Coded Bit Error Rate Research Articles

New Structure of Channel Coding: Serial Concatenation of Polar Codes

In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust error-correcting codes. The primary objective here is to optimize the behavior of individual elementary codes within polar codes. In this structure, we incorporate interleaving, a technique that rearranges bits to maximize the separation between originally neighboring symbols. This rearrangement is instrumental in converting error clusters into distributed errors across the entire sequence. To evaluate their performance, we proposed to model a communication system with seven components: an information source, a channel encoder, a modulator, a channel, a demodulator, a channel decoder, and a destination. This work focuses on evaluating the bit error rate (BER) of codes for different block lengths and code rates. Next, we compare the bit error rate (BER) performance between our proposed method and polar codes.

Application of the method of equivalent message encoding structures to simplify coding complexity

Formulation of the problem. Modern telecommunication technologies make it possible to transmit data over long distances with limitations in the form of low power consumption and low error rate using error correction codes. The use of such codes plays an important role and is necessary to detect and correct errors caused by signal distortion and noise in the communication channel. According to Shannon's channel coding theorem, the probability of error can be arbitrarily small or close to zero if the encoding rate of transmission R is less than or equal to the bandwidth of channel C. Assuming that the bandwidth C is achievable, we can calculate the minimum signal-to-noise power ratio (SNR) to achieve zero error, or an arbitrarily small error called the Shannon limit, while maintaining R ≤ C. This article discusses a method of applying equivalent message encoding structures to construct low-density parity-checking (LDPC) codes. Low-density parity-checking (LDPC) codes are a class of linear block codes in which the complexity of iterative decoding increases linearly with increasing block length. Standard LDPC codes without modifications are considered to demonstrate the effectiveness of the proposed method, which is expected to provide high encoding speed when transmitting messages with a short block length. The method of obtaining equivalent structures allows: to reduce the computational complexity of encoding and decoding; to provide the possibility of finding a new encoding scheme and evaluating its effectiveness. The validity of the method for obtaining equivalent message encoding structures is evaluated by modeling the bit error rate (BER) of LDPC codes. Purpose. to show the effectiveness of the use of equivalent structures for various methods of compression of transmitted information, to minimize the complexity of encoding, while maintaining energy efficiency, correcting ability and data transfer rate. Results. A method is considered for obtaining equivalent message element encoding structures that can be used to create more LDPC codes for data transmission applications with a short block length. The cascade principle of constructing an equivalent generator and a parity check matrix was analyzed, which also leads to minimizing the computational complexity of the encoder and decoder. An equivalent structure G can be obtained from cascading two (or more) matrices by modifying the second matrix so that it has a unit matrix with the size of the parity check length and a shift to the right by k bits. On the other hand, the equivalent structure H can be obtained by simply cascading directly the second matrix and shifting to the right by k bits. According to the simulation results, the proposed method is adequate, since LDPC codes have the same BER characteristics as codes based on the low density generator matrix (LDGM). During the simulation, it was concluded that the SPC codes (single parity check (single parity check (SPC)) are the most efficient codes (for a given block length), since SPC codes have the smallest interval up to the Shannon limit. Practical significance. The results presented in this article will give a new insight into the development of simple channel coding of LDPC codes of short block length with high encoding speed for future applications with lower power consumption.

Tight Upper Bound on the Bit Error Rate of Convolutional Codes over Correlated Nakagami-<i>m</i> Fading Channels

Tight Upper Bound on the Bit Error Rate of Convolutional Codes over Correlated Nakagami-<i>m</i> Fading Channels

Rate-Splitting for Multicarrier Multigroup Multicast: Precoder Design and Error Performance

Employing multi-antenna rate-splitting (RS) at the transmitter and successive interference cancellation (SIC) at the receivers, has emerged as a powerful transceiver strategy for multi-antenna networks. In this paper, we design RS precoders for an overloaded multicarrier multigroup multicast downlink system, and analyse the error performance. RS splits each group message into degraded and designated parts. The degraded parts are combined and encoded into a degraded stream, while the designated parts are encoded in designated streams. All streams are precoded and superimposed in a non-orthogonal fashion before being transmitted over the same time-frequency resource. We first derive the optimized RS-based precoder, where the design philosophy is to achieve a fair user group rate for the considered scenario by solving a joint max-min fairness and sum subcarrier rate optimization problem. Comparing with other precoding schemes including the state-of-the-art multicast transmission scheme, we show that the RS precoder outperforms its counterparts in terms of the fairness rate, with Gaussian signalling, i.e., idealistic assumptions. Then we integrate the optimized RS precoder into a practical transceiver design for link-level simulations (LLS), with realistic assumptions such as finite alphabet inputs and finite code block length. The performance metric becomes the coded bit error rate (BER). In the system under study, low-density parity-check (LDPC) encoding is applied at the transmitter, and iterative soft-input soft-output detection and decoding are employed at the successive interference cancellation based receiver, which completes the LLS processing chain and helps to generate the coded error performance results which validate the effectiveness of the proposed RS precoding scheme compared with benchmark schemes, in terms of the error performance. More importantly, we unveil the corresponding relations between the achievable rate in the idealistic case and coded BER in the realistic case, e.g., with finite alphabet input, for the RS precoded multicarrier multigroup multicast scenario.

Research of Multi-Rate LDPC Decoding in Optical Communication System

Low-density parity-check code (LDPC) not only has good performance approaching the Shannon limit, but also has low decoding complexity and flexible structure. It is a research hot-spot in the field of channel coding in recent years and has a wide range of application prospects in optical communication systems. In this paper, the decoding aspects and performance of LDPC codes are analyzed and compared according to the bit error rate (BER) of LDPC codes. The computer simulation was carried out under additive white Gaussian noise (AWGN) channel and binary phase shift keying (BPSK) modulation. Through theoretical analysis and simulation results, this paper explores the way of multi-rate LDPC decoding.

Comparison of Bit Error Rate of Line Codes in NG-PON2

This article focuses on simulation and comparison of line codes NRZ (Non Return to Zero), RZ (Return to Zero) and Miller’s code for NG-PON2 (Next-Generation Passive Optical Network Stage 2) using. Our article provides solutions with Q-factor, BER (Bit Error Rate), and bandwidth comparison. Line codes are the most important part of communication over the optical fibre. The main role of these codes is digital signal representation. NG-PON2 networks use optical fibres for communication that is the reason why OptSim v5.2 is used for simulation.

Accurate Closed-Form Approximation of BER for OSTBCs with Estimated CSI on Spatially Correlated Rayleigh Fading MIMO Channels

In this contribution, we present a novel accurate closed-form approximation for the bit error rate (BER) of orthogonal space-time block codes (OSTBCs) employing quadrature amplitude modulation with Gray-mapping on spatially correlated Rayleigh fading MIMO channels, in the presence of channel estimation errors. The presented BER expression allows to accurately examine the impact of spatial correlation and channel estimation errors on the BER for any OSTBC or signal-to-noise ratio, even in case of highly correlated channels.

Bounds for the BER of Codes With Fixed Cross Correlation in SAC-OCDMA Systems

In this paper, two lower and upper bounds for the bit error rate of codes with fixed cross-correlation in spectral-amplitude-coding optical code-division multiple access systems are offered. In this study, we consider only the phase-induced intensity noise and neglect other noises such as shot and thermal noises, in the performance analysis. Also, it is assumed that users are synchronous. This bound is obtained using combinatorics approach and utilizing simple inequalities. In numerical results, the comparison between the upper bound, lower bound, and simulation results for MQC, MFH, BIBD, and Hadamard codes is presented, and the tightness of the bounds is evaluated.

Symbol and bit error probabilities of orthogonal space-time block codes with antenna selection over keyhole fading channels

The symbol error rate (SER) and the bit error rate (BER) of orthogonal space-time block codes (OSTBCs) with antenna selection over keyhole fading channels are examined. Considered are receive antenna selection, transmit antenna selection, and joint antenna selection at both the transmitter and the receiver. The exact SERs of OSTBCs for M-PSK and square MQAM constellations are obtained using the technique of moment generating function (MGF). By applying the Bonferroni-type bounds, tight lower and upper bounds for both the SER and BER are provided in closed-form expressions with finite-range single integrals. The bounds can be applied to arbitrary constellations and mappings. Numerical results show that the bounds can be used to provide practically the exact SER and BER over a wide range of the signal-to-noise ratio.

Exact error probability of Orthogonal Space-Time Block Codes over flat fading channels

Space time block coding is a modulation scheme recently discovered for the transmit antenna diversity to combat the effects of wireless fading channels. Using the equivalent Single-Input Single-Output (SISO) model, this paper presents closed-form expressions for the exact Symbol Error Rate (SER) and Bit Error Rate (BER) of Orthogonal Space-Time Block Codes (OSTBCs) with M-ary Phase-Shift Keying (MPSK) and M-ary Quadrature Amplitude Modulation (MQAM) over flat uncorrelated Nakagami-m and Ricean fading channels.

SISO algorithms based on Max-Log-MAP and Log-MAP turbo decoding

Novel soft-input soft-output (SISO) decoding algorithms suitable for turbo codes are proposed with good compromise between complexity and bit error rate (BER) performance. The algorithms are based on the application of the max/max* (i.e. Jacobian logarithm) operations at different levels when computing the decoder soft-output value. It is observed that some decoding schemes from the authors' previously published work fall into the family of methods described here. The effect is to provide a range of possibilities allowing system designers to make their own choices for turbo code BER performance against complexity.

The input–output weight enumeration of binary Hamming codes

AbstractWe show that binary Hamming codes can be constructed recursively. The recursive structure is used to efficiently enumerate the input–output weights. Hence, the bit error rate of binary Hamming codes with antipodal signalling and hard‐decision demodulation used on additive white Gaussian noise channels can be evaluated exactly. The numerically computed coding gain of Hamming codes reveals a surprising fact that the coding gain is not monotonically increasing with signal‐to‐noise ratio. Copyright © 2006 AEIT

BER analysis of QAM on fading channels with transmit diversity

In this letter, we derive analytical expressions for the bit error rate (BER) of space-time block codes (STBC) from complex orthogonal designs (COD) using quadrature amplitude modulation (QAM) on Rayleigh fading channels. We take a bit log-likelihood ratio (LLR) based approach to derive the BER expressions. The approach presented here can be used in the BER analysis of any STBC from COD with linear processing for any value of M in an M-QAM system. Here, we present the BER analysis and results for a 16-QAM system with i) (2-Tx, L-Rx) antennas using Alamouti code (rate-1 STBC), ii) (3-Tx, L-Rx) antennas using a rate-1/2 STBC, and iii) (5-Tx, L-Rx) antennas using a rate-7/11 STBC. In addition to being used in the BER analysis, the LLRs derived can also be used as soft inputs to decoders for various coded QAM schemes, including turbo coded QAM with space-time coding as in high speed downlink packet access (HSDPA) in 3G.

DC-Free Error-Control Block Codes

DC-free codes and error-control (EC) codes are widely used in digital transmission and storage systems. To improve system performance in terms of code rate, bit-error rate (BER), and low-frequency suppression, and to provide a flexible tradeoff between these parameters, this paper introduces a new class of codes with both dc-control and EC capability. The new codes integrate dc-free encoding and EC encoding, and are decoded by first applying standard EC decoding techniques prior to dc-free decoding, thereby avoiding the drawbacks that arise when dc-free decoding precedes EC decoding. The dc-free code property is introduced into standard EC codes through multimode coding techniques, at the cost of minor loss in BER performance on the additive white Gaussian noise channel, and some increase in implementation complexity, particularly at the encoder. This paper demonstrates that a wide variety of EC block codes can be integrated into this dc-free coding structure, including binary cyclic codes, binary primitive BCH codes, Reed-Solomon codes, Reed-Muller codes, and some capacity-approaching EC block codes, such as low-density parity-check codes and product codes with iterative decoding. Performance of the new dc-free EC block codes is presented.

The Impact of Pulsed RFI on the Coded BER Performance of the Nonlinear Satellite Communication Channel

The coded bit error rate (BER) performance of a satellite communications system, wherein the satellite repeater contains an arbitrary nonlinearity and the system operates in the presence of pulsed radio frequency interference (RFI), is examined. A major result is an analytic method for determining soft decision statistics of the receiver demodulator output in which pulsed RFI effects are accounted for. It is further demonstrated how this result can be analytically applied to the approximate determination of the BER at the output of the Viterbi decoder when convolutional coding is employed. Computed results specialize the nonlinearity to either a hard limiter or clipper, in conjunction with an arbitrarily specified AM/PM characteristic. Performance curves examine BER sensitivity to RFI duty cycle, form of RFI (CW or noise), and various coding/decoding conditions.