With iterative turbo decoding, the reliability of each bit in a frame is not same after some iterations. We propose novel bit-level hybrid automatic repeat request (HARQ) schemes with turbo codes in which only the unreliable bit and its neighboring bits are retransmitted based on the decoding reliability. The proposed bit-level HARQ schemes improve error performance compared with conventional HARQ schemes.

Parallel concatenated convolutional codes, turbo codes, are very attractive scheme at a point of view of an error probability performance. An bit error rate (BER) evaluation for turbo codes is done by a uniform interleaver bound calculation and/or a computer simulation. The former is calculated under the assumption of uniform interleaver, and is only effective for an BER evaluation with a pseudo random interleaver. The latter dose not have any interleaver restrictions. However, for a very low BER evaluation, it takes enormous simulation time. In this paper, a new error probability evaluation method for turbo codes is proposed. It is based on the error event simulation method. For each evaluation for the predetermined error sequence, importance sampling, which is one of the fast simulation methods, is applied. To prove the effectiveness of the proposed method, numerical examples are shown. The proposed method well approximates the BER at the error floor region. Under the same accuracy, the IS estimation time at BER = 10-7 is reduced to 1/6358 of the ordinary Monte-Carlo simulation time.

Rate compatible (RC) codes are used for adaptive coding schemes or hybrid ARQ schemes in order to adapt varying channel conditions. This can improve overall service quality or the system throughput. Conventional RC codes have usually been designed on the basis of convolutional codes. This letter proposes an efficient RC code based on block codes. We use a high dimensional product code and divide it into the information block and a number of parity blocks. We form RC product codes using various combinations of these blocks. Because we can decode the RC product codes iteratively, these result in block turbo codes and they can be used efficiently for hybrid ARQ schemes.

A new stopping criterion of turbo decoding based on the maximum a posteriori (MAP) decoder is proposed and applied to the turbo processing system. The new criterion suggested as the combined parity check (CPC) counts the sign difference between combined parity bits and the re-encode parity bits determined from decoded information bits. The CPC requires decoded parity bits and a turbo encoder but it performs better in terms of the bit error rate and the average number of iterations in the turbo processing system.

A new algorithm for the LogMAP decoding of linear block codes is considered. The decoding complexity is evaluated analytically and by computer simulation. The proposed algorithm is an improvement of the recursive LogMAP algorithm proposed by the authors. The recursive LogMAP algorithm is more efficient than the BCJR algorithm for low-rate codes, but the complexity grows considerably large for high-rate codes. The aim of the proposed algorithm is to solve the complexity explosion of the recursive LogMAP algorithm for high-rate codes. The proposed algorithm is more efficient than the BCJR algorithm for well-known linear block codes.

In this letter, we propose the Low-Density Parity-Check (LDPC) coded Orthogonal Frequency Division Multiplexing (OFDM) systems to improve the error rate performance of OFDM. We also evaluate the iterative decoding performance on both an AWGN and a frequency-selective fading channels. We show that when the energy per information bit to the noise power spectral density ratio Eb/N0 is not small, the LDPC coded OFDM (LDPC-COFDM) systems have the good error rate performance with a small number of iterations. We also show that when the Eb/N0 is small, the BER of the LDPC-COFDM systems is worse than that of the Turbo coded OFDM (TCOFDM) systems, while when the Eb/N0 is not small, the BER of the LDPC-COFDM systems is better with a small number of iterations.

Space-time transmit diversity (STTD) and space-time block coding (STBC) are attractive techniques for high bit-rate and high capacity transmission. The concatenation scheme of turbo codes and STBC (Turbo-STBC) was proposed and it has been shown that the Turbo-STBC can achieve the good error rate performance. Recently, low-density parity-check (LDPC) codes have attracted much attention as the good error correcting codes achieving the near Shannon limit performance like turbo codes. The decoding algorithm of LDPC codes has less complexity than that of turbo codes. Furthermore, when the block length is large, the error rate performance of the LDPC codes is better than that of the turbo codes with almost identical code rate and block length. In this letter, we propose a concatenation scheme of LDPC codes and STBC. We refer to it as the LDPC-STBC. We evaluate the error rate performance of the LDPC-STBC by the computer simulation and show that the error rate performance of the LDPC-STBC is almost identical to or better than that of the Turbo-STBC in a flat Rayleigh fading channel.

Power Line Communication (PLC) is very attractive for achieving high-rate in-home networks. Noise in power lines is modeled as a cyclostationary Gaussian process. In order to achieve reliable communication using power lines, effective measures including error control techniques need to be taken against this particular noise. This paper focuses its attention on an effect of turbo codes on PLC. We adopt two noise environments for examining the effect in terms of BER performance. The result of the examination provides that turbo codes have enough capability to limit the effect of the noise. It also provides that the effect depends on size of a channel interleaver. Since an effective SNR estimation scheme should be required to apply turbo codes to PLC, we also examine the effect of two SNR estimation schemes in terms of BER performance.

DC-free error-correcting codes based on partition chain are presented in this paper. The partition chain can be constructed from code partition chain of Reed-Muller codes. The line coding parameters for the partition chain such as maximum runlength and running digital sum are obtained. The trellis and multilevel code structure can be used to design the DC-free error-correcting codes. Especially, by adopting DC-free trellis codes as constituent codes, DC-free turbo codes can be designed. As results, the presented DC-free error-correcting codes have good coding characteristics.

New algorithms for the MAP (also known as the APP) decoding and the MAX-LogMAP decoding of linear block codes are presented. The algorithms are devised based on the structural properties of linear block codes, and succeeds in reducing the decoding complexity without degrading the error performance. The proposed algorithms are suitable for the parallel and pipeline processing which improves the throughput of the decoder. To evaluate the decoding complexity of the proposed algorithms, simulation results for some well-known codes are presented. The results show that the algorithms are especially efficient than the conventional BCJR-based algorithms for codes whose rate are relatively low.

In this paper, we suggest the interference cancellation (IC) technique suitable for turbo coded code division multiple access (CDMA) systems, that merges IC processes into turbo decoding processes to improve system performance and reduce system complexity. To ensure the reliability of the temporary decision bits for cancellation, we use cyclic redundancy code (CRC) check as a measure. Prior to design turbo coded CDMA system, we first derive the optimized polynomials of low-rate turbo codes appropriate to CDMA systems. According to the simulation results with setting the processing gain (PG) to 120, the turbo coded CDMA system with the proposed IC technique can accommodate 60 users over additive white Gaussian noise (AWGN) channel when signal to noise ratio (SNR) is about 2. 5 dB and required frame error ratio (FER) is 10-2. Compared this result with the performance of single user's system, it requires only additional 1 dB SNR.

The binary parallel concatenated codes called turbo codes provide relatively large coding gains with reasonable computation complexity. The application of turbo codes to a coherent DS-CDMA mobile radio link with antenna diversity and coherent RAKE combining is considered. A soft-in/soft-out Viterbi decoder that requires less computation complexity is employed instead of maximum a posteriori probability (MAP) decoder. The effect of turbo codes on the achievable bit error rate (BER) performance in frequency selective multipath fading channels is evaluated by computer simulation. It is demonstrated that turbo codes can achieve better BER performance than convolutional codes having the same code rate for the relatively large interleaver size. How the coding gains are impacted by the interleaver size and constraint length of the turbo codes and by the propagation channel condition (power delay profile, the number of resolvable propagation paths, and the maximum Doppler frequency) is discussed.

Soft-in/soft-out Viterbi algorithm (SOVA) originally proposed for rate 1/n code is applied to rate m/(m+1) trellis-coded modulation (TCM). In TCM, 2m branches merge into a node in a code trellis. After pruning the branches on path with less path-metric until two best paths remain, SOVA is applied to the pruned trellis. Based on the pruned trellis, an iterative decoding algorithm of turbo TCM is developed. Effects of path memory length and scaling of a value transferred between decoding stages are investigated through simulation. Turbo TCM over 8 PSK and 16 QAM channel with Gaussian noise realize a bit error rate (BER) of 10-5 within 1 dB from the Shannon limit.

A turbo TCM system is applied to a channel with overall noise which is equal to the additive combination of impulsive Gaussian noise and Additive White Gaussian Noise (AWGN). By taking the distribution of the previously mentioned overall noise into account, a decoding algorithm for Poisson occurrence impulsive noise is derived as an extension of that for AWGN. A simulation result shows that Eb/N0 difference from Shannon limit to realize BER=10-4 is 0. 493 dB. To investigate the effect of burst noise, we discuss the case of additive impulsive noise with Markovian occurrence which is represented by Hidden Markov Model. A decoding algorithm for Markovian noise is proposed. In the iterative decoding for the Markovian channel, the decoding algorithms for Markovian and Poisson noise are applied separately to the two component decoders. The decoding algorithm for Markovian noise is used in the component decoder wherein received signal is directly fed, while the decoding algorithm for Poisson noise is used in the component decoder wherein received signal is fed after passing an interleaver. This paper also shows simulation results that include the effects of varying the noise parameters in the decoding. In the Markovian case, when smaller value of variance of impulsive noise is used, the observed flattening of BER performance is more serious compared to the effect in the Poisson noise channel. No flattening is observed when large value is used.

This paper gives an overview of Turbo codes principles, performance, and design issues for practical application. As fundamentals of Turbo codes, encoder structure, interleaver, and iterative decoding are explained. The performance is analyzed through their weight distribution, and the analysis gives code design rules for component codes. Practical decoding algorithms are presented in addition to MAP algorithm. Design issues are discussed for mobile communications as an example of practical application. Finally, research trends are briefly mentioned.