On turbo code decoder performance in optical-fiber communication systems with dominating ASE noise

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.

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, 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

Non binary turbo codes are gaining a lot of attention since the recent adoption of duo binary circular turbo codes by the Digital Video Broadcasting (DVB) community. In this paper, a Joint Source Channel Decoding (JSCD) scheme is proposed for circular non-binary turbo codes. With a view to exploit a-priori probabilities from source statistics, a symbol level trellis is incorporated into the circular trellis of the non-binary turbo decoder. Reversible Variable Length Codes (RVLC) are used as the input source in all simulations. Results show that with JSCD, circular duo binary turbo codes provide an average gain of 0.4 dB at Bit Error Rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> as compared to conventional decoding of circular duo binary turbo codes. With circular triple binary turbo codes, JSCD provides a striking average gain of 3.5 dB at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> compared to conventional decoding of circular triple binary turbo codes.

An urgent task is to correct errors that occur during the transmission and storage of information. To solve this problem, various noise-resistant codes have recently been increasingly used. Turbo codes have the best correcting ability in data transmission channels with a high probability of an erroneous bit. To obtain the necessary characteristics, various combinations of codes and encoding and decoding methods are used. If another block of information bits is added to the codeword of a systematic block or systematic convolutional code, then it will be possible to implement decoding of such a codeword by a turbo code decoder. The disadvantage of the resulting combined code is its extremely low correcting ability in the presence of errors in the check bits of the codeword. The article shows that the correcting ability of the presented code can be significantly increased by multiplying the decoded values of the check bits by reduction factors.

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.

It is well known that binary error-correcting codes with iterative decoders can achieve near Shannon-limit performance on the additive white Gaussian noise (AWGN) channel, but their performance on more realistic wireless channels can become degraded due to the presence of burst errors or impulsive noise due to interference. A better performing coding scheme is the class of non-binary codes, which are known to be more effective in correcting burst errors, but interestingly there is no research reported in the literature investigating non-binary codes on impulsive noise channels. In this paper, we investigate the performance of non-binary turbo codes defined in a finite field GF(4) on symmetric alpha-stable impulsive noise channels and compare with comparable binary turbo codes. A Cauchy receiver is also employed to mitigate the effects of the channel to assist the turbo decoding. Our simulation results show that although the non-binary turbo code performs similarly to the binary turbo code on the AWGN channel, it achieves a significant coding gain over the binary turbo code as impulsiveness increases.

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.

This correspondence analyzes the performance of concatenated coding systems and modulation schemes operating over the additive white Gaussian noise (AWGN) channel by examining the loss of capacity resulting from each of the processing steps. The techniques described in this correspondence allow the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. Knowledge of this capacity loss is very useful for the overall design of a communications system, e.g., for evaluating the benefits of inner decoders that produce information beyond the maximum-likelihood (ML) estimate. The first two sections of this correspondence provide a general technique for calculating the composite capacity of an orthogonal or a bi-orthogonal code and the AWGN channel in isolation. The later sections examine the composite capacities of an orthogonal or a bi-orthogonal code, the AWGN channel, and various inner decoders including the decoder estimating the bit-by-bit probability of a one, as is used in turbo codes. The calculations in these examples show that the ML decoder introduces a large loss in capacity. Much of this capacity loss can be regained by using only slightly more complex inner decoders, e.g., a detector for M-ary frequency-shift keying (MFSK) that puts out the two most likely frequencies and the probability the ML estimate is correct produces significantly less degradation than one that puts out only the most likely frequency.

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.

For radio communication systems, powerful error correction codes are necessary to operate in noisy and fading channel conditions. Iterative forward error correction schemes like Turbo codes can achieve near Shannon capacity performance on memory-less channels and also perform well on correlated fading channels. The key to the excellent decoding performance of the Turbo coding systems is the BCJR algorithm in conjunction with the iterative processing of soft information. A very popular modulation technique is Differential Phase Shift Key (DPSK) which is not only a simple non-coherent modulation and demodulation technique; it is also a recursive rate one code. Combining DPSK with a single convolutional code structure as an iterative inner outer forward error correction system can provide excellent Turbo like performance. Bit Interleaved Coded Modulation with Iterative Demodulation (BICM-ID), which is a similar iterative coding system that allows full coherent processing, will be analyzed and compared to the DPSK BCJR iterative system. Monte Carlo simulation results will be shown for the Additive White Gaussian Noise (AWGN) and Rayleigh fading channels.

This paper discusses a code-division multiple access (CDMA) iterative multi-user receiver with forward error control (FEC) decoding. The maximum a-posteriori probability (MAP) criteria is used to derive the receiver. The decoding is done using a turbo-code decoder with modifications which are discussed. Iterations of the system are used to attain large performance improvements over conventional systems.

Motivated by recent results in Joint Source/Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

Motivated by recent results in Joint Source/ Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

As compared to uncoded unitary space-time modulation (USTM), channel coded USTM has received increased attention for its large coding gain. However, low-density parity-check (LDPC) coded USTM has only received limited attention. This paper proposes a scheme of combining LDPC code with USTM for noncoherent MIMO communication system over Rayleigh flat fading and additive white Gaussian noise (AWGN) channel. At the receiver, considering the soft information required by the belief-propagation (BP) iterative decoder of the LDPC code, we deduce a low complexity maximum a posteriori probability (MAP) demodulating algorithm for a special USTM based on the sine-cosine function, SC-USTM for short. We combine the MAP with the maximum likelihood (ML) demodulating algorithm based on the SC-USTM in order to generate a novel dual-demodulator for further decreasing the computational complexity of the demodulating/decoding system. For improving the performance of the receiver, the iterative feedback scheme between the MAP demodulator and the BP decoder is designed. Comparing with the uncoded USTM, our LDPC-coded USTM can obtain about 15 - 17 dB coding gain at 10-5 BER.