2,422 research outputs found

    Finite Length Analysis of LDPC Codes

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    In this paper, we study the performance of finite-length LDPC codes in the waterfall region. We propose an algorithm to predict the error performance of finite-length LDPC codes over various binary memoryless channels. Through numerical results, we find that our technique gives better performance prediction compared to existing techniques.Comment: Submitted to WCNC 201

    Anatomy of F_D-Term Hybrid Inflation

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    We analyze the cosmological implications of F-term hybrid inflation with a subdominant Fayet--Iliopoulos D-term whose presence explicitly breaks a D-parity in the inflaton-waterfall sector. This scenario of inflation, which is called F_D-term hybrid model for brevity, can naturally predict lepton number violation at the electroweak scale, by tying the mu-parameter of the MSSM to an SO(3)-symmetric Majorana mass m_N, via the vacuum expectation value of the inflaton field. We show how a negative Hubble-induced mass term in a next-to-minimal extension of supergravity helps to accommodate the present CMB data and considerably weaken the strict constraints on the theoretical parameters, resulting from cosmic string effects on the power spectrum P_R. The usual gravitino overabundance constraint may be significantly relaxed in this model, once the enormous entropy release from the late decays of the ultraheavy waterfall gauge particles is properly considered. As the Universe enters a second thermalization phase involving a very low reheat temperature, which might be as low as about 0.3 TeV, thermal electroweak-scale resonant leptogenesis provides a viable mechanism for successful baryogenesis, while thermal right-handed sneutrinos emerge as new possible candidates for solving the cold dark matter problem. In addition, we discuss grand unified theory realizations of F_D-term hybrid inflation devoid of cosmic strings and monopoles, based on the complete breaking of an SU(2) subgroup. The F_D-term hybrid model offers rich particle-physics phenomenology, which could be probed at high-energy colliders, as well as in low-energy experiments of lepton flavour or number violation.Comment: 73 pages, LaTeX, minor rewordings, references added, to appear in JHE

    Analysis of Minimal LDPC Decoder System on a Chip Implementation

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    This paper presents a practical method of potential replacement of several different Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes with one, with the intention of saving as much memory as required to implement the LDPC encoder and decoder in a memory-constrained System on a Chip (SoC). The presented method requires only a very small modification of the existing encoder and decoder, making it suitable for utilization in a Software Defined Radio (SDR) platform. Besides the analysis of the effects of necessary variable-node value fixation during the Belief Propagation (BP) decoding algorithm, practical standard-defined code parameters are scrutinized in order to evaluate the feasibility of the proposed LDPC setup simplification. Finally, the error performance of the modified system structure is evaluated and compared with the original system structure by means of simulation

    Improved construction of irregular progressive edge-growth Tanner graphs

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    The progressive edge-growth algorithm is a well-known procedure to construct regular and irregular low-density parity-check codes. In this paper, we propose a modification of the original algorithm that improves the performance of these codes in the waterfall region when constructing codes complying with both, check and symbol node degree distributions. The proposed algorithm is thus interesting if a family of irregular codes with a complex check node degree distribution is used.Comment: 3 pages, 3 figure

    On a Low-Rate TLDPC Code Ensemble and the Necessary Condition on the Linear Minimum Distance for Sparse-Graph Codes

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    This paper addresses the issue of design of low-rate sparse-graph codes with linear minimum distance in the blocklength. First, we define a necessary condition which needs to be satisfied when the linear minimum distance is to be ensured. The condition is formulated in terms of degree-1 and degree-2 variable nodes and of low-weight codewords of the underlying code, and it generalizies results known for turbo codes [8] and LDPC codes. Then, we present a new ensemble of low-rate codes, which itself is a subclass of TLDPC codes [4], [5], and which is designed under this necessary condition. The asymptotic analysis of the ensemble shows that its iterative threshold is situated close to the Shannon limit. In addition to the linear minimum distance property, it has a simple structure and enjoys a low decoding complexity and a fast convergence.Comment: submitted to IEEE Trans. on Communication

    Decomposition Methods for Large Scale LP Decoding

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    When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at bit-error-rates comparable to state-of-the-art belief propagation (BP) decoders, but with significantly stronger theoretical guarantees. However, LP decoding when implemented with standard LP solvers does not easily scale to the block lengths of modern error correcting codes. In this paper we draw on decomposition methods from optimization theory, specifically the Alternating Directions Method of Multipliers (ADMM), to develop efficient distributed algorithms for LP decoding. The key enabling technical result is a "two-slice" characterization of the geometry of the parity polytope, which is the convex hull of all codewords of a single parity check code. This new characterization simplifies the representation of points in the polytope. Using this simplification, we develop an efficient algorithm for Euclidean norm projection onto the parity polytope. This projection is required by ADMM and allows us to use LP decoding, with all its theoretical guarantees, to decode large-scale error correcting codes efficiently. We present numerical results for LDPC codes of lengths more than 1000. The waterfall region of LP decoding is seen to initiate at a slightly higher signal-to-noise ratio than for sum-product BP, however an error floor is not observed for LP decoding, which is not the case for BP. Our implementation of LP decoding using ADMM executes as fast as our baseline sum-product BP decoder, is fully parallelizable, and can be seen to implement a type of message-passing with a particularly simple schedule.Comment: 35 pages, 11 figures. An early version of this work appeared at the 49th Annual Allerton Conference, September 2011. This version to appear in IEEE Transactions on Information Theor

    Finite Length Analysis of Irregular Repetition Slotted ALOHA in the Waterfall Region

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    A finite length analysis is introduced for irregular repetition slotted ALOHA (IRSA) that enables to accurately estimate its performance in the moderate-to-high packet loss probability regime, i.e., in the so-called waterfall region. The analysis is tailored to the collision channel model, which enables mapping the description of the successive interference cancellation process onto the iterative erasure decoding of low-density parity-check codes. The analysis provides accurate estimates of the packet loss probability of IRSA in the waterfall region as demonstrated by Monte Carlo simulations.Comment: Accepted for publication in the IEEE Communications Letter
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