally in the literature when the codeword lengths are large. Examples are given for parallel concatenated convolutional codes, serially concatenated convolutional codes, and the generalized low-density parity-check (LDPC) codes of Gallager and Cheng--McEliece. Convergence-based design of asymmetric parallel concatenated convolutional codes (PCCC) is also discussed.
Turbo Encoder Design For Symbol Interleaved Parallel Concatenated Trellis Coded Modulation
, 2000
"... This paper addresses turbo-encoder design for coding with high spectral efficiency using parallel concatenated trellis coded modulation (PCTCM) and symbol interleaving. The turbo-encoder design involves the constituent encoder design and the interleaver design. The constituent encoders are optimized ..."
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Cited by 39 (8 self)
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This paper addresses turbo-encoder design for coding with high spectral efficiency using parallel concatenated trellis coded modulation (PCTCM) and symbol interleaving. The turbo-encoder design involves the constituent encoder design and the interleaver design. The constituent encoders are optimized for symbol-wise effective free distance, and each has an infinite symbol-wise 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 turbo-code constituent encoders for parallel concatenation and is not restricted to symbol interleaving. To lower the error floor, a new semi-random interleaver design criteria and a construction method extends the spread-interleaver 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.
Measures for Tracing Convergence of Iterative Decoding Algorithms
- in Proc. 4th IEEE/ITG Conf. on Source and Channel Coding
, 2002
"... We study the convergence behavior of turbo decoding, turbo equalization, and turbo bit-interleaved coded modulation in a unified framework, which is to regard all three principles as instances of iterative decoding of two serially concatenated codes. There is a collection of measures in the recent l ..."
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Cited by 36 (5 self)
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We study the convergence behavior of turbo decoding, turbo equalization, and turbo bit-interleaved coded modulation in a unified framework, which is to regard all three principles as instances of iterative decoding of two serially concatenated codes. There is a collection of measures in the recent literature, which trace the convergence of iterative decoding algorithms based on a single parameter. This parameter is assumed to completely describe the behavior of the soft-in soft-out decoders being part of the iterative algorithm. The measures observe different parameters and were originally applied to different types of decoders. In this paper, we show how six of those measures are related to each other and we compare their convergence prediction capability for the decoding principles mentioned above. We observed that two measures predict the convergence very well for all regarded decoding principles and others suffer from systematic prediction errors independent of the decoding principle.
Concatenated tree codes: A low complexity, high performance approach
- IEEE Trans. Inform. Theory
, 2001
"... Abstract—This paper is concerned with a family of concate-nated tree (CT) codes. CT codes are special low-density parity-check (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recur-sive/nonrecursive parts and multiple constituen ..."
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Cited by 27 (8 self)
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Abstract—This paper is concerned with a family of concate-nated tree (CT) codes. CT codes are special low-density parity-check (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recur-sive/nonrecursive parts and multiple constituent codes. CT codes are decodable by the belief-propagation algorithm. They combine many advantages of LDPC and turbo codes, such as low decoding cost, fast convergence speed, and good performance. Index Terms—Bayesian networks, graph codes, iterative de-coding, low-density parity-check (LDPC) codes, multidimensional concatenated codes, Tanner graphs, turbo codes. I.
Design of Fixed-Point Iterative Decoders for Concatenated Codes with Interleavers
- IEEE J. Select. Areas Commun
, 2001
"... We discuss the effects of quantization on the performance of the iterative decoding algorithm of concatenated codes with interleavers. Quantization refers here to the log-likelihood ratios coming from the soft demodulator and to the extrinsic informations passed from one stage of the decoder to the ..."
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Cited by 27 (1 self)
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We discuss the effects of quantization on the performance of the iterative decoding algorithm of concatenated codes with interleavers. Quantization refers here to the log-likelihood ratios coming from the soft demodulator and to the extrinsic informations passed from one stage of the decoder to the next. We discuss the cases of a single soft-input soft-output (SISO) module, in its additive log-likelihood version (L-SISO), performing sequentially all iterations (an implementation solution coping with medium-low data rate as compared with the hardware clock), and that of a pipelined structure in which a dedicated hardware is in charge of each SISO operation (an implementation suitable for high data rates). We give design rules in both cases, and show that a suitable rescaling of the extrinsic informations yields almost ideal performance with the same number of bits (five) representing both loglikelihood ratios and extrinsic information at any decoder stage.
Zigzag codes and concatenated zigzag codes
- IEEE Trans. Information Theory
, 2001
"... Abstract—This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, ba ..."
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Cited by 22 (6 self)
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Abstract—This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-APP (MLA) formulation, which requires a total of only 20 addition-equivalent operations per information bit, per iteration. Simulation of a rate-I P concatenated zigzag code with four constituent encoders with interleaver length TS SQT, yields a bit error rate (BER) of IH S at 0.9 dB and 1.4 dB away from the Shannon limit by optimal (APP) and low-cost suboptimal (MLA) decoders, respectively. A union bound analysis of the bit error probability of the zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also illustrated that, for a fixed interleaver size, the concatenated code has increased code potential as the number of constituent encoders increases. Finally, the analysis shows that zigzag codes with four or more constituent encoders have lower error floors than comparable turbo codes with two constituent encoders. Index Terms—Low-complexity decoding, parallel-concatenated codes, turbo codes, zigzag codes.
Bit-interleaved coded irregular modulation
, 2006
"... We consider a simple method to improve the adaptiveness and flexibility of bit-interleaved coded modulation (BICM) with different iterative decoding schemes for bandwidth efficient transmission. The basic idea is to apply different signal constellations and mappings within one code word. The combina ..."
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Cited by 14 (2 self)
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We consider a simple method to improve the adaptiveness and flexibility of bit-interleaved coded modulation (BICM) with different iterative decoding schemes for bandwidth efficient transmission. The basic idea is to apply different signal constellations and mappings within one code word. The combination of different signal constellations allows a fine adaptation of the data rate to the channel characteristics with the modulation, even if only the average channel state is known at the transmitter. For a receiver performing iterative demapping and decoding (so called BICM-ID system), the mixture of different mappings enables an optimisation of the iterative decoding process according to the system requirements. We call this approach bit-interleaved coded irregular modulation (BICIM) and analyse it using EXIT charts, capacity, error bounds and error rate simulations.
Adaptive concatenated coding for wireless realtime communications
, 2004
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