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Video Engineering

Construction of Regular LDPC Codes with Lower Bounds on the Minimum Distance

Liu Li

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

A new method to get lower bound on the minimum distance of regular LDPC codes is presented in this paper.This method,LDPC code is constructed based on indenpendent tree of each variable node in LDPC code.Compared with the random LDPC codes and PEG codes,the LDPC codes constructed in this method result in greater girth and lower bound on the minimum distance.Using the Matlab to simulate,in the AWGN channel,when the length of the codes is 1 008 and 1 512.Simulation results show that new independent tree-based LDPC codes perform the best as the signal-to-noise ration increases.

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A new method to get lower bound on the minimum distance of regular LDPC codes is presented in this paper.This method,LDPC code is constructed based on indenpendent tree of each variable node in LDPC code.Compared with the random LDPC codes and PEG codes,the LDPC codes constructed in this method result in greater girth and lower bound on the minimum distance.Using the Matlab to simulate,in the AWGN channel,when the length of the codes is 1 008 and 1 512.Simulation results show that new independent tree-based LDPC codes perform the best as the signal-to-noise ration increases.
An independent tree-based method for lower bounding the minimum distance of low-density parity-check (LDPC) codes is presented. This lower-bound is then used as the decision criterion during the iterative construction of regular LDPC codes. The new construction algorithm results in LDPC codes with greater girth and improved minimum-distance bounds when compared to regular LDPC codes constructed using the progressive edge-growth (PEG) construction and the approximate cycle extrinsic message degree (ACE)-constrained PEG construction. Simulation results of codes constructed with the new method show improved performance on the additive white Gaussian noise channel at moderate signal-to-noise ratios.
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We present a tree-based construction of low-density parity-check (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 addd-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 degreesd=psd=p^sd=psandd=ps+1d = p^s+1d=ps+1, forpppa 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 forppp-ary LDPC codes. Treating these codes asppp-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 wherep>2p > 2p>2.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
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 ddd-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=psd=p^sd=ps and d=ps+1d = p^s+1d=ps+1, for ppp 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 ppp-ary LDPC codes. Treating these codes as ppp-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>2p > 2p>2.
In this paper, we present a construction method based on the progressive edge-growth (PEG) algorithm to design irregular low-density parity-check (LDPC) codes without small stopping sets. We show how to choose the connections in the PEG algorithm when having multiple choices to connect a variable node with a check node. Since preventing small stopping sets also prevents a low minimum distance, our construction method also leads to LDPC codes with a higher minimum distance. Furthermore, we show by simulation that our construction method improves the performance over the binary erasure channel and over the additive white Gaussian noise channel for a low erasure probability and a high signal-to-noise ratio, respectively.