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610
Turbo decoding as an instance of Pearl’s belief propagation algorithm
- IEEE Journal on Selected Areas in Communications
, 1998
"... Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pear ..."
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Cited by 404 (16 self)
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Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pearl’s belief propagation algorithm. We shall see that if Pearl’s algorithm is applied to the “belief network ” of a parallel concatenation of two or more codes, the turbo decoding algorithm immediately results. Unfortunately, however, this belief diagram has loops, and Pearl only proved that his algorithm works when there are no loops, so an explanation of the excellent experimental performance of turbo decoding is still lacking. However, we shall also show that Pearl’s algorithm can be used to routinely derive previously known iterative, but suboptimal, decoding algorithms for a number of other error-control systems, including Gallager’s
Achieving near-capacity on a multiple-antenna channel
- IEEE Trans. Commun
, 2003
"... Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve near-capacity on a single-antenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve nea ..."
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Cited by 402 (2 self)
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Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve near-capacity on a single-antenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve near-capacity on a multiple-antenna system where the receiver knows the channel. Combining iterative processing with multiple-antenna channels is particularly challenging because the channel capacities can be a factor of ten or more higher than their single-antenna counterparts. Using a “list ” version of the sphere decoder, we provide a simple method to iteratively detect and decode any linear space-time mapping combined with any channel code that can be decoded using so-called “soft ” inputs and outputs. We exemplify our technique by directly transmitting symbols that are coded with a channel code; we show that iterative processing with even this simple scheme can achieve near-capacity. We consider both simple convolutional and powerful turbo channel codes and show that excellent performance at very high data rates can be attained with either. We compare our simulation results with Shannon capacity limits for ergodic multiple-antenna channel. Index Terms—Wireless communications, BLAST, turbo codes, transmit diversity, receive diversity, fading channels, sphere decoding, soft-in/soft-out, concatenated codes 1
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 372 (32 self)
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A serially concatenated code with an interleaver consists of the cascade of an outer code...
On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit
- IEEE COMMUNICATIONS LETTERS
, 2001
"... We develop improved algorithms to construct good low-density parity-check codes that approach the Shannon limit very closely. For rate 1/2, the best code found has a threshold within 0.0045 dB of the Shannon limit of the binary-input additive white Gaussian noise channel. Simulation results with a ..."
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Cited by 306 (6 self)
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We develop improved algorithms to construct good low-density parity-check codes that approach the Shannon limit very closely. For rate 1/2, the best code found has a threshold within 0.0045 dB of the Shannon limit of the binary-input additive white Gaussian noise channel. Simulation results with a somewhat simpler code show that we can achieve within 0.04 dB of the Shannon limit at a bit error rate of 10 T using a block length of 10 U.
Applications of Error-Control Coding
, 1998
"... An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video t ..."
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Cited by 276 (0 self)
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An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video transmission. Examples, both historical and current, are given that typify the different approaches used in each application area. Although no attempt is made to be comprehensive in our coverage, the examples chosen clearly illustrate the richness, variety, and importance of error-control coding methods in modern digital applications.
Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation
- IEEE TRANS. INFORM. THEORY
, 2001
"... Density evolution is an algorithm for computing the capacity of low-density parity-check (LDPC) codes under messagepassing decoding. For memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels and sum-product decoders, we use a Gaussian approximation for message densi ..."
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Cited by 244 (2 self)
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Density evolution is an algorithm for computing the capacity of low-density parity-check (LDPC) codes under messagepassing decoding. For memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels and sum-product decoders, we use a Gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm. We convert the infinite-dimensional problem of iteratively calculating message densities, which is needed to find the exact threshold, to a one-dimensional problem of updating means of Gaussian densities. This simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better, but also makes it easier to design good irregular LDPC codes for AWGN channels. For various regular LDPC codes we have examined, thresholds can be estimated within 0.1 dB of the exact value. For rates between 0.5 and 0.9, codes designed using the Gaussian approximation perform within 0.02 dB of the best performing codes found so far by using density evolution when the maximum variable degree is IH. We show that by using the Gaussian approximation, we can visualize the sum-product decoding algorithm. We also show that the optimization of degree distributions can be understood and done graphically using the visualization.
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.
Low-density parity-check codes based on finite geometries: A rediscovery and new results
- IEEE Trans. Inform. Theory
, 2001
"... This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and thei ..."
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Cited by 186 (8 self)
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This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner graphs have girth T. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
Extrinsic Information Transfer Functions: A Model and Two Properties,”
- in Proc. Conference on Information Sciences and Systems (CISS),
, 2002
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Irregular Repeat-Accumulate Codes
, 2000
"... In this paper we will introduce an ensemble of codes called irregular repeat-accumulate (IRA) codes. IRA codes are a generalization of the repeat-accumulate codes introduced in [1], and as such have a natural linear time encoding algorithm. We shall prove that on the binary erasure channel, IRA code ..."
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Cited by 151 (1 self)
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In this paper we will introduce an ensemble of codes called irregular repeat-accumulate (IRA) codes. IRA codes are a generalization of the repeat-accumulate codes introduced in [1], and as such have a natural linear time encoding algorithm. We shall prove that on the binary erasure channel, IRA codes can be decoded reliably in linear time, using iterative sum-product decoding,a# ra#SJ a#SJ8T a#SJ8 close tocha#T36 ca pa#J464 Asimila# resulta#u ea#S to be true on the AWGN channel, although we have no proof of this. We illustrate our results with numerical and experimental examples.
