A link between quasi-cyclic codes and convolutional codes

Esmaeili, Morteza; Gulliver, T. Aaron; Secord, N.P.; Mahmoud, S.A.

doi:10.1109/18.651076

Cited by 50 publications

(45 citation statements)

References 7 publications

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“…We begin this section by presenting an important link between QC block codes and convolutional codes that was first introduced in a paper by Tanner [9] and later extended in [10,11]. Similar to the connection between codewords in an unwrapped convolutional code and codewords in the underlying QC code, we will show that pseudo-codewords in the convolutional code give pseudocodewords when projected onto an underlying QC code.…”

Section: Pseudo-codewords For Qc and Convolutional Codesmentioning

confidence: 99%

“…Given the polynomial parity-check matrix of a QC-code, it is easy to see the natural connection that exists between quasi-cyclic codes and convolutional codes (see, e.g., [7,[9][10][11]17]). Briefly, with any QC block code C (r) QC of length r · L, given by a J × L polynomial matrix parity-check matrix H (r)…”

Section: Any Lengthmentioning

confidence: 99%

“…11 Using some more sophisticated lower bounds from [22], one can actually show that 7.19 ≤ w AWGNC,min p ≤ 9.09 for the length-40 code. This implies that the lower bounds for the length-80 and length-160 codes can also be tightened.…”

Section: Analysis Of Problematic Pseudo-codewords In Convolutional Codesmentioning

confidence: 99%

“…This link was first introduced in a paper by Tanner [9], where it was shown that the free distance of the unwrapped convolutional code, if non-trivial, cannot be smaller than the minimum distance of the underlying QC code. This idea was later extended in [10,11]. More recently, a construction for LDPC convolutional codes based on QC-LDPC block codes was introduced by Tanner et al [6,7], and a sliding-window MPI decoder was described.…”

Section: Introductionmentioning

confidence: 99%

“…The larger parameters of the other three codes allowed us to only lower and upper bound the minimum pseudo-weights. 11 The slight increase in the lower bound from 6, which is the minimum weight of the [20,7,6] code, to 6.05 and 6.20 shows that the minimum AWGNC pseudo-weight of the [20,7,6] code is less than that of the [40, 12,10], [80,22,10], and [160, 42, 10] codes. The slight increase in the lower bounds from 6.05 to 6.20 only suggests, but unfortunately gives no further evidence of, the existece of an increasing sequence of minimum AWGNC pseudo-weights for these codes, according to the results of this section.…”

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confidence: 99%

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Pseudocodeword Performance Analysis for LDPC Convolutional Codes

Smarandache

Pusane

Vontobel

et al. 2009

IEEE Trans. Inform. Theory

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Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of message-passing iterative decoding to be worse than that predicted by the maximum-likelihood decoding union bound.In this paper we address the pseudo-codeword problem from the convolutional-code perspective. In particular, we compare the performance of LDPC convolutional codes with that of their "wrapped" quasi-cyclic block versions and we show that the minimum pseudo-weight of an LDPC convolutional code is at least as large as the minimum pseudo-weight of an underlying quasi-cyclic code. This result, which parallels a well-known relationship between the minimum Hamming weight of convolutional codes and the minimum Hamming weight of their quasi-cyclic counterparts, is due to the fact that every pseudo-codeword in the convolutional code induces a pseudo-codeword in the block code with pseudo-weight no larger than that of the convolutional code's pseudo-codeword. This difference in the weight spectra leads to improved performance at low-to-moderate signal-to-noise ratios for the convolutional code, a conclusion supported by simulation results.

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Section: Pseudo-codewords For Qc and Convolutional Codesmentioning

confidence: 99%

Section: Any Lengthmentioning

confidence: 99%

Section: Analysis Of Problematic Pseudo-codewords In Convolutional Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Pseudocodeword Performance Analysis for LDPC Convolutional Codes

Smarandache

Pusane

Vontobel

et al. 2009

IEEE Trans. Inform. Theory

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References

2013

Wireless Communications

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DFT Domain Characterization of Quasi-Cyclic Codes

Dey

Rajan

2003

Applicable Algebra in Engineering, Communication and Computing

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Abstract. The transform domain characterization of linear cyclic codes over finite fields using Discrete Fourier Transform (DFT) over an appropriate extension field is well known. In this paper, we extend this transform domain characterization for linear quasi-cyclic codes over finite fields. We show how one can derive a lower bound on the minimum Hamming distance of a quasicyclic code and decode the code upto that minimum Hamming distance using this characterization.

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A link between quasi-cyclic codes and convolutional codes

Cited by 50 publications

References 7 publications

Pseudocodeword Performance Analysis for LDPC Convolutional Codes

Pseudocodeword Performance Analysis for LDPC Convolutional Codes

References

DFT Domain Characterization of Quasi-Cyclic Codes

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