Linear programming bounds on the degree distributions of LDPC code ensembles

Sason, Igal

doi:10.1109/isit.2009.5205866

Cited by 2 publications

(2 citation statements)

References 10 publications

(26 reference statements)

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“…These methods are heuristic approaches and they change the degree distribution of the nodes in the TG. It is known that the degree distribution affects the error correction capability of an LDPC code [8]. Hence, it is important to eliminate as few edges from TG as possible.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

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A Branch-and-Cut Algorithm to Design LDPC Codes without Small Cycles in Communication Systems

Kabakulak,

Taşkın,

Pusane

2017

Preprint

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In a digital communication system, information is sent from one place to another over a noisy communication channel using binary symbols (bits). Original information is encoded by adding redundant bits, which are then used by low-density parity-check (LDPC) codes to detect and correct errors that may have been introduced during transmission. Error correction capability of an LDPC code is severely degraded due to harmful structures such as small cycles in its bipartite graph representation known as Tanner graph (TG). We introduce an integer programming formulation to generate a TG for a given smallest cycle length. We propose a branch-and-cut algorithm for its solution and investigate structural properties of the problem to derive valid inequalities and variable fixing rules. We introduce a heuristic to obtain feasible solutions of the problem. Our computational experiments show that our algorithm can generate LDPC codes without small cycles in acceptable amount of time for practically relevant code lengths.

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Section: Introduction and Literature Reviewmentioning

confidence: 99%

“…Hence, it is important to eliminate as few edges from TG as possible. There are studies based on optimization techniques in the literature to find the best degree distribution of an irregular TG in terms of error correction capability [8,9].…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%