Performance Analysis of Turbo Codes, LDPC Codes, and Polar Codes over an AWGN Channel in the Presence of Inter Symbol Interference

Abstract

This paper discusses the results of simulations relating to the performances of turbo codes, low density parity check (LDPC) codes, and polar codes over an additive white Gaussian noise (AWGN) channel in the presence of inter symbol interference, denoting the disturbances that altered the original signal. To eliminate the negative effects of inter symbol interference (ISI), an equalizer was used at the level of the receiver. Practically, two types of equalizers were used: zero forcing (ZF) and minimum mean square error (MMSE), considering the case of perfect channel estimation and the case of estimation using the least square algorithm. The performance measure used was the modification of the bit error rate compared to a given signal to noise ratio; in this sense, the MMSE equalizer offered a higher performance than the ZF equalizer. The aspect of channel equalization considered here is not novel, but there have been very few works that dealt with equalization in the context of the use of turbo codes, especially LDPC codes and polar codes for channel coding. In this respect, this research can be considered a contribution to the field of digital communications.

Iterative Equalization and Decoding over an Additive White Gaussian Noise Channel with ISI Using Low-Density Parity-Check Codes

“…BER vs. SNR in an ISI channel, at the SNR of 5 dB, using the proposed system for different impulse responses h. Table 2. BER vs. SNR in an ISI channel, at the SNR of 5 dB, using the proposed system for different impulse responses h. The second system consists of the equalization performed separately before the decoding process using MMSE equalizer and LDPC decoder at a rate of 1 / 2 , similar to [13]. For example, for a channel with h1, at the SNR of 5 dB, in the case of our proposed system, as was specified earlier, the BER is situated between 10 −4 and 10 −5 if ten iterations are made in the LDPC decoder and for 20 iterations within the LDPC decoder at the SNR of 5 dB for iterations 1-5 no more errors were found.…”

“…The current work is a continuation of the previous papers in which a performance comparison was made between the zero forcing (ZF) or MMSE equalization preceded the decoding process using different codes [13,14], intending to evaluate the performance of the equalization that takes place inside the decoding process as in the case of turbo equalization. In this respect, the contributions of this article can be summarized as follows:…”

“…The performances in terms of BER vs. SNR of the proposed system were also correlated in comparison with other decoding and equalization systems described in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Equalizer Parameters’ Adjustment Based on an Oversampled Channel Model for OFDM Modulation Systems

“…This channel type, characterized by only two closely located paths, results in a deep zero in the channel's frequency response, rendering the subchannels useless for transmission. However, if the channel estimation results closely resemble its original shape, the probability of successful error correction in the FEC (Forward Error Correction) decoder [23][24][25] is enhanced.…”

Raptor Codes with LT-LDPC Precoding Performance Analysis and FPGA Optimization

“…LDPC Code, a category of linear block codes, is generated by a sparse, nonsystematic parity-check matrix and is employed to correct bit errors during information transmission. The encoding of these codes involves the multiplication of information bits by this sparse matrix, resulting in the generation of codewords [8]. Decoding is primarily conducted using iterative algorithms such as belief propagation, which is designed to recover the original information from the received codewords.…”