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Performance Analysis of Enhanced Verification-Based Decoding for Packet-Based LDPC Codes over Binary Symmetric Channel

Bin Zhu, Defeng David Huang, Sven Erik Nordholm, Ying–Jun Angela Zhang

Published Dec 1, 2011• 0 citations
Publisher

Abstract

In this paper, frame error rate (FER) performance of enhanced verification-based decoding algorithm (EVA) is investigated for packet-based low-density parity-check (LDPC) codes over binary symmetric channel (BSC). By taking the false verification into account, a recursive statistical model is proposed to analyze the FER performance based on the packet-level analysis. Simulation results demonstrate that the proposed model works for various packet sizes and channel parameters of practical interest with different verification constraints.

DOI
10.1109/glocom.2011.6133747

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In this paper, frame error rate (FER) performance of enhanced verification-based decoding algorithm (EVA) is investigated for packet-based low-density parity-check (LDPC) codes over binary symmetric channel (BSC). By taking the false verification into account, a recursive statistical model is proposed to analyze the FER performance based on the packet-level analysis. Simulation results demonstrate that the proposed model works for various packet sizes and channel parameters of practical interest with different verification constraints.
In this paper, we propose a statistical model to analyze the performance of verification-based algorithm (VA) for packet-based low-density parity-check (LDPC) codes over binary symmetric channel (BSC). In contrast to the analysis of VA in the literature, we propose to take the false verification into consideration. For a given ensemble of LDPC codes and channel parameters, the proposed analysis model gives an efficient way to find the average performance of packet-based LDPC codes with verification-based decoding. Through numerical results, we find that the proposed method can provide a close estimation of frame error rate (FER) for packet-based LDPC codes with verification- based decoding over BSC for all crossover probabilities of practical interests.
Research on low-density parity-check (LDPC) codes has traditionally been focused on small alphabets. With the development of communication networks and high-speed wireless communication systems, the operation units are normally blocks of bits organized as packets. Packet-based LDPC codes have a great potential to be used in multi-cast and content delivery networks to help achieve reliable communications. To decode packet-based LDPC codes, a verification-based decoding algorithm (VA) has been proposed by Luby and Mitzenmacher for q-ary symmetric channels (q-SC) with large q. However, as a packet-level block code, packet-based LDPC codes are most likely used as outer codes in concatenated coding schemes. Due to the fact that in a typical communication system, an interleaver is employed between the inner encoder and the outer encoder and the output from the inner decoder is normally in a hard-decision form, a binary symmetric channel (BSC) is thereby most proper to model such a scenario. We will show that in contrast to q-SC with large q, when VA is used for BSC, the probability that a packet is falsely verified plays a dominant role in determining system performance. In this dissertation, we propose an enhanced verification-based decoding algorithm (EVA) to improve the verification conditions and significantly reduce the possibility of the false verifications. In contrast to VA, EVA has much better performance over BSC with only moderate computation complexity increase. We also analyze the performance of VA and EVA over BSC. By reformulating VA (EVA) as a message-passing algorithm, a statistical model is proposed to analyze the frame error rate (FER) performance of VA (EVA). Using a recursive method to find the values of the parameters during the iterative process, the proposed model provides a good estimate of FER for the various packet sizes and channel parameters of practical interest.
In this letter, an enhanced verification-based decoding algorithm (EVA) for packet level low-density parity-check (LDPC) codes is proposed. Compared with the verification algorithm (VA) in the literature, the proposed algorithm reduces the likelihood of false verification by enhancing the verification condition to achieve a better decoding performance. For example, simulation results in this letter show that EVA reduces frame error rate (FER) by two orders when comparing the VA over binary symmetric channel (BSC), while the increase of the computational load is less than 90%.
In this paper, we apply the enhanced verification-based decoding algorithm (EVA) for packet-based LDPC codes over wireless channels. Compared with the verification algorithm (VA) in the literature, the EVA algorithm enhances the verification condition thereby reducing the likelihood of false verification. The wireless channels in simulations are modeled by binary symmetric channel (BSC) and Gilbert-Elliott (GE) channel. The numerical results indicate the proposed algorithm gives a superior performance but with only moderate computation increase compared with VA. For example, when the bit error probability is less than 10-3in bad state of GE channel, the EVA reduces the frame error rate (FER) by one order with less than 35% complexity increase compared with VA.
A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates.
A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSCs) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates.