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17
Asymptotic enumeration methods for analyzing LDPC codes
 IEEE Trans. Inform. Theory
, 2004
"... We show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of lowdensity paritycheck (LDPC) codes. In particular we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular LDPC code ense ..."
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Cited by 59 (2 self)
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We show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of lowdensity paritycheck (LDPC) codes. In particular we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular LDPC code ensembles. We then consider the binary erasure channel (BEC). Using these estimates we derive lower bounds on the error exponent, under iterative decoding, of LDPC codes used over the BEC. Both regular and irregular code structures are considered. These bounds are compared to the corresponding bounds when optimal (maximum likelihood) decoding is applied.
Design and analysis of nonbinary LDPC codes for arbitrary discretememoryless channels
 IEEE TRANS. INFORM. THEORY
, 2005
"... We present an analysis, under iterative decoding, of coset LDPC codes over GF(q), designed for use over arbitrary discretememoryless channels (particularly nonbinary and asymmetric channels). We use a randomcoset analysis to produce an effect that is similar to outputsymmetry with binary channels ..."
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Cited by 41 (0 self)
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We present an analysis, under iterative decoding, of coset LDPC codes over GF(q), designed for use over arbitrary discretememoryless channels (particularly nonbinary and asymmetric channels). We use a randomcoset analysis to produce an effect that is similar to outputsymmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) paritycheck matrix induces a permutationinvariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q − 1 dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop EXIT charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the AWGN channel, including results within 0.56 dB of the unconstrained Shannon limit (i.e. not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.
Analysis of lowdensity paritycheck codes for the GilbertElliott channel
 IEEE TRANS. INF. THEORY
, 2005
"... Density evolution analysis of lowdensity paritycheck (LDPC) codes in memoryless channels is extended to the Gilbert–Elliott (GE) channel, which is a special case of a large class of channels with hidden Markov memory. In a procedure referred to as estimation decoding, the sum–product algorithm (S ..."
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Cited by 34 (8 self)
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Density evolution analysis of lowdensity paritycheck (LDPC) codes in memoryless channels is extended to the Gilbert–Elliott (GE) channel, which is a special case of a large class of channels with hidden Markov memory. In a procedure referred to as estimation decoding, the sum–product algorithm (SPA) is used to perform LDPC decoding jointly with channelstate detection. Density evolution results show (and simulation results confirm) that such decoders provide a significantly enlarged region of successful decoding within the GE parameter space, compared with decoders that do not exploit the channel memory. By considering a variety of ways in which a GE channel may be degraded, it is shown how knowledge of the decoding behavior at a single point of the GE parameter space may be extended to a larger region within the space, thereby mitigating the large complexity needed in using density evolution to explore the parameter space pointbypoint. Using the GE channel as a straightforward example, we conclude that analysis of estimation decoding for LDPC codes is feasible in channels with memory, and that such analysis shows large potential gains.
Towards a communicationtheoretic understanding of systemlevel power consumption
"... Traditional communication theory focuses on minimizing transmit power. Increasingly, however, communication links are operating at shorter ranges where transmit power can drop below the power consumed in decoding. In this paper, we model the required decoding power and investigate the minimization o ..."
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Cited by 28 (6 self)
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Traditional communication theory focuses on minimizing transmit power. Increasingly, however, communication links are operating at shorter ranges where transmit power can drop below the power consumed in decoding. In this paper, we model the required decoding power and investigate the minimization of total system power from two complementary perspectives. First, an isolated pointtopoint link is considered. Using new lower bounds on the complexity of messagepassing decoding, lower bounds are derived on decoding power. These bounds show that 1) there is a fundamental tradeoff between transmit and decoding power; 2) unlike the implications of the traditional “waterfall ” curve which focuses on transmit power, the total power must diverge to infinity as error probability goes to zero; 3) Regular LDPCs, and not their capacityachieving counterparts, can be shown to be power order optimal in some cases; and 4) the optimizing transmit power is bounded away from the Shannon limit. Second, we consider a collection of pointtopoint links. When systems both generate and face interference, coding allows a system to support a higher density of transmitterreceiver pairs (assuming interference is treated as noise). However, at low densities, uncoded transmission may be more power efficient in some cases. I.
Upper Bounds on the Rate of LDPC Codes
 IEEE Trans. on Information Theory
, 2002
"... We derive upper bounds on the rate of low density parity check (LDPC) codes for which reliable communication is achievable. We rst generalize Gallager's bound to a general binaryinput symmetricoutput channel. We then proceed to derive tighter bounds. We also derive upper bounds on the rate as ..."
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Cited by 27 (2 self)
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We derive upper bounds on the rate of low density parity check (LDPC) codes for which reliable communication is achievable. We rst generalize Gallager's bound to a general binaryinput symmetricoutput channel. We then proceed to derive tighter bounds. We also derive upper bounds on the rate as a function of the minimum distance of the code. We consider both individual codes and ensembles of codes. Index Terms  Low density parity check (LDPC) codes, iterative decoding, maximumlikelihood decoding, error probability, minimum distance. I
An Efficient MaximumLikelihood Decoding of LDPC Codes Over the Binary Erasure Channel
 IEEE Trans. Inform. Theory
, 2004
"... Abstract — We propose an efficient maximum likelihood decoding algorithm for decoding lowdensity paritycheck codes over the binary erasure channel. We also analyze the computational complexity of the proposed algorithm. Index Terms — Lowdensity paritycheck (LDPC) codes, Binary erasure channel (B ..."
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Cited by 23 (0 self)
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Abstract — We propose an efficient maximum likelihood decoding algorithm for decoding lowdensity paritycheck codes over the binary erasure channel. We also analyze the computational complexity of the proposed algorithm. Index Terms — Lowdensity paritycheck (LDPC) codes, Binary erasure channel (BEC), Iterative decoding, Maximum likelihood (ML) decoding. I.
Finitedimensional bounds on Zm and binary LDPC codes with beliefpropagation decoders
 IEEE Trans. on Information Theory
, 2007
"... This paper focuses on finitedimensional upper and lower bounds on decodable thresholds of Zm and binary LDPC codes, assuming belief propagation decoding on memoryless channels. Two noise measures will be considered: the Bhattacharyya noise parameter and the soft bit value for a MAP decoder on the u ..."
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Cited by 7 (1 self)
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This paper focuses on finitedimensional upper and lower bounds on decodable thresholds of Zm and binary LDPC codes, assuming belief propagation decoding on memoryless channels. Two noise measures will be considered: the Bhattacharyya noise parameter and the soft bit value for a MAP decoder on the uncoded channel. For Zm LDPC codes, an iterative mdimensional bound is derived for maryinput/symmetricoutput channels, which gives a sufficient stability condition for Zm LDPC codes and will be complemented by a matched necessary stability condition introduced herein. Applications to the coded modulations and to codes with nonequiprobable distributed codewords will also be discussed. For binary codes, two new lower bounds are provided for symmetric channels, including a twodimensional iterative bound and a onedimensional noniterative bound, the latter of which is the best known bound that is tight for BSCs. By adapting the reverse channel perspective, a pair of upper and lower bounds on the decodable Bhattacharyya noise parameter is derived for nonsymmetric channels, which coincides with the existing bound for symmetric channels.
On finitedimensional bounds for LDPClike codes with iterative decoding
 in Proc. Int’l Symp. Inform. Theory & its Applications
, 2004
"... This paper focuses on finitedimensional upper and lower bounds on decodable thresholds assuming iterative decoding. Two noise measures will be considered: the Bhattacharyya noise parameter, and the expected soft bit of the considered channel. An iterative mdimensional lower bound is derived for Zm ..."
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Cited by 6 (4 self)
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This paper focuses on finitedimensional upper and lower bounds on decodable thresholds assuming iterative decoding. Two noise measures will be considered: the Bhattacharyya noise parameter, and the expected soft bit of the considered channel. An iterative mdimensional lower bound is derived for Zm LDPC codes in symmetric channels, which gives a sufficient stability condition for Zm LDPC codes and will be complemented by a new necessary stability condition introduced herein. Two new lower bounds are provided for binaryinput/symmetricoutput channels, including a twodimensional iterative bound and a onedimensional noniterative bound, the latter of which is the best known bound that is tight for BSCs. A reverse channel perspective is then used to generalize existing bounds from binaryinput/symmetricoutput channels to binaryinput/nonsymmetricoutput channels. 1.
An MSEbased transfer chart for analyzing iterative decoding schemes using a Gaussian approximation
 IEEE Trans. Inf. Theory
, 2007
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