Analysis of puncturing pattern for high rate turbo codes

In this paper, we investigate in detail the performance of turbo codes in quasi-static fading channels both with and without antenna diversity. First, we develop a simple and accurate analytic technique to evaluate the performance of turbo codes in quasi-static fading channels. The proposed analytic technique relates the frame error rate of a turbo code to the iterative decoder convergence threshold, rather than to the turbo code distance spectrum. Subsequently, we compare the performance of various turbo codes in quasi-static fading channels. We show that, in contrast to the situation in the AWGN channel, turbo codes with different interleaver sizes or turbo codes based on RSC codes with different constraint lengths and generator polynomials exhibit identical performance. Moreover, we also compare the performance of turbo codes and convolutional codes in quasi-static fading channels under the condition of identical decoding complexity. In particular, we show that turbo codes do not outperform convolutional codes in quasi-static fading channels with no antenna diversity; and that turbo codes only outperform convolutional codes in quasi-static fading channels with antenna diversity

The performance of turbo codes has been shown to be near the theoretical limit in the additive while Gaussian noise channel. By using orthogonal signaling, which allows for bandwidth expansion, the performance of the turbo coding scheme can be improved even further. Since this is a low-rate code, the code is mainly suitable for spread-spectrum modulation applications. In classical turbo codes the frame length is set equal to the interleaver size, however, the codeword distance spectrum of turbo codes improves with an increasing interleaver size. It has been reported that by using repetition and puncturing the performance of turbo codes can be improved. Repeat-Punctured Turbo Codes has shown a significant increase in performance at moderate to high signal-to-noise ratios. In this paper, we study the use of orthogonal signaling and parallel concatenation together with repetition and puncturing to improve the performance of superorthogonal convolutional turbo codes for reliable and effective communications. Simulation results for the additive white Gaussian noise channel are presented together with analytical upper bounds, which have been derived using transfer function bounding techniques.

In this paper, the puncturing pattern design criteria for rate-compatible punctured turbo (RCPT) codes are reviewed at first. Then the optimal puncturing pattern design problem for RCPT codes are highlighted for turbo codes with specific interleaver instead of the uniform interleaver assumption. By employing the constrained subcode algorithm to calculate the low weight spectrum sequence, the optimized weight spectrum sequence (OWSS) criterion is utilized to determine the optimal puncturing pattern. Two algorithms are utilized to realize the OWSS design criterion for both the periodic puncturing pattern design and the non-periodic puncturing pattern design. And simulation results are presented to validate the performance for the long term evolution (LTE) standard turbo codes. The analysis in this paper unveils that, non-periodic puncturing pattern design will always outperform the periodic puncturing pattern design. However, the performance difference between the periodic puncturing and the non-periodic puncturing will tend to be negligible with the increase in the puncturing period. As a conclusion, when the simplified implementation in practical application is concerned, it seems that the periodic puncturing pattern with long enough puncturing period is recommended.

In this paper, the performance of turbo codes in speech transmission over AWGN channels is presented. Turbo codes of short block sizes suitable for real time communication systems have drawn attention recently. Embedded channel coding is used which means permitting rate variability using a single encoder/decoder. Puncturing patterns that minimize the BER were implemented and tested. The puncturing of systematic bits is completely excluded and thus puncturing is only done for parity bits. A comparison between the performances of different puncturing patterns shows that the puncturing patterns outperform other patterns.

We study the performance of turbo codes for magnetic recording channels using realistic channel models. The main objective is to provide a benchmark for the future studies on the subject. We examine a variety of schemes including the use of parallel concatenated turbo codes with and without turbo equalization and convolutional codes with an interleaver (can be regarded as a serial concatenation of convolutional codes with the partial response channel). We investigate the effect of the (turbo) code block length, the use of different code structures, and the effects of precoding and the media noise on the system performance. We assume that the partial response target is EPR4.

Turbo codes were the first error-correcting codes that demonstrated reliable communications near the channel capacity with practically feasible hardware. Due to their excellent error-correcting capability, they are part of many modern communication technologies, like 3G, 4G, LTE, etc. An LTE turbo encoder is a rate-1/3 systematic encoder made of a first 8-state recursive convolutional encoder and a second 8-state recursive convolutional encoder. Recursive convolutional encoders are identical, coupled in parallel concatenation scheme, and connected with pseudo-random QPP interleaver. The decoding of LTE Turbo codes is iterative. One iteration starts with decoding of the first convolutional code and continues with decoding the second convolutional code. In order to achieve higher decoding speeds, recursive convolutional codes are decoded with the MAX-Log-MAP algorithm. In this paper, we decode LTE turbo codes with two decoding processes. In one of the decoding processes iterations start with the first convolution code, wherein in the other decoding process iterations start with the second convolution code. We combine the results of both decoding processes to improve turbo decoding process. In channel coding in many communications systems, the speed of decoding is the main design goal. Proposed decoding technique may be used to reduce the number of iterations of LTE turbo decoders, thus improving the decoding speed.

Turbo codes have a wide range of applications in 3G mobile communications, deep-sea communications, satellite communications and other power constrained fields. In the paper, the Turbo Code Decoding Principle and several major decoding methods are introduced. Simulations of Turbo code performance under different parameters of AWGN channel are made and the effects of the different interleaving length, the number of iterations, and the decoding algorithm to Turbo code performance are also discussed in AWGN channel. Simulation results show that under the same signal-to-noise ratio, the more the number of iterations is, the longer the sequence of information is, and the more excellent decoding algorithm is, the better the performance of Turbo codes is.

Turbo codes (TC) is a powerful branch of error-control coding that has exhibited performances close to the Shannon limit, whilst offering a reasonable level of computational complexity. Repeat-punctured turbo codes (RPTCs) exploit the fact that the use of larger interleavers correspond to better bit-error rate (BER) performances for the conventional turbo code, and makes use of repetition and puncturing to improve the performance of the conventional turbo code for moderate to high signal-to-noise ratios (SNRs). Motivated by turbo codes and repeat-punctured turbo codes, we study the use of a new scheme, dual-repeat-punctured turbo codes (DRPTC) in the additive white Gaussian noise (AWGN) channel. DRPTCs primarily make use of repetition and puncturing and the structure of the conventional turbo code to yield a more superior performance. The decoding in principle follows the technique of turbo decoding but needs some changes to yield the performance improvement. Simulation results for the AWGN channel is presented together with the analytical union bounds derived from transfer-function bounding techniques, and the codeword distance-spectrum for the proposed scheme is presented and evaluated.

In this paper, the performance evaluation of an asymmetric turbo code for different codec parameters have been done. The asymmetric turbo codes performances are compared with symmetric counter part of the turbo code. With proper selection of weight configuration, the turbo code can show better results in both water fall region as well as error floor region simultaneously. So, in some cases asymmetric turbo code's performance is more nearer to Shannon limit than symmetric one. This paper includes the effect of different codec parameters (like no. of iteration, frame size, code-rate, and generator polynomial Structure & constraint length etc) on asymmetric turbo code and also explains its performance in comparison with symmetric turbo code. Although, the asymmetric turbo code of all combinations don't show better performance always. Here, we have evaluated the bit error rate (BER) performance using sub-optimal Log-MAP (Logarithmic Maximum-A-Posteriori) decoding algorithm under Additive White Noise (AWGN) channel. The simulation model was developed for AWGN case using MATLAB.

Multi-carrier code division multiple access (MC-CDMA) technique is a combination of two radio access techniques: CDMA and orthogonal frequency division multiplexing and has the advantages of both techniques. The paper presents the design of transmitter and receiver for MC-CDMA radio interface. It also presents encoders and decoders of turbo codes which were used in simulation of the MC-CDMA technique. Two turbo codes with 8-state recursive systematic convolutional were used in the simulation. The simulation results of the transmission quality in additive white Gaussian noise (AWGN) channel presented in the paper show bit error rate and frame error rate performance of MC-CDMA technique with the turbo codes and allow for comparison the performance of both turbo codes.

In this paper, we study the effects of different ASE noise models on the performance of turbo code (TC) decoders. A soft-decoding algorithm, the Bahl, Cocke, Jelinek, and Raviv (BCJR) decoding algorithm, is generally used in TC decoders. The BCJR algorithm is a maximum a posteriori probability (MAP) algorithm, and is very sensitive to noise statistics. The Gaussian approximation of ASE noise is widely used in the study of optical-fiber communication systems, and there exist standard TCs for additive white Gaussian noise (AWGN) channels. We show that using a MAP decoding algorithm based on the Gaussian noise assumptions, however, may significantly degrade the TC decoder performance in an optical-fiber channel with non-Gaussian ASE noise. To take full advantage of TC, accurate noise statistics in optical-fiber transmissions should be used in the MAP decoding algorithm.

The performance of partial unit memory-based turbo codes (PUM-TC) with standard convolutional-based turbo codes (RSC-TC) are analysed and compared. Resulting extrinsic information transfer charts indicate that the proposed PUM-based codes have higher mutual information during iterative decoding than the equivalent RSC-TC for the same SNR, i.e. the output of the decoders provides a better approximation of the decoded bits. It is shown that the PUM-TC outperforms known equivalent RSC-TC at the error-floor region, with comparable performance in the waterfall region.

本論文中我們探討在快速跳頻/MFSK(Fast Frequency Hopping/Multiple Frequency Shift Keying, FFH/MFSK)通訊系統中，加上多音頻干擾後並經過通道，再使用不同的錯誤更正碼(Error Correcting Codes, ECC)並分析其效能。我們的系統所採取的通道為可加性白色高斯雜訊(Additional White Gaussian Noise, AWGN)和頻率選擇性雷利衰減(frequency selective Rayleigh fading)通道。在錯誤更正碼的使用上，分別是摺積碼(convolutional codes)與渦輪碼(turbo codes)。解碼器是採用遞迴解碼的方式。而我們為了比較各種編、解碼器的效能優劣，因此在效能分析方面是使用Extrinsic information transfer(EXIT) chart這個方法。另外本論文將模擬的是位元交錯二位元碼的效能。由電腦模擬結果可知，在遞迴解碼的時候，若是採用串接符元碼-遞迴解碼，效果會比沒有串接符元碼的好。至於錯誤更正碼解碼的部分，摺積碼的效能則是優於渦輪碼。

We propose and evaluate a novel method of constructing hybrid ARQ systems with turbo codes that addresses the convergence problems of the turbo decoders. The puncturing pattern is chosen in such a way that the parts of the trellis that present difficulties to the decoder are given priority in retransmission. This is different from the traditional construction of rate compatible punctured turbo codes (RCPT) which attempts to obtain optimal weight distance properties of the codes without taking the convergence properties of the turbo decoder into account. We show that in the 'turbo cliff' region our system outperforms the best known hybrid ARQ scheme in terms of the throughput, the number of retransmissions and the total number of iterations required to decode a frame at the receiver. Moreover, the design of the puncturing pattern is greatly simplified and requires no extensive computer simulations.

The turbo code performance over Rayleigh flat-fading channel using QPSK modulation is evaluated. By utilizing the orthogonal character, we have proposed a simplified turbo coding scheme which can greatly decrease the complexity. On the basis of this scheme, we have further simulated the turbo code performance over a Rayleigh flat-fading channel using different iterations. The influence of channel side information (SI) on the performance of turbo code is also addressed.