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Selected Areas in Communications, IEEE Journal on

Issue 6 • Date August 2009

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  • IEEE Journal on Selected Areas in Communications - Front cover

    Publication Year: 2009 , Page(s): c1
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  • IEEE communications society

    Publication Year: 2009 , Page(s): i - ii
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  • Guest editorial capacity approaching codes

    Publication Year: 2009 , Page(s): 825 - 830
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  • Geometrically-structured maximum-girth LDPC block and convolutional codes

    Publication Year: 2009 , Page(s): 831 - 845
    Cited by:  Papers (6)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (477 KB) |  | HTML iconHTML  

    Four classes of maximum-girth geometrically structured column-weight-two regular quasi-cyclic (QC) low-density parity-check (LDPC) codes are introduced. Two classes of these codes, referred to as Type-I and Type-II codes, are with row-weights 4 and 3, and maximum girths 16 and 24, respectively. The idea behind the construction of these two classes of codes, with rates at least 1/2 and 1/3, is slightly generalized to obtain two classes of variable-high-rate codes, referred to as Type-III1 and Type-III2 codes, with maximum girth 20 and 16, respectively. A low-complexity deterministic algorithm for constructing these four classes of codes is given. The algorithm generates maximum-girth Type-I and Type-II codes with almost arbitrary length eta not less than 216 and 243, respectively. The output of the algorithm substantially improves on some of the previously best known codes constructed using a randomized progressive edge-growth (RPEG) algorithm. For instance, we have rate-0.71 Type-III1 codes of lengths 308 and 728 with girths 10 and 12, respectively, versus the code lengths 385 and 840 obtained by the RPEG algorithm. Simulation results on AWGN channel confirm that, from BER performance perspective, the constructed LDPC codes are superior to the column-weight-two LDPC codes constructed by the previously reported methods. The generator matrix G(D) of the convolutional codes associated with Type-I and Type-II codes is given. The free distance dfree of such a convolutional code is equal to the minimum distance of the corresponding QC block code. View full abstract»

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  • Efficient encoding of QC-LDPC codes related to cyclic MDS codes

    Publication Year: 2009 , Page(s): 846 - 854
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (373 KB) |  | HTML iconHTML  

    In this paper, we present an efficient systematic encoding algorithm for quasi-cyclic (QC) low-density parity check (LDPC) codes that are related to cyclic maximum-distance separable (MDS) codes. The algorithm offers linear time complexity, and it can be easily implemented by using polynomial multiplication and division circuits. We show that the division polynomials can be completely characterized by their zeros and that the sum of the respective numbers of their zeros is equal to the parity-length of the codes. View full abstract»

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  • Instanton-based techniques for analysis and reduction of error floors of LDPC codes

    Publication Year: 2009 , Page(s): 855 - 865
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (975 KB) |  | HTML iconHTML  

    We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result in decoding failures. We show that the general idea and the respective optimization technique are applicable broadly to a variety of channels, discrete or continuous, and variety of sub-optimal decoders. Specifically, we consider: iterative belief propagation (BP) decoders, Gallager type decoders, and linear programming (LP) decoders performing over the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC). The instanton analysis suggests that the underlying topological structures of the most probable instanton of the same code but different channels and decoders are related to each other. Armed with this understanding of the graphical structure of the instanton and its relation to the decoding failures, we suggest a method to construct codes whose Tanner graphs are free of these structures, and thus have less significant error floors. View full abstract»

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  • Quasi-systematic doped LT codes

    Publication Year: 2009 , Page(s): 866 - 875
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (456 KB) |  | HTML iconHTML  

    We propose a family of binary erasure codes, namely, quasi-systematic doped Luby-Transform (QS-DLT) codes, that are rate-less, almost systematic, and universally capacity-achieving without the prior knowledge of channel erasure rate. The encoding and decoding complexities of QS-DLT codes are O(Klog(1/epsiv)), where K is the information length, and epsiv is the overhead. Stopping-set analysis is carried out to study the error-floor behavior of QS-DLT codes. Analysis and numerical results demonstrate that QS-DLT codes provide a low-complexity alternative to systematic Raptor codes with comparable performance. View full abstract»

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  • Capacity-approaching protograph codes

    Publication Year: 2009 , Page(s): 876 - 888
    Cited by:  Papers (35)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (728 KB) |  | HTML iconHTML  

    This paper discusses construction of protograph-based low-density parity-check (LDPC) codes. Emphasis is placed on protograph ensembles whose typical minimum distance grows linearly with block size. Asymptotic performance analysis for both weight enumeration and iterative decoding threshold determination is provided and applied to a series of code constructions. Construction techniques that yield both low thresholds and linear minimum distance growth are introduced by way of example throughout. The paper also examines implementation strategies for high throughput decoding derived from first principles of belief propagation on bipartite graphs. View full abstract»

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  • Design and analysis of E2RC codes

    Publication Year: 2009 , Page(s): 889 - 898
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (592 KB) |  | HTML iconHTML  

    We consider the design and analysis of the efficiently-encodable rate-compatible (E2RC) irregular LDPC codes proposed in previous work. In this work we introduce semi-structured E2RC-like codes and protograph E2RC codes. EXIT chart based methods are developed for the design of semi-structured E2RC-like codes that allow us to determine near-optimal degree distributions for the systematic part of the code while taking into account the structure of the deterministic parity part, thus resolving one of the open issues in the original construction. We develop a fast EXIT function computation method that does not rely on Monte-Carlo simulations and can be used in other scenarios as well. Our approach allows us to jointly optimize code performance across the range of rates under puncturing. We then consider protograph E2RC codes (that have a protograph representation) and propose rules for designing a family of rate-compatible punctured protographs with low thresholds. For both the semi-structured and protograph E2RC families we obtain codes whose gap to capacity is at most 0.3 dB across the range of rates when the maximum variable node degree is twenty. View full abstract»

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  • On asymptotic ensemble weight enumerators of LDPC-like codes

    Publication Year: 2009 , Page(s): 899 - 907
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (330 KB) |  | HTML iconHTML  

    For LDPC-like codes such as LDPC, GLDPC, and DGLDPC codes, it is well known that the error floor can be caused by the codewords of small weights or stopping sets of small sizes. In this paper, we investigate the computation of asymptotic weight enumerators such that it becomes a convenient tool to determine a good distribution of code ensembles. In addition, by analyzing the first order approximation, we derive a condition to obtain a negative asymptotic growth rate of the codewords of small linear-sized weights, which is an important constraint for distribution optimization. Also the weight enumerators of turbo and repeat-accumulate codes are investigated. Furthermore, we extend our results to nonbinary DGLDPC codes. Generalization to N-layer and convolutional code based LDPC-like codes are also developed. View full abstract»

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  • Predicting error floors of structured LDPC codes: deterministic bounds and estimates

    Publication Year: 2009 , Page(s): 908 - 917
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1670 KB) |  | HTML iconHTML  

    The error-correcting performance of low-density parity check (LDPC) codes, when decoded using practical iterative decoding algorithms, is known to be close to Shannon limits for codes with suitably large blocklengths. A substantial limitation to the use of finite-length LDPC codes is the presence of an error floor in the low frame error rate (FER) region. This paper develops a deterministic method of predicting error floors, based on high signal-to-noise ratio (SNR) asymptotics, applied to absorbing sets within structured LDPC codes. The approach is illustrated using a class of array-based LDPC codes, taken as exemplars of high-performance structured LDPC codes. The results are in very good agreement with a stochastic method based on importance sampling which, in turn, matches the hardware-based experimental results. The importance sampling scheme uses a mean-shifted version of the original Gaussian density, appropriately centered between a codeword and a dominant absorbing set, to produce an unbiased estimator of the FER with substantial computational savings over a standard Monte Carlo estimator. Our deterministic estimates are guaranteed to be a lower bound to the error probability in the high SNR regime, and extend the prediction of the error probability to as low as 10-30. By adopting a channel-independent viewpoint, the usefulness of these results is demonstrated for both the standard Gaussian channel and a channel with mixture noise. View full abstract»

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  • Finite-length scaling of turbo-like code ensembles on the binary erasure channel

    Publication Year: 2009 , Page(s): 918 - 927
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (581 KB) |  | HTML iconHTML  

    A possibility of estimating the finite-length performance of sparse-graph code ensembles gives two opportunities: to compare different codes of the same length in a context very close to real, practical applications and to perform the parameter optimization for a given code length [2]. We need a finite-length approximation that is valid for any code ensemble. The scaling approach seems to be a tool, general enough to provide such an approximation. However, the analytical derivation of parameters of the scaling approximation has been successful only for LDPC codes [1]; despite several attempts [25], [20], no such result was proposed for other code ensembles. In this paper, we focus on the finite-length performance of turbo-like codes, by applying the scaling approach to this case. In particular, by assuming the transmission over the binary erasure channel, we conjecture the scaling law and derive its scaling parameter. As examples, we present the performance estimation for Repeat-Accumulate codes [11], parallel turbo codes [8] and TLDPC codes [5], in all cases matching well the numerical results. View full abstract»

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  • Good concatenated code ensembles for the binary erasure channel

    Publication Year: 2009 , Page(s): 928 - 943
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (877 KB) |  | HTML iconHTML  

    In this work, we give good concatenated code ensembles for the binary erasure channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code ensembles formed by the serial concatenation of a repetition code with multiple accumulators, and the hybrid concatenated code (HCC) ensembles recently introduced by Koller et al. (5th Int. Symp. on Turbo Codes & Rel. Topics, Lausanne, Switzerland) consisting of an outer multiple parallel concatenated code serially concatenated with an inner accumulator. We introduce stopping sets for iterative constituent code oriented decoding using maximum a posteriori erasure correction in the constituent codes. We then analyze the asymptotic stopping set distribution for RMA and HCC ensembles and show that their stopping distance hmin, defined as the size of the smallest nonempty stopping set, asymptotically grows linearly with the block length. Thus, these code ensembles are good for the BEC. It is shown that for RMA code ensembles, contrary to the asymptotic minimum distance dmin, whose growth rate coefficient increases with the number of accumulate codes, the hmin growth rate coefficient diminishes with the number of accumulators. We also consider random puncturing of RMA code ensembles and show that for sufficiently high code rates, the asymptotic hmin does not grow linearly with the block length, contrary to the asymptotic dmin, whose growth rate coefficient approaches the Gilbert-Varshamov bound as the rate increases. Finally, we give iterative decoding thresholds for the different code ensembles to compare the convergence properties. View full abstract»

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  • Analysis and design of punctured rate-1/2 turbo codes exhibiting low error floors

    Publication Year: 2009 , Page(s): 944 - 953
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (585 KB) |  | HTML iconHTML  

    The objective of this paper is two-fold. Initially, we present an analytic technique to rapidly evaluate an approximation to the union bound on the bit error probability of turbo codes. This technique exploits the most significant terms of the union bound, which can be calculated straightforwardly by considering the properties of the constituent convolutional encoders. Subsequently, we use the bound approximation to demonstrate that specific punctured rate-1/2 turbo codes can achieve a lower error floor than that of their rate-1/3 parent codes. In particular, we propose pseudo-random puncturing as a means of improving the bandwidth efficiency of a turbo code and simultaneously lowering its error floor. View full abstract»

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  • Turbo coded multiple-antenna systems for near-capacity performance

    Publication Year: 2009 , Page(s): 954 - 964
    Cited by:  Papers (5)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (993 KB) |  | HTML iconHTML  

    For a turbo coded BLAST (Bell LAbs Space-Time architecture) system with Nt transmit antennas and Nr receive antennas, there is a significant gap between its detection threshold and the capacity in case Nt > Nr. In this paper, we show that by introducing a convolutional interleaver with block delay between the BLAST mapper and the turbo encoder, the threshold can be improved. Near-capacity thresholds can be achieved for some cases. To take advantage of the low detector complexity in Alamouti STBC (space-time block code), we also investigate a STBC system, which is the concatenation of the Alamouti STBC with a turbo trellis coded modulation. By using a proper labelling and adding a convolutional interleaver with block delay to such a STBC system, we achieve both lower error floors and lower thresholds. View full abstract»

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  • Design of rate-compatible structured LDPC codes for hybrid ARQ applications

    Publication Year: 2009 , Page(s): 965 - 973
    Cited by:  Papers (12)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (872 KB) |  | HTML iconHTML  

    In this paper, families of rate-compatible protograph-based LDPC codes that are suitable for incrementalredundancy hybrid ARQ applications are constructed. A systematic technique to construct low-rate base codes from a higher rate code is presented. The base codes are designed to be robust against erasures while having a good performance on error channels. A progressive node puncturing algorithm is devised to construct a family of higher rate codes from the base code. The performance of this puncturing algorithm is compared to other puncturing schemes. Using the techniques in this paper, one can construct a rate-compatible family of codes with rates ranging from 0.1 to 0.9 that are within 1 dB from the channel capacity and have good error floors. View full abstract»

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  • Capacity-achieving codes for finite-state channels with maximum-likelihood decoding

    Publication Year: 2009 , Page(s): 974 - 984
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (367 KB) |  | HTML iconHTML  

    Codes on sparse graphs have been shown to achieve remarkable performance in point-to-point channels with low decoding complexity. Most of the results in this area are based on experimental evidence and/or approximate analysis. The question of whether codes on sparse graphs can achieve the capacity of noisy channels with iterative decoding is still open, and has only been conclusively and positively answered for the binary erasure channel. On the other hand, codes on sparse graphs have been proven to achieve the capacity of memoryless, binary-input, output-symmetric channels with finite graphical complexity per information bit when maximum likelihood (ML) decoding is performed. In this paper, we consider transmission over finite-state channels (FSCs). We derive upper bounds on the average error probability of code ensembles with ML decoding. Based on these bounds we show that codes on sparse graphs can achieve the symmetric information rate (SIR) of FSCs, which is the maximum achievable rate with independently and uniformly distributed input sequences. In order to achieve rates beyond the SIR, we consider a simple quantization scheme that when applied to ensembles of codes on sparse graphs induces a Markov distribution on the transmitted sequence. By deriving average error probability bounds for these quantized code ensembles, we prove that they can achieve the information rates corresponding to the induced Markov distribution, and thus approach the FSC capacity. View full abstract»

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  • High-throughput layered decoder implementation for quasi-cyclic LDPC codes

    Publication Year: 2009 , Page(s): 985 - 994
    Cited by:  Papers (20)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (925 KB) |  | HTML iconHTML  

    This paper presents a high-throughput decoder design for the Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes. Two new techniques are proposed, including parallel layered decoding architecture (PLDA) and critical path splitting. PLDA enables parallel processing for all layers by establishing dedicated message passing paths among them. The decoder avoids crossbar-based large interconnect network. Critical path splitting technique is based on articulate adjustment of the starting point of each layer to maximize the time intervals between adjacent layers, such that the critical path delay can be split into pipeline stages. Furthermore, min-sum and loosely coupled algorithms are employed for area efficiency. As a case study, a rate-1/2 2304-bit irregular LDPC decoder is implemented using ASIC design in 90 nm CMOS process. The decoder can achieve the maximum decoding throughput of 2.2 Gbps at 10 iterations. The operating frequency is 950 MHz after synthesis and the chip area is 2.9 mm2. View full abstract»

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  • Superposition coded modulation and iterative linear MMSE detection

    Publication Year: 2009 , Page(s): 995 - 1004
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1192 KB) |  | HTML iconHTML  

    We study superposition coded modulation (SCM) with iterative linear minimum-mean-square-error (LMMSE) detection. We show that SCM offers an attractive solution for highly complicated transmission environments with severe interference. We analyze the impact of signaling schemes on the performance of iterative LMMSE detection. We prove that among all possible signaling methods, SCM maximizes the output signal-to-noise/ interference ratio (SNIR) in the LMMSE estimates during iterative detection. Numerical examples are used to demonstrate that SCM outperforms other signaling methods when iterative LMMSE detection is applied to multi-user/multi-antenna/multipath channels. View full abstract»

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  • A cutting-plane method based on redundant rows for improving fractional distance

    Publication Year: 2009 , Page(s): 1005 - 1012
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (373 KB) |  | HTML iconHTML  

    Decoding performance of linear programming (LP) decoding is closely related to geometrical properties of a fundamental polytope: fractional distance, pseudo codeword, etc. In this paper, an idea of the cutting-plane method is employed to improve the fractional distance of a given binary parity-check matrix. The fractional distance is the minimum weight (with respect to lscr1-distance) of nonzero vertices of the fundamental polytope. The cutting polytope is defined based on redundant rows of the parity-check matrix. The redundant rows are codewords of the dual code not yet appearing as rows in the parity-check matrix. The cutting polytope plays a key role to eliminate unnecessary fractional vertices in the fundamental polytope. We propose a greedy algorithm and its efficient implementation based on the cutting-plane method. It has been confirmed that the fractional distance of some parity-check matrices are actually improved by using the algorithm. View full abstract»

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  • Convergence analysis of generalized serial message-passing schedules

    Publication Year: 2009 , Page(s): 1013 - 1024
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1576 KB) |  | HTML iconHTML  

    Schedule is the order of passing messages between vertices of the bipartite graph defining an LDPC code in the process of decoding. Schedules affect the rate of decoding convergence. New efficient generalized serial schedules are described and analyzed, exhibiting significantly faster convergence compared to previously known schedules. For the proposed schedules, combinatorial and probabilistic analysis is presented, explaining the fast convergence observed in simulations. Using it, LDPC ensembles for which significantly better convergence rates can be achieved are identified. Specific code constructions from lifted graphs are further proposed, efficiently supporting the schedules. Examples based on regular LDPC codes are provided, in which the schedules achieve convergence speedup factors of up to 6 in comparison with the flooding schedule. Higher speedup factors are predicted by the analysis for irregular codes. View full abstract»

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  • IEEE communications society 2009 board of governors

    Publication Year: 2009 , Page(s): c2
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    Freely Available from IEEE
  • [Back cover - table of contents continued from front cover]

    Publication Year: 2009 , Page(s): c3
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Aims & Scope

IEEE Journal on Selected Areas in Communications focuses on all telecommunications, including telephone, telegraphy, facsimile, and point-to-point television, by electromagnetic propagation.

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Meet Our Editors

Editor-in-Chief
Muriel Médard
MIT