Performance of rate compatible punctured turbo codes over AWGN channels

Designing a channel code is always a tradeoff between the complexity of encoder and decoder in conjunction with efficient energy and bandwidth goals. 'Turbo codes' code with mostly high-weight Code Words (hwCW), eventually make the task of the decoder easier. Through a parallel concatenation of two codes separated by an interleaver, turbo codes usually correct significant errors. In this paper, we provide an extended mathematical description for AWGN and Rayleigh channel response for turbo codes. The robustness of description is verified for a 3G communication system to show the effectiveness of iterative processing in extrinsic information. Performance comparison of the optimal decoding technique have been presented which shows that turbo codes have near Shannonian limit over AWGN channel but fading environment is still a challenging task for further improvement.

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.

Turbo codes have performance superior than all other coding techniques. The main factors that make turbo codes so efficient include, parallel concatenation structure of the encoding system, recursive convolutional encoder, interleaver, puncturing pattern and iterative decoding. In this research, we have investigated the effect of the puncturing pattern on the performance of high rate turbo codes. Based on simulation results, we claim that for most of the code rates, when a pseudo random interleaver is applied, the selection of puncturing pattern does not have significant effect on the code performance. However, for some rates, a commonly used puncturing patterns does cause much poorer performance. For these rates, a modified puncturing pattern is proposed which restores the performance back to the Shannon limit.

In this paper, we mainly studied the coding and decoding principles of convolutional codes and turbo codes and verified the coding and decoding process and bit error rate performance of the two codes. In different channel conditions (AWGN and Rayleigh fading channels), with different code rates (1/2 code rate and 1/3 code rate), the convolutional codes with different constraint lengths (3 and 7) and turbo codes are simulated and compared. We can know from the simulation results that the performance of the two codes in AWGN channel is better than that in Rayleigh channel. In these two channels, the performance of the two codes with small bit rate is better than that of the ones with large bit rate; the performance of turbo codes improves with the increase of the constraint length. The performance of convolution code decreases with the increase of the constraint length when the SNR is small, but it improves with the increase of the constraint length when the SNR is large.

This chapter discusses fundamentals of information theory and channel coding (error correction coding ECC, Forward error correction FEC). First, key results of Shannon, including channel capacity and the relationship between transmit power and bandwidth, are discussed. Block codes multiply a block of data with an encoding matrix. For systematic codes, the resulting codeword consists of systematic bits and parity check bits. Decoding is achieved by multiplication with a parity check matrix and determination of the syndrome vector. Correction of errors within the correction sphere can be done, e.g., through lookup tables. Convolutional codes send the source data stream through shift registers and adders, a process described by a trellis diagram. Maximum-likelihood sequence estimation (Viterbi algorithm) determines the (transmit) bit sequence with best distance metric (Hamming or Euclidean) from the received signal. Methods for combining coding and higher-order modulation include trellis coded modulation (using set partitioning for code design) and bit-interleaved coded modulation (BICM). Turbo codes are close to capacity-achieving. They are based on transmitting differently interleaved convolutional codes; receivers use soft decoding of the constituent codes and iterative exchange of soft information (log-likelihood ratios). Low-density parity check codes (LDPCC) are decoded by belief propagation (message passing), where variable nodes and constraint nodes exchange beliefs about the codeword. In fading channels, (block or convolutional) interleaving is essential to provide diversity. From an information-theoretic point of view, in fading channels we can distinguish between the ergodic capacity and the outage capacity. If the channel state information is known at the transmitter, waterfilling is the optimum power allocation strategy. Automatic Repeat Request ARQ) and Hybrid ARQ (including chase combining or incremental redundancy) are described in the appendix.

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

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.

This paper compares a number of decision feedback schemes that improve the initial channel estimates provided by the pilot symbols alone. The decision feedback scheme that feeds back the systematic bits achieves about the same performance as feeding back both the systematic and parity bits at the low fading rate. Its performance is slightly degraded at the higher fading rate. The advantage of this scheme is its lower complexity as the LLRs of the systematic bits are readily available in the turbo decoding process. Soft decision feedback does not always provide large improvement in performance. Noticeable gain in performance using soft decision feedback is seen only when the bits to be fed back are not reliable during the first few iterations.

A bandwidth-efficient joint network-channel coding scheme based on distributed turbo codes is proposed for relay-based wireless communications systems. The proposed scheme provides a solution to increase the transmission rate and/or improve the error performance. To enhance the system performance over the adverse block fading channels, the relay not only delivers the additional parity bits as in the conventional turbo coded systems but also repeats a portion of systematic bits by using higher-order constellations. This increases the number of information bits having a diversity order of 2. As a result, the proposed scheme yields a 3-dB gain in the transmitted power compared to the conventional scheme for the case of symmetric channels. The gain is further increased when the relay has a better channel condition to the destination than the users.

In this chapter, a novel algorithm named as modified ant lion optimizer (MALO) algorithm has been suggested for the improvement of convergence behavior of the existing ALO algorithm. Moreover, a new form of turbo code (TC) termed as 4D-TC has also been projected for the enhancement of the minimum Hamming distance of the existing TCs. Thereafter, the MALO algorithm has been judiciously used for the design of power efficient 4D-TC. From the simulated outcomes, it is obvious that the high-grade act of MALO algorithm is pretty remarkable than the existing ALO as well as other optimization procedures like particle swarm optimization, Cuckoo search and Harmony search in the matter of exactness and confluence standpoint. Additionally, it has been witnessed that the projected modification on ALO algorithm provides the best optimum value close to theoretical limit by adopting fast exploration and exploitation process over the other algorithms. At the same time, it has also been established that the projected 4D-TC offers substantial improvement in BER act over the others like parallel concatenated convolution turbo code (PCCTC), serially concatenated convolution turbo code (SCCTC), and 3D-TC. The supremacy of MALO has been observed for eight states as well as 16 states 4D-TCs over the other variance like PCCTC, SCCTC, 3D-TC and proposed 4D-TC by means of bit error rate (BER) performance by allocating the optimum power to the systematic and parity bits. Analogous enhancements in BER act have been detected with puncturing as well.

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 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.

An iterative detection and decoding (IDD) technique has recently received much attention due to its capacity approaching performance and manageable complexity for (parallel) turbo-coded systems. The existing IDD receivers process indiscriminately the a priori information of the systematic bits and the parity bits generated by the turbo decoder in the front-end detection. In this paper, we first show that the parity bits of the parallel turbo codes are inherently less protected than the systematic bits, which leads to suboptimality for the IDD receivers. Based on this observation, we then propose an unequal-error-correcting-capability-aware technique to mitigate the associated performance loss. As an illustrative example, the minimum-mean-square-error (MMSE) filtering and soft interference cancelation (MMSE-SIC)-aided iterative receiver for parallel-turbo-coded multiple-input-multiple-output (MIMO) systems is employed in this paper. Numerical results manifest that the MMSE-SIC-aided iterative receiver based on the proposed paradigm achieves noticeable performance gains over the conventional unequal-error-correcting-capability-agnostic one even with reduced computational complexity. The extension of the proposed principle to other iterative algorithms for parallel-turbo-coded data transmission is straightforward.

In this contribution we investigate the performance of the UMTS Long Term Evolution (LTE) physical layer using turbo coding and 64QAM with Gray mapping. We show how the mapping of systematic and parity bits to the six different bit positions defining one complex 64QAM symbol influences the convergence of the turbo decoder and thereby the bit error rate (BER) performance as well as number of necessary decoding iterations. Exploiting the unequal error protection (UEP) property of Gray mapped 64QAM results in an SNR performance gain of approximately 2 dB for the non-iterative system and in addition leads to a significant reduction of the necessary decoding iterations when iterative decoding is performed.

Orthogonal frequency division multiplexing (OFDM) is a very attractive technique for high-bit-rate data transmission in a multipath fading environment that causes intersymbol interference (ISI). There are many error-correcting codes applied to OFDM, convolutional codes, Reed-Solomon codes, turbo codes, and so on. Low-density parity-check (LDPC) codes have attracted much attention particularly in the field of coding theory. LDPC codes were proposed by Gallager (1962) and the performance is very close to the Shannon limit with practical decoding complexity like turbo codes. We propose LDPC coded OFDM (LDPC-COFDM) systems to improve the bit error rate (BER) of OFDM. We show that the BER of the LDPC-COFDM is worse than that of the TCOFDM on an AWGN channel, while that of the LDPC-COFDM is better than that of the turbo-coded OFDM (TCOFDM) on a frequency-selective fading channel.