On Minimal Pseudo-Codewords of Tanner Graphs from Projective Planes
نویسندگان
چکیده
We would like to better understand the fundamental cone of Tanner graphs derived from finite projective planes. Towards this goal, we discuss bounds on the AWGNC and BSC pseudo-weight of minimal pseudo-codewords of such Tanner graphs, on one hand, and study the structure of minimal pseudo-codewords, on the other.
منابع مشابه
Bounds on the Pseudo-Weight of Minimal Pseudo-Codewords of Projective Geometry Codes
In this paper we focus our attention on a family of finite geometry codes, called type-I projective geometry low-density parity-check (PGLDPC) codes, that are constructed based on the projective planes PG(2, q). In particular, we study their minimal codewords and pseudo-codewords, as it is known that these vectors characterize completely the code performance under maximum-likelihood decoding an...
متن کاملGraph-covers and iterative decoding of finite length codes
Codewords in finite covers of a Tanner graph G are characterized. Since iterative, locally operating decoding algorithms cannot distinguish the underlying graph G from any covering graph, these codewords, dubbed pseudo-codewords are directly responible for sub-optimal behavior of iterative decoding algorithms. We give a simple characterization of pseudocodewords from finite covers and show that...
متن کاملSmall weight codewords in the codes arising from Desarguesian projective planes
We study codewords of small weight in the codes arising from Desarguesian projective planes. We first of all improve the results of K. Chouinard on codewords of small weight in the codes arising from PG(2, p), p prime. Chouinard characterized all the codewords up to weight 2p in these codes. Using a particular basis for this code, described by Moorhouse, we characterize all the codewords of wei...
متن کاملOn Low Weight Codewords of Generalized Affine and Projective Reed - Muller Codes ( Extended abstract )
We propose new results on low weight codewords of affine and projective generalized Reed-Muller codes. In the affine case we give some results on codewords that cannot reach the second weight also called the next to minimal distance. In the projective case the second distance of generalized Reed-Muller codes is estimated, namely a lower bound and an upper bound of this weight are given.
متن کاملBlocking sets in finite projective spaces and coding theory
Preface The book in front of you represents my work as a PhD student. Using the word 'work' in this context is not really appropriate. During the past three years, I never had the feeling to 'work', but rather to play around with various structures, to have fun trying to prove theorems and to enjoy discovering just a tiny bit of the enormous mathematical world. This thesis is a structured way o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/cs/0510043 شماره
صفحات -
تاریخ انتشار 2005