Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights

We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees $d=p^s$ and $d = p^s+1$, for $p$ a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for $p$-ary LDPC codes. Treating these codes as $p$-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite geometry LDPC codes where $p > 2$.Comment: Submitted to Transactions on Information Theory. Submitted: Oct. 1, 2005; Revised: May 1, 2006, Nov. 25, 200

Algebraic Design and Implementation of Protograph Codes using Non-Commuting Permutation Matrices

Random lifts of graphs, or equivalently, random permutation matrices, have been used to construct good families of codes known as protograph codes. An algebraic analog of this approach was recently presented using voltage graphs, and it was shown that many existing algebraic constructions of graph-based codes that use commuting permutation matrices may be seen as special cases of voltage graph codes. Voltage graphs are graphs that have an element of a finite group assigned to each edge, and the assignment determines a specific lift of the graph. In this paper we discuss how assignments of permutation group elements to the edges of a base graph affect the properties of the lifted graph and corresponding codes, and present a construction method of LDPC code ensembles based on noncommuting permutation matrices. We also show encoder and decoder implementations for these codes

Advances of the error-floor study of LDPC codes

低密度奇偶校验(ldPC)码在迭代译码下具有优越的性能,但是在高信噪比区呈现出误码平台(ErrOrflOOr)现象。综合分析了低密度奇偶校验码的误码平台现象及其产生的原因,重点描述了陷阱集及其对ldPC码误码平台的影响,同时阐述了估计和降低ldPC码误码平台的方法,并对今后ldPC码误码平台研究的重点和方向提出了展望。Low-density parity check(LDPC)codes are known to perform very well under iterative decoding.However,these codes often exhibit an error floor phenomenon in the high signal-to-noise(SNR)region.This paper provides a comprehensive description of the cause of the error floor phenomenon of LDPC codes.It presents a detailed description of the trapping sets,describes the methods to estimate and reduce the error floor of LDPC codes.Finally,it proposes the future development of the error floor of LDPC codes

Matlab Implementation of a Tornado Forward Error Correction Code

This research discusses how the design of a tornado forward error correcting channel code (FEC) sends digital data stream profiles to the receiver. The complete design was based on the Tornado channel code, binary phase shift keying (BPSK) modulation on a Gaussian channel (AWGN). The communication link was simulated by using Matlab, which shows the theoretical systems efficiency. Then the data stream was input as data to be simulated communication systems using Matlab. The purpose of this paper is to introduce the audience to a simulation technique that has been successfully used to determine how well a FEC expected to work when transferring digital data streams. The goal is to use this data to show how FEC optimizes a digital data stream to gain a better digital communications systems. The results conclude by making comparisons of different possible styles for the Tornado FEC code

Tree-based construction of LDPC codes

Abstract — We present a construction of LDPC codes that have minimum pseudocodeword weight equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d = p s and d = p s +1,forp a prime, – one of which includes the well-known finite-geometry-based LDPC codes. I