Construction of Low-Density Parity-Check Codes Based on Balanced Incomplete Block Designs

Ammar, Bassem; Honary, Bahram; Kou, Yu; Xu, Jun; Lin, Shu

doi:10.1109/tit.2004.828144

Cited by 127 publications

(68 citation statements)

References 33 publications

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“…(2)]). 1 For a block error probability of 10 −5 , the ISP bound provides gains of about 0.19 and 0.33 dB over the VF bound and gaps of 0.54 dB and 0.84 dB to the channel capacity for the AWGN and Rayleigh-fading channels, respectively. Also, for both channels the ISP bound is more informative than the CLB for block error probabilities below 10 −2 while the VF bound requires block error probabilities below 10 −3 to outperform the capacity limit.…”

Section: A M-ary Psk Block Coded Modulation Schemes Over Fully Intermentioning

confidence: 97%

“…Let P 1 and P 2 be probability assignments defined over a discrete set of sequences, let Y 1 and Y 2 = Y c 1 be (disjoint) decision regions for these sequences, let P e,1 and P e,2 be given by (1), and assume that P 1 (y)P 2 (y) ̸ = 0 for at least one sequence y. Then, for all s ∈ (0, 1)…”

Section: A the 1967 Sphere-packing Boundmentioning

confidence: 99%

“…In this section, we consider some practically decodable codes taken from some recent papers ( [1], [7], [8], [29], [31], [35]). We examine the gap between channel capacity and the Eb N0 for which they achieve a required block error probability as a function of the block length of these codes.…”

Section: Minimal Block Length As a Function Of Performancementioning

confidence: 99%

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An improved sphere-packing bound for finite-length codes over symmetric memoryless channels

Wiechman

Sason

2008

2008 Information Theory and Applications Workshop

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This paper derives an improved sphere-packing (ISP) bound for finite-length codes whose transmission takes place over symmetric memoryless channels, and which are decoded with an arbitrary list decoder. We first review classical results, i.e., the 1959 sphere-packing (SP59) bound of Shannon for the Gaussian channel, and the 1967 sphere-packing (SP67) bound of Shannon et al. for discrete memoryless channels. An improvement on the SP67 bound by Valembois and Fossorier is also discussed. These concepts are used for the derivation of a new lower bound on the error probability of list decoding (referred to as the ISP bound) which is uniformly tighter than the SP67 bound and its improved version. The ISP bound is applicable to symmetric memoryless channels, and some of its applications are exemplified. Its tightness under ML decoding is studied by comparing the ISP bound to previously reported upper and lower bounds on the ML decoding error probability, and also to computer simulations of iteratively decoded turbo-like codes. This paper also presents a technique which performs the entire calculation of the SP59 bound in the logarithmic domain, thus facilitating the exact calculation of this bound for moderate to large block lengths without the need for the asymptotic approximations provided by Shannon.

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Section: A M-ary Psk Block Coded Modulation Schemes Over Fully Intermentioning

confidence: 97%

Section: A the 1967 Sphere-packing Boundmentioning

confidence: 99%

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An improved sphere-packing bound for finite-length codes over symmetric memoryless channels

Wiechman

Sason

2008

2008 Information Theory and Applications Workshop

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“…In this letter, we focus our attention on the construction of QLDPC 42 codes from the family of classical row-circulant quasi-cyclic 43 (QC)-LDPC matrices, which are known to generate efficient 44 high-rate short and moderate-length QC-LDPC codes [5]- [7]. 45 The balanced incomplete block design (BIBD) [6] and the 46 cyclic difference family based LDPC code structures [7] [10], which do not exhibit the unavoidable 61 length-4 cycles in the binary formalism, Djordjevic [11] con-62 ceived the EA counterparts of the BIBD-based designs of 63 [9]. The resultant EA-QLDPC codes required a single pre-64 shared entangled qubit (ebit), which constitutes a valuable 65 resource, because maintaining a noiseless entangled state is 66 not a trivial task.…”

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confidence: 99%

Construction of Quantum LDPC Codes From Classical Row-Circulant QC-LDPCs

et al. 2016

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“…For a cyclic code, we have x = 1. For instance, each row of the PCM of a cyclic code, such as the balanced incomplete block design (BIBD)-based LDPC codes [91]- [93], is constituted by a cyclic shift of the previous row and the first row is the cyclic shift of the last row.…”

Section: A Encoding Of Low-density Parity-check Codesmentioning

confidence: 99%