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Online bit error rate (BER) estimation (OBE) has been used as a stopping iterative turbo decoding criterion. However, the stopping criteria only work at high signal-to-noise ratios (SNRs), and fail to have early termination at low SNRs, which contributes to an additional iteration number and an increase in computational complexity. The failure of the stopping criteria is caused by the unsuitable BER threshold, which is obtained by estimating the expected BER performance at high SNRs, and this threshold does not indicate the correct termination according to convergence and non-convergence outputs (CNCO). Hence, in this paper, the threshold computation based on the BER of CNCO is proposed for an OBE stopping criterion (OBEsc). From the results, OBEsc is capable of terminating early in a varying SNR environment. The optimum number of iterations achieved by the OBEsc allows huge savings in decoding iteration number and decreasing the delay of turbo iterative decoding.

Viterbi decoders are widely employed along with convolutional encoders to provide an excellent error correction probability in digital wireless transmissions. To achieve lower error rates, the constraint length (k) of the encoder, has to be defined at higher values. However, higher (k) results in increasingly complex implementations of the Viterbi algorithm. As a result, the power consumption of the Viterbi decoder will increase exponentially which is to the disadvantage of many wireless communication devices. Many reduced complexity decoding techniques of the Viterbi decoder presented in the past focused on algorithm and architecture specific levels. Most of the studies concentrated on the Add-Compare Select Unit (ACSU) of the decoder, due to its nature of repetitive processing; also add to the complexity of the process. This paper presents a review of several variations of the Viterbi algorithm performed in the ACSU. The comparison was made among several different algorithms with the most optimal algorithm presented in this paper. A combined algorithm approach is proposed at the end of the review for future improvement.

Cross-entropy (CE) based stopping criteria is known for its early termination capability of the turbo decoding iterations without scarifying its performance, in terms of bit error rate (BER). This advantage, however, performs well in high signal-to-noise ratio (SNR) albeit requiring infinite iterations at low SNR, thereby resulting in more unwanted computations and decoding delays. In this paper, a simple turning point (TP) measurement from the BER and average iteration number (AIN) graphs of the Genie stopping criterion has been introduced. The motivation is twofold; to terminate the iteration at the early stage in low SNR and maintaining the same level of performance of the existing method in high SNR, by using the proposed TP measurement. From the simulation results, the enhanced CE-based stopping criteria improve the early termination in low SNR and maintain the BER performance for various frame sizes compared to existing stopping criteria.

Most of the turbo decoding stopping criteria assume perfect channel reliability available at the receiver since they require a threshold based on signal-to-noise ratio (SNR) information. However, operational environments can vary according to frame sizes, code structures and channel reliability requirements, further aggravating the difficulty in threshold determination and convergence or non-convergence detection. This paper aims to provide a robustness analysis of improved minimum descriptive length (IMDL) stopping criterion peculiar to these factors: the frame sizes, the channel reliability requirements, the code structures, and the code rate. The robustness analysis is benchmarked to the well-known Genie stopping criterion based on the average iteration number (AIN) and bit error rate (BER) performance.

A robust stopping criterion (called online-BER [OB]) that can terminate iterative turbo decoding in a signal-to-noise ratio (SNR) uncertainty environment is proposed. OB is based on the online bit error rate (BER) estimation and the BER thresholds. Both values are used to detect convergence and non-convergence decoder output and also to halt iterative decoding in various SNRs. Unlike other well-known stopping criteria, OB does not depend on SNR information in its stopping rules and hence it is less complex. OB is also more robust than other stopping criteria in a SNR uncertainty environment while being capable of reducing the average iteration number and resulting in less degradation in BER performance.

Measurement of reliability (MOR) stopping criterion is able to terminate early in the low and high signal-to-noise ratio (SNR) while maintaining the bit error rate (BER) performance. However, the performance of MOR is only based on one code structure and hence, the robustness of MOR is still unknown in turbo iterative decoding. Thus, this paper will test the robustness of MOR based on the following parameters: frame size, code structure, channel reliability and code rate. Then, we analyse and compare the average iteration number (AIN) and the BER performance of MOR with the benchmark stopping criterion known as Genie to determine the robustness of MOR. From the analysis, MOR has a BER degradation for low code rate. MOR also fails to perform well if the corret channel reliability is not available at the receiver and this results a large degradation in BER performance. However, MOR has close performance to Genie in terms of BER for various frame sizes, code structures and high code rate with the assistance of correct channel reliability. MOR is also able to save AIN at low SNR as compared to Genie and this can reduce delay and complexity of turbo codes.

The Cross-Entropy-based (CE-based) stopping criteria advantage is able to terminate early in the high signal-to-noise ratio (SNR) while maintain the bit error rate (BER) performance. Unfortunately, the criteria fails to cope with low SNR region and make the decoder iterates until maximum or infinite iteration. This paper proposed an early termination technique at low SNR for the CE-based stopping criteria using the decoding threshold derived by the measurement of reliability (MOR) at low SNR. In the simulation results and analysis, we compare the average iteration number (AIN) and the bit-error rate (BER) performance between the proposed combination methods with the existing CE-based stopping criteria. From the results, the combination method capable to reduce the AIN at low SNR with minimum one AIN while maintaining the AIN at high SNR as the traditional method. This significant reduction could reduce delay and complexity of existing CE-based stopping criteria while maintaining the BER performances.

The invention of turbo codes has attracted many researchers to explore various fields regarding turbo codes since it provides better error rate performance compared to the existing codes. Good error rate performance gives a penalty to the complexity of the codes. It includes the complexity of decoding algorithm and iterative decoding. This paper reviews the history of turbo codes and its structures. This paper also discusses the turbo decoding stopping criteria algorithm and analyses the performance of fixed and cross-entropy (CE) based stopping criteria. From the results, both criteria fail to terminate early in low SNR. However, CE-based stopping criteria outperform the fixed stopping criterion at high SNR and able to save more iteration and delay. This leads to an energy saving preservation while maintaining the performance of turbo codes.