In this paper we propose a new design methodology targeted for core-based designs using parameterized macrocells (PMC’s). This methodology provides the flexibility for instance-based cores to be easily customized for application requirements. By using few scaling parameters to characterize a PMC, a macrocell can be instantiated in virtually any size depending on the required performance. Moreov...

We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn based on a finite-length scaling result to model large scale erasures and a union bound involving minimal stopping sets to take into account small error events. We show that the performances of optimize...

A method to construct girth-12 (3,L) quasi-cyclic lowdensity parity-check (QC-LDPC) codes with all lengths larger than a certain given number is proposed, via a given girth-12 code subjected to some constraints. The lengths of these codes can be arbitrary integers of the form LP, provided that P is larger than a tight lower bound determined by the maximal element within the exponent matrix of t...

We derive the density evolution equations for non-binary low-density parity-check (LDPC) ensembles when transmission takes place over the binary erasure channel. We introduce ensembles defined with respect to the general linear group over the binary field. For these ensembles the density evolution equations can be written compactly. The density evolution for the general linear group helps us in...

In this paper three outer bounds on the storage-repair bandwidth (S-RB) tradeoff of regenerating codes having parameter set {(n, k, d), (α, β)} under the exact-repair (ER) setting are presented. The tradeoff under the functionalrepair (FR) setting was settled in the seminal work of Dimakis et al. that introduced the framework of regenerating codes as well as a subsequent paper by Wu. While it i...

This paper extends the class of low-density paritycheck (LDPC) codes that can be algebraically constructed. We present regular LDPC codes based on resolvable Steiner 2-designs which have Tanner graphs free of four-cycles. The resulting codes are -regular or -regular for any value of and for a flexible choice of code lengths.

We construct various classes of low-density parity-check codes using point-line incidence structures in the classical projective plane PG(2, q). Each incidence structure is based on the various point classes (internal, external) and line classes (skew, tangent, secant) created by the geometry of a conic in the plane. For each class, we prove various properties about dimension and minimum distan...

In this paper we describe how to use special induced subgraphs of generalized m-gons to obtain the LDPC error correcting codes. We compare the properties of codes related to the affine parts of q-regular generalised 6-gons with the properties of known LDPC codes corresponding to the graphs D(5, q).

صلاخلا ــ ة : مت ةقرولا هذه يف ءاشنإ يف هدعاسملل مدقتم ماظن بناوج ذيفنتو ميمصت ضرع قتو و مي ءادأ حيحصت تارفش لأا ءاطخ ةليلق لا ةناتم ، ةينبم ىلع ءوفاكتلا رايتخا . موقي امه نيتيسيئر نيتفيظوب ةساردلا هذه يف مدقتملا ماظنلا : 1 ادأ باسحل ةيزاوتملا هاآاحملا ء تارفش حيحصت لأا ءاطخ ةليلق نمزب ةفاثكلا ادج ريصق ةنراقم ةمظنأب ةاآاحملا ةدوجوملا . 2 ةليلق ءاطخلأا حيحصت تارفشو فعضلا قطانم صحف نع ة...