tailieunhanh - Báo cáo hóa học: " Research Article Structured LDPC Codes over Integer Residue Rings"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Structured LDPC Codes over Integer Residue Rings | Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2008 Article ID 598401 9 pages doi 2008 598401 Research Article Structured LDPC Codes over Integer Residue Rings Elisa Mo and Marc A. Armand Department of Electrical and Computer Engineering National University of Singapore Singapore 117576 Correspondence should be addressed to Marc A. Armand eleama@ Received 31 October 2007 Revised 31 March 2008 Accepted 3 June 2008 Recommended by Jinhong Yuan This paper presents a new class of low-density parity-check LDPC codes over Z2a represented by regular structured Tanner graphs. These graphs are constructed using Latin squares defined over a multiplicative group of a Galois ring rather than a finite field. Our approach yields codes for a wide range of code rates and more importantly codes whose minimum pseudocodeword weights equal their minimum Hamming distances. Simulation studies show that these structured codes when transmitted using matched signal sets over an additive-white-Gaussian-noise channel can outperform their random counterparts of similar length and rate. Copyright 2008 E. Mo and MarcA. Armand. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION The study of nonbinary LDPC codes over GF was initiated by Davey and Mackay 1 . However the symbols of a nonbinary code over a finite field cannot be matched to any signal constellation. In other words it is not possible to obtain a geometrically uniform code wherein every codeword has the same error probability from a nonbinary finite field code. The subject of geometrically uniform codes has been well studied by various authors including Slepian 2 and Forney Jr. 3 . More recently Sridhara and Fuja 4 introduced geometrically uniform nonbinary LDPC codes over certain rings including .