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arXiv:1912.09463

Finite State Markov Modeling of Fading Channels Towards Decoding of LDPC Codes

M. Sravan Kumar

Published Oct 19, 2019• 0 citations
arXivHTMLPDF

Abstract

Here we have proposed two decoding strategies of low-density parity-check (LDPC) codes over Markov noise channels with bit flipping noise. The sum-product algorithm used for decoding LDPC codes over memoryless channels is extended to include channel estimation and how much gain we obtain by doing so is simulated and verified. LDPC codes have been studied for years over memoryless channels and are known to have excellent performance. However, these codes over channels with memory is the topic of current research. Here, channels with memory are characterized by Markov modeling which is a useful busty channel model. With sufficient no. of states, they are able to model sufficient noise characteristics. We have gone for a two-state system as it shows a good compromise between complexity and performance.

DOI
10.48550/arxiv.1912.09463

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Here we have proposed two decoding strategies of low-density parity-check (LDPC) codes over Markov noise channels with bit flipping noise. The sum-product algorithm used for decoding LDPC codes over memoryless channels is extended to include channel estimation and how much gain we obtain by doing so is simulated and verified. LDPC codes have been studied for years over memoryless channels and are known to have excellent performance. However, these codes over channels with memory is the topic of current research. Here, channels with memory are characterized by Markov modeling which is a useful busty channel model. With sufficient no. of states, they are able to model sufficient noise characteristics. We have gone for a two-state system as it shows a good compromise between complexity and performance.
LDPC decoding algorithm on channels with memory is of great significance to high speed digital com- munications.Currently used low-density parity-check codes iterative decoding algorithms on channels with memo- ry,such as Belief-Propagation iterative decoding algorithm based on channel estimation,are commonly complex and thus requiring large amount of calculation.In this paper,a min-sum algorithm is firstly introduced into LDPC itera- tive decoding algorithm based on soft noise decisions and channel estimation on hidden Markov noisy channels.Algo- rithm and calculation complexity are effectively reduced by using the functions'characteristics.Simulation results show that the algorithm not only excels conventional Belief-Propagation iterative decoding algorithms that do not concern channel memory,but also outperforms iterative decoding algorithms based on hard noise decisions and channel esti- mation.So a good compromise is made between decoding performance and algorithm complexity with low performance loss,which is useful real time communications.
We propose a modified algorithm for decoding of low-density parity check codes over finite-state binary Markov channels. The hidden Markov model representing the channel is incorporated into the bipartite graph of the low-density parity check code, and the message passing algorithm is modified accordingly. This approach clearly outperforms systems in which the channel statistics are not exploited in the decoding, allowing reliable communication at rates which are above the capacity of a memoryless channel with the same stationary bit error probability as the Markov channel. Moreover, we introduce a joint estimation/decoding method that allows the estimation of the parameters of the channel when they are not known a priori.
Communications systems suffer from impulsive in- terference, generally modeled as a memory channel to account for the inherent bursts of impulse even though conventional receivers take into account the additive white Gaussian noise only. In this paper, finite- field based constructions of Low Density Parity Check (LDPC) coding over the Markov Gaussian channel are investigated. In contrast with existing approaches assuming the impulse noise statistics, this paper proposes a modified maximum- a-priori method, which forfeits using the statistical knowledge of impulse, to estimate whether or not each transmitted symbol is corrupted by impulse noise. Subsequently, the sum-product algorithm LDPC decoder invokes a clipper to diminish impulsive interference when the channel state is identified to be impulse- corrupted. The bit error rate (BER) performance versus the signal-to-noise ratio for the proposed decoder is conducted using computer simulation. The experimental results in terms of the BER performance justified the robustness of our proposed receiver and also revealed its competitiveness with the optimal benchmark decoder in the hostile environment. Moreover, using the proposed receiver, our calibrated quasi-cyclic LDPC code is shown to slightly outperform its 5G New Radio counterpart under certain circumstances.
The problem of low-density parity-check (LDPC) decoding in channels with memory has been attracting increasing attention in the literature. In this thesis, we use LDPC codes in an estimation-decoding scheme for the Gilbert-Elliott (GE) channel and more general Markov-modulated channels. The major accomplishments of this thesis include both analysis and design components. To analyze our estimation-decoding scheme, we derive density evolution for the GE channel, which has previously been used largely in memoryless channels. Furthermore, we develop techniques that use density evolution results to more efficiently characterize the space of Markov-modulated parameters. We begin by applying a characterization to the GE channel, following which we generalize this characterization into a partial ordering of Markov-modulated channels in terms of probability of symbol error. We also consider the design problem of developing LDPC degree sequences that are optimized for the GE channel. We obtain a novel design tool that approximates density evolution for our estimation-decoding algorithm, and present degree sequences that represent the best known codes in the GE channel. We also present a method of generalizing this tool to Markov-modulated channels, and give some of the first optimized degree sequences ever obtained for these channels.
An improved decoding algorithm for low-density parity-check code(LDPC) on finite-state Markov channels was presented and the corresponding factor graph representation was given.It consists of two parts: standard sum-product algorithm(SPA) for LDPC and forward-backward(FB) algorithm for Markov channel.After each iteration for SPA,FB re-estimated the channel likelihood ratio for the next iteration of SPA based on soft decisions for noise bits from SPA.Considering more cycles in the factor graph with the introduction of the Markov channel node,the probabilistic schedule was used to update the message during the iterations for decoding.Simulation results show that the algorithm not only performs much better than the standard sum-product algorithm,but also outperforms the algorithm based on hard decisions for noise bits.
Low density parity checking codes (LDPC) are one of the most important issues in coding theory at present. LDPC-code are a type of linear-block LDPC-codes. Channel coding might be considered as the finest conversant and most potent components of cellular communications systems, that was employed for transmitting errors corrections imposed by noise, fading and interfering. LDPC-codes are advanced coding gain, i.e., new area in coding. the performances of LDPC-code are similar to the Shannon-limiting, this led to the usage of decoding in several applications in digital communications systems, like DVB-S2 and WLAN802.1..This paper aims to know what is LDPC,what its application and introduce encoding algorithms that gives rise to a linear encoding time and also show that the regular and irregular LDPC performance and also introduce different methods for decoding LDPC. I discuss in detail LDPC decoding algorithm: bit flipping algorithm, as a type from hard decision .belief propagation algorithm, sum product algorithm and minimum sum algorithm as examples from soft decision .I expect that at least some students or researchers involved in researching LDPC codes would find this paper helpful.