Asymptotic Spectra of Trapping Sets in Regular and Irregular LDPC Code Ensembles

Milenković, Olgica; Soljanin, Emina; Whiting, Philip

doi:10.1109/tit.2006.887060

Cited by 102 publications

(76 citation statements)

References 15 publications

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“…Trapping sets are defined in [32] and [33] as any lengthbit vector denoted by a pair ( , ), where is the Hamming weight of the bit vector and is the number of unsatisfied checks. An absorbing set could be understood as a special type of such trapping set where each variable node is connected to strictly more satisfied than unsatisfied checks.…”

Section: A Characterization Of Error Eventsmentioning

confidence: 99%

Design of LDPC decoders for improved low error rate performance: quantization and algorithm choices

Zhang¹,

Dolecek²,

Nikolić³

et al. 2009

IEEE Trans. Commun.

122

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Abstract-Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such a structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit-error rate (BER) region and provides statistics of the error traces, which illuminate the causes of the error floors of the (2048, 1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209, 1978) array-based LDPC code. Two classes of error events are observed: oscillatory behavior and convergence to a class of non-codewords, termed absorbing sets. The influence of absorbing sets can be exacerbated by message quantization and decoder implementation. In particular, quantization and the log-tanh function approximation in sum-product decoders strongly affect which absorbing sets dominate in the errorfloor region. We show that conventional sum-product decoder implementations of the (2209, 1978) array-based LDPC code allow low-weight absorbing sets to have a strong effect, and, as a result, elevate the error floor. Dually-quantized sum-product decoders and approximate sum-product decoders alleviate the effects of low-weight absorbing sets, thereby lowering the error floor.Index Terms-Low-density parity-check (LDPC) code, message-passing decoding, iterative decoder implementation, error floor, absorbing set.

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Section: A Characterization Of Error Eventsmentioning

confidence: 99%

Design of LDPC decoders for improved low error rate performance: quantization and algorithm choices

Zhang¹,

Dolecek²,

Nikolić³

et al. 2009

IEEE Trans. Commun.

122

View full text Add to dashboard Cite

show abstract

“…It was also observed that in the error-floor region, after running extensive Monte Carlo simulations, most of the error patterns correspond to the so-called elementary trapping sets [27], whose induced subgraphs have only degree-one and degree-two CNs. That is, for an elementary trapping set, the unsatisfied CNs are usually connected to the trapping set exactly once (there is one bit error per unsatisfied CN).…”

Section: Bi-mode Decodermentioning

confidence: 95%

LDPC decoder strategies for achieving low error floors

Han

Ryan

2008

2008 Information Theory and Applications Workshop

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Abstract-One of the most significant impediments to the use of LDPC codes in many communication and storage systems is the error-rate floor phenomenon associated with their iterative decoders. The error floor has been attributed to certain subgraphs of an LDPC code's Tanner graph induced by so-called trapping sets. We show in this paper that once we identify the trapping sets of an LDPC code of interest, a sum-product algorithm (SPA) decoder can be custom-designed to yield floors that are orders of magnitude lower than the conventional SPA decoder. We present three classes of such decoders: (1) a bi-mode decoder, (2) a bit-pinning decoder which utilizes one or more outer algebraic codes, and (3) three generalized-LDPC decoders. We demonstrate the effectiveness of these decoders for two codes, the rate-1/2 (2640,1320) Margulis code which is notorious for its floors and a rate-0.3 (640,192) quasi-cyclic code which has been devised for this study. Although the paper focuses on these two codes, the decoder design techniques presented are fully generalizable to any LDPC code.

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“…They correspond to specific topological structures which characterize the behavior of the algorithm when it does not converge to a codeword. A fully absorbing set is a special type of trapping sets [24][32] [33], and is a fixed point of the Gallager B decoding algorithm [34]. For instance, if the all zero codeword is sent and the bits corresponding to the variables of the absorbing set are erroneous ('1' instead of '0'), the decoder will not be able to correct them and thus will not converge.…”

Section: Absorbing Setsmentioning

confidence: 99%

Selection of Parity Check Equations For the Iterative Message-Passing Detection of M-Sequences

Noes

Savin

Ros

et al. 2017

IEEE Trans. Commun.

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Abstract-We consider the joint detection and decoding of msequences. The receiver has to decide whether an m-sequence is received and possibly to decode its initial state. To do so, it implements an iterative message-passing decoding algorithm that operates on a parity check matrix, built upon a number of reference parity-check equations satisfied by the m-sequence. This matrix concatenates several elementary parity check matrices which are derived from reference equations. Unlike the conventional decoding case, the detection problem imposes to consider false alarms that may occur when the decoder is only fed with noise. While absorbing sets are known to be responsible for the error floor phenomenon of iterative message-passing decoders, we show that they may have a beneficial effect on the detection performance, in that they may prevent the decoder to produce false alarms. We further compute the number of hybrid cycles of length 6 and 8 in the Tanner graph of the decoder and use the minimization of this number as criterion to derive an algorithm for selecting the reference parity check equations. This algorithm was found to be efficient for minimizing the probability of false alarm and decreases also the probability of wrong detection in the very small SNR region. This has been achieved at the cost of a reduction of the probability of correct detection.

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Asymptotic Spectra of Trapping Sets in Regular and Irregular LDPC Code Ensembles

Cited by 102 publications

References 15 publications

Design of LDPC decoders for improved low error rate performance: quantization and algorithm choices

Design of LDPC decoders for improved low error rate performance: quantization and algorithm choices

LDPC decoder strategies for achieving low error floors

Selection of Parity Check Equations For the Iterative Message-Passing Detection of M-Sequences

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