The universality of LDPC codes on wireless channels (original) (raw)

Disjoint LDPC Coding for Gaussian Broadcast Channels

Computing Research Repository, 2009

Low-density parity-check (LDPC) codes have been used for communication over a two-user Gaussian broadcast channel. It has been shown in the literature that the optimal decoding of such system requires joint decoding of both user messages at each user. Also, a joint code design procedure should be performed. We propose a method which uses a novel labeling strategy and is based on the idea behind the bit-interleaved coded modulation. This method does not require joint decoding and/or joint code optimization. Thus, it reduces the overall complexity of near-capacity coding in broadcast channels. For different rate pairs on the boundary of the capacity region, pairs of LDPC codes are designed to demonstrate the success of this technique.

LDPC codes for gaussian broadcast channels

IEEE 5th Workshop on Signal Processing Advances in Wireless Communications, 2004., 2004

We study coding over a class of two-user broadcast channels with additive white Gaussian noise and fading known at the receivers only. Joint decoding of low-density parity-check codes is analyzed. The message update rule at the mapping node linking the users' codes is derived and is shown to exhibit an interesting soft interference cancellation property. Good degree distributions are found using the differential evolution optimization technique and extrinsic information transfer analysis. The corresponding codes have rates close to the boundary of the achievable region for binary constrained input channels, both with and without fading. Simulation results for moderate blocklength show that the optimized codes operate within 1dB of their thresholds.

The error-floor of LDPC codes in the Laplacian channel

2005

We analyze the performance of Low-Density-Parity-Check codes in the error-floor domain where the Signal-to-Noise-Ratio, s, is large, s ≫ 1. We describe how the instanton method of theoretical physics, recently adapted to coding theory, solves the problem of characterizing the error-floor domain in the Laplacian channel. An example of the (155, 64, 20) LDPC code with four iterations (each iteration consisting of two semi-steps: from bits-tochecks and from checks-to-bits) of the min-sum decoding is discussed. A generalized computational tree analysis is devised to explain the rational structure of the leading instantons. The asymptotic for the symbol Bit-Error-Rate in the error-floor domain is comprised of individual instanton contributions, each estimated as ∼ exp(−l inst;L · s), where the effective distances, l inst;L , of the the leading instantons are 7.6, 8.0 and 8.0 respectively. (The Hamming distance of the code is 20.) The analysis shows that the instantons are distinctly different from the ones found for the same coding/decoding scheme performing over the Gaussian channel. We validate instanton results against direct simulations and offer an explanation for remarkable performance of the instanton approximation not only in the extremal, s → ∞, limit but also at the moderate s values of practical interest.

On the Design of Universal LDPC Codes

Computing Research Repository, 2008

Low-density parity-check (LDPC) coding for a multitude of equal-capacity channels is studied. First, based on numerous observations, a conjecture is stated that when the belief propagation decoder converges on a set of equal-capacity channels, it would also converge on any convex combination of those channels. Then, it is proved that when the stability condition is satisfied for a number of channels, it is also satisfied for any channel in their convex hull. For the purpose of code design, a method is proposed which can decompose every symmetric channel with capacity C into a set of identical-capacity basis channels. We expect codes that work on the basis channels to be suitable for any channel with capacity C. Such codes are found and in comparison with existing LDPC codes that are designed for specific channels, our codes obtain considerable coding gains when used across a multitude of channels.

The universality of LDPC codes on correlated fading channels with decision feedback based receiver

GLOBECOM '05. IEEE Global Telecommunications Conference, 2005., 2005

This paper proves that low density parity check (LDPC) codes are universal codes on correlated fading channels if a successive decoding receiver is used. A universal LDPC code is defined as a code with the same performance over a class of channels, in which the performance is measured by the threshold of the code in terms of mutual information (in bits/sec/Hz). The receiver proposed in this paper decomposes the fading channel into a bank of memoryless sub-channels. Each sub-channel is encoded with a LDPC code. An MMSE estimator followed by a LDPC decoder is used to successively decodes the channel code. With this scheme, we show that LDPC codes have the universal performance on fading channels with variant fading rates. We also prove that the LDPC code design is unified. Hence, the optimal LDPC codes for the perfect CSI receiver is also optimal for correlated fading channels without CSI. matter experts for publication in the IEEE GLOBECOM 2005 proceedings. This full text paper was peer reviewed at the direction of IEEE Communications Society subject IEEE Globecom 2005 1142 0-7803-9415-1/05/$20.00 © 2005 IEEE Authorized licensed use limited to: UNIVERSITY NOTRE DAME. Downloaded on June 21, 2009 at 20:49 from IEEE Xplore. Restrictions apply.

Low-density parity check ( LDPC ) codes : A new era in coding

2015

“Low Density” comes from the characteristic of their parity-check matrix that contains small number of 1’s in comparison to the amount of 0’s in them. This sparseness of parity check matrix guarantees two features: First, ‘a decoding complexity’ which increases only linearly with the code length and second, ‘a minimum distance’ which also increases linearly with the code length. These codes are practical implementation of Shannon noisy coding theorem[1]. LDPC codes are similar to other linear block codes. Actually, every existing code can be successfully implemented with the LDPC iterative decodSukhleen Bindra Narang, Kunal Pubby*, Hashneet Kaur Department of Electronics Technology, Guru Nanak Dev University, Amritsar, (INDIA) E-mail: kunalpubby02@gmail.com

Performance Evaluation of LDPC Codes Over Various Channels

2014

Due to the rapid evolution of global wireless communication which demands for high data rate transmission via satellites, which in turn requires spectrally efficient modulation technique and power efficient forward-error correction (FEC), schemes. The main objective of any communication system is error free transmission with maximum possible data rate. Noisy communication channels are the major problems in this case. To overcome this problem one can use the channel coding along with the suitable modulation scheme. Thus the objective of Channel coding and modulation is to produce an appropriate signal waveform to cope with the noisy channel. Low density parity check (LDPC) codes are one of the best error correcting codes in today’s coding world and are known to approach the Shannon limit. As with all other channel coding schemes, LDPC codes add redundancy to the uncoded input data to make it more immune to channel impairments. The impact of low-Density Parity-Check code (LDPC) on the...

Performance of spatially-coupled LDPC codes and threshold saturation over BICM channels

We study the performance of binary spatiallycoupled low-density parity-check codes (SC-LDPC) when used with bit-interleaved coded-modulation (BICM) schemes. This paper considers the cases when transmission takes place over additive white Gaussian noise (AWGN) channels and Rayleigh fast-fading channels. The technique of upper bounding the maximum-a-posteriori (MAP) decoding performance of LDPC codes using an area theorem is extended for BICM schemes. The upper bound is computed for both the optimal MAP demapper and the suboptimal max-log-MAP (MLM) demapper. It is observed that this bound approaches the noise threshold of BICM channels for regular LDPC codes with large degrees. The rest of the paper extends these techniques to SC-LDPC codes and the phenomenon of threshold saturation is demonstrated numerically. Based on numerical evidence, we conjecture that the belief-propagation (BP) decoding threshold of SC-LDPC codes approaches the MAP decoding threshold of the underlying LDPC ensemble on BICM channels. Numerical results also show that SC-LDPC codes approach the BICM capacity over different channels and modulation schemes.

Identical-capacity channel decomposition for design of universal LDPC codes

IEEE Transactions on Communications, 2009

Design of low-density parity-check (LDPC) codes suitable for all channels which exhibit a given capacity C is investigated. Such codes are referred to as universal LDPC codes. First, based on numerous observations, a conjecture is put forth that a code working on N equal-capacity channels, also works on any convex combination of these N channels. As a supporting evidence, we prove that a code satisfying the stability condition on N channels, also satisfies the stability condition on the convex hull of these N channels. Then, a channel decomposition method is suggested which spans any given channel with capacity C in terms of a number of identical-capacity basis channels. We expect codes that work on the basis channels to be suitable for any convex combination of the bases, i.e., all channels with capacity C. Such codes are found over a wide range of rates. An upper bound on the achievable rate of universal LDPC codes is suggested. Through examples, it is shown that our codes achieve rates extremely close to this upper bound. In comparison with existing LDPC codes designed for a given channel, significant performance gain is reported when codes are used over various channels of equal capacity.

Analysis of random regular LDPC codes on Rayleigh fading channels

2006

Low-density parity check (LDPC) codes of small, realizable size and regular form are analyzed in different multipath fading conditions. The multipath fading conditions vary from uncorrelated channels (with and without channel state information (CSI)) to a correlated land mobile channel at a frequency of 900 MHz. The effects of an external channel interleaver and varying mobile speed in a correlated fading channel are investigated. Obtained results show that the channel interleaver does not provide substantial improvement in the performance of the codes. However, the increasing speed of a mobile in a correlated channel can provide better bit error rate (BER) performance.