Turbo decoding with coherent detection requires accurate channel estimation. In this paper, we consider outer-turbo channel estimation (OTCE), which carries out iterative channel estimation before turbo decoding, and inner-turbo channel estimation (ITCE), which incorporates iterative channel estimation into turbo decoding process. The average bit error rate (BER) performances with OTCE and ITCE in a frequency nonselective Rayleigh fading channel with antenna diversity reception are evaluated by means of computer simulations to be compared. It is found that although ITCE is superior to OTCE, OTCE provides the average BER performance very close to ITCE when dual antenna diversity reception is used.

In this paper, an online SNR estimator is proposed for parallel combinatorial SS (PC/SS) systems in Nakagami fading channels. The PC/SS systems are called as partial-code-parallel multicode DS/SS systems, which have the higher-speed data transmission capability comparing with conventional multicode DS/SS systems referred to as all-code-parallel systems. We propose an SNR estimator based on a statistical ratio of correlator outputs at the receiver. The SNR at the correlator output is estimated through a simple polynomial from the statistical ratio. We investigate the SNR estimation accuracy in Nakagami fading channels through computer simulations. In addition, we apply it to the convolutional coded PC/SS systems with iterative demodulation and decoding to evaluate the estimation performance from the viewpoint of error rate. Numerical results show that the PC/SS systems with the proposed SNR estimator have superior estimation performance to conventional DS/SS systems. It is also shown that the bit error rate performance using our SNR estimation method is close to the performance with perfect knowledge of channel state information in Nakagami fading channels and correlated Rayleigh fading channels.

A receiver structure, which has linear computational complexity with the number of users, is proposed for decoding multiuser information data in a convolutionally coded asynchronous DS-CDMA system in multipath fading channels. The proposed receiver architecture consists of a multiuser likelihood calculator followed by a bank of soft-input soft-output (SISO) channel decoders. Information is fed back from SISO channel decoders to multiuser likelihood calculator, and the processing proceeds in an iterative fashion analogous to the decoding of turbo codes. A simplification to the above receiver structure is given too. Simulation results demonstrate that for both receiver structures at high signal-to-noise ratios (SNR) both multiple-access interference (MAI) and inter-symbol interference (ISI) are efficiently suppressed, and single-user performance is approached. Furthermore, the proposed iterative receiver is near-far resistant.

This paper addresses a novel scheme for variable rate error correction coding with interleavered puncturing serially concatenated convolutional code. In order to obtain a variable coding rate, the bits of the outer coder are perforated with a given puncturing pattern, and randomly interleaved. The effect of interleavered puncturing on the overall coding performance is analyzed, and the upper bound to the bit error probability of the proposed coder is derived. Moreover, to evaluate the effectiveness of the proposed scheme some simulation results are presented with the iterative decoding procedure, in which the channel models of Rayleigh fading and additive white Gaussian noises are assumed.

In this paper, we present a new soft-decision iterative decoding algorithm using an efficient minimum distance search (MDS) algorithm. The proposed MDS algorithm is a top-down and recursive MDS algorithm, which finds a most likely codeword among the codewords at the minimum distance of the code from a given codeword. A search is made in each divided section by a "call by need" from the upper section. As a consequence, the search space and computational complexity are reduced significantly. The simulation results show that the proposed decoding algorithm achieves near error performance to the maximum likelihood decoding for any RM code of length 128 and suboptimal for the (256, 37), (256, 93) and (256, 163) RM codes.

This paper presents an iterative algorithm for decoding product codes based on syndrome decoding of component codes. This algorithm is devised to achieve an effective trade-off between error performance and decoding complexity. A simplified list decoding algorithm, which uses a modified syndrome decoding method, for linear block codes is devised to deliver soft outputs for iterative decoding of product codes. By adjusting the size of the list, the decoder can achieve a proper trade-off between decoding complexity and performance. Compared to the other iterative decoding algorithms for product codes, the proposed algorithm has lower complexity while offers at least the same performance, which is demonstrated by analyses and simulations. The proposed algorithm has been simulated for BPSK and 16-QAM modulations over both the additive white Gaussian noise (AWGN) and Raleigh fading channels. This paper also presents an efficient scheme for applying product codes and their punctured versions. This scheme can be implemented with variable packet size and channel data block.

Space-time turbo codes have both advantages of space-time codes and turbo codes, and the space-time turbo code proposed by Su and Geraniotis is known to achieve full coding rate and full antenna diversity. This paper presents some improvements of their space-time turbo code in a two-antenna configuration. We first propose a new condition for full antenna diversity which imposes less constraints on the interleaver. Next, by applying a method used to improve turbo trellis-coded modulation to the space-time turbo code, we propose a new decoding algorithm which utilizes more precise estimates on extrinsic information. Simulation results show that the proposed condition assures full antenna diversity and the new decoding algorithm provides a better performance than that of Su and Geraniotis'.

We examine a concatenated code which consists of a rate 1/2, 4-state turbo code (an inner code) and a single-parity-check product code (an outer code), and discuss the decoding structure called a double concatenated decoding scheme. From our Monte Carlo simulation trials, we show the advantage of the concatenated codes over turbo codes alone. Specifically, when we use an interleaver of 4096 bits, the Eb/No to obtain a BER of 10-6 is about 1.45 dB for the concatenated code. On the other hand, it is more than 2.5 dB for the turbo code alone. So, the Eb/No improvement can be achieved by about 1 dB. This improvement in Eb/No was also obtained for the interleavers of 8192 and 2048 bits. Therefore, the concatenated codes using a double concatenated decoding scheme can solve the problem of the BER flattening in decoding of turbo codes.

Gallager has defined an ensemble of regular low density parity check (LDPC) codes for deriving the ensemble performance of regular LDPC codes. The ensemble is called the Gallager ensemble. In this paper, we define a new ensemble of LDPC codes, called extended Gallager ensemble, which is a natural extension of the Gallager ensemble. It is shown that an extended Gallager ensemble has potential to achieve larger typical minimum distance ratio than that of the original Gallager ensemble. In particular, the extended Gallager ensembles based on the Hamming and extended Hamming codes have typical minimum distance ratio which is very close to the asymptotic Gilbert-Varshamov bound. Furthermore, decoding performance of an instance of an extended Gallager ensemble, called an extended LDPC code, has been examined by simulation. The results show good block error performance of extended LDPC codes.

In this paper, the iterative decoding of BCH product codes also called Block Turbo Codes (BTC) is evaluated for the HIPERLAN/2 OFDM system. Simulations show that expurgated BCH codes should be chosen as constituent codes in order to outperform the specified convolutional code. We also show that the bit-by-bit frequency interleaver has a big impact on the behaviour of the turbo decoding process and that increasing its size together with time diversity lead to good performance when compared to the convolutional code.

This paper proposes iterative demodulation/decoding for parallel combinatorial spread spectrum (PC/SS) systems. A PC/SS system conveys information data by a combination of pre-assigned orthogonal spreading sequences with polarity. In this paper, convolutional coding with a uniform random interleaver is implemented in channel coding, just like as a serial concatenated coding. A 'soft-in/soft-out' PC/SS demodulator based on a posteriori probability algorithm is proposed to perform the iterative demodulation and decoding. Simulation results demonstrate that the proposed iterative demodulation/decoding scheme bring significant improvement in bit error rate performance. This proposed decoding scheme achieves high-speed transmission by two approaches. One is a puncturing operation, and the other is to increase the number of transmitting sequences. In the latter approach, lower error rate performance is achieved comparing with that the punctured convolutional code is used to increase the information bit rate.

We consider iterative soft-decision decoding algorithms in which bounded distance decodings are carried out with respect to successively selected input words, called search centers. Their error performances are degraded by the decoding failure of bounded distance decoding and the duplication in generating candidate codewords. To avoid those weak points, we present a new method of selecting sequences of search centers. For some BCH codes, we show the effectiveness by simulation results.

Performance of parallel concatenated trellis-coded modulation (turbo TCM) with Ungerboeck type constituent codes with maximum likelihood decoding over the AWGN channel is analyzed by extending the method of performance evaluation proposed by Benedetto et al. for binary turbo codes with uniform interleaving. Although a performance evaluation of turbo TCM has been proposed, the system model discussed in the proposal has some auxiliary interleavers only necessary for the evaluation. This paper removes such auxiliaries. Since the direct extension of Benedetto's method for turbo TCM needs huge memories for computation, an efficient numerical evaluation method is proposed in order to reduce the memory requirement. Based on the analysis, the relation between bit error rate and interleaver size is discussed. The analyzed performance is compared with simulation results of iterative decoding of turbo TCM.

This paper addresses a complexity reduction scheme for turbo decoding and demonstrates its impact on bit error rate performance in a wideband direct sequence code division multiple access (W-CDMA) mobile radio environment. The complexity reduction scheme combines concatenation of CRC with turbo coding and incorporates a CRC error-detection flag for terminating schemes of decoding iteration. The impact of the scheme on complexity reduction of turbo decoding is investigated using several coding parameters such as the maximum number of decoding iterations and interleaver length of the turbo codes. Miss-detection probability of CRC error-detection is also investigated in this paper.

Iterative decoding is a key feature of turbo code and each decoding results in additional power consumption of the decoder and decoding delay. In this letter, we propose an effective stop criterion based on the Gaussian assumption at the decoder output. Simulation results show that the proposed method can dynamically stop the iterative process with a negligible degradation of the error performance.

For binary linear block codes, we introduce "multiple GMD decoding algorithm. " In this algorithm, GMD-like decoding is iterated around a few appropriately selected search centers. The original GMD decoding by Forney is a GMD-like decoding around the hard-decision sequence. Compared with the original GMD decoding, this decoding algorithm provides better error performance with moderate increment of iteration numbers. To reduce the number of iterations, we derive new effective sufficient conditions on the optimality of decoded codewords.

Iterative decoding of serially concatenated code is extended to punctured trellis-coded modulation. A system configuration, a decoding algorithm and a performance evaluation method are proposed. It realizes a total coding rate of m/(m+1) by puncturing parity bits. Simulation results indicate that the proposed system shows no flattening effect which is observed in parallel concatenated system and realizes BER of 10-6 at Eb/N0=4.43 dB even with a small interleaver of size 2047.

In this paper, we consider sufficient conditions for ruling out some useless iteration steps in a class of soft-decision iterative decoding algorithms for binary block codes used over the AWGN channel using BPSK signaling. Sufficient conditions for ruling out the next single decoding step, called ruling-out conditions and those for ruling out all the subsequent iteration steps, called early termination conditions, are formulated in a unified way without degradation of error performance. These conditions are shown to be a type of integer programming problems. Several techniques for reducing such an integer programming problem to a set of subprograms with smaller computational complexities are presented. As an example, an early termination condition for Chase-type decoding algorithm is presented. Simulation results for the (64, 42, 8) Reed-Muller code and (64, 45, 8) extended BCH code show that the early termination condition combined with a ruling-out condition proposed previously is considerably effective in reducing the number of test error patterns, especially as the total number of test error patterns concerned grows.

Recently, it is widely known that the partial response maximum-likelihood (PRML) system has attracted much attention as one of indispensable signal processing technique for achieving high density digital magnetic recording. But, the performance of PRML system is degraded by many undesirable causes in recording channel. For improving the performance, it is desirable to use any high order PRML system or high rate code. Our proposed two-track recording method increases the coding rate over 1, and contributes to decrease these degradation effects. The recording code in our system adopts a turbo code which provides a substantial near-ML performance by the suboptimum iterative decoding algorithm. In this paper, the turbo coded class four partial response (PR4) systems using the rate 4/6, 8/10 and 16/18 codes for high density two track digital magnetic recording are proposed. The error rate performance of the proposed system is obtained by computer simulation taking account of the partial erasure, which is one of nonlinear distortions at high densities. The performance of our system is compared with that of the conventional NRZ coded PR4ML system. The result shows that the proposed system is hardly affected by partial erasure and keeps good performance in high density recording. In especial, the proposed system using the rate 16/18 turbo code can achieve a bit error rate of 10-4 with SNR of approximately 12.2 dB less than the conventional NRZ coded PR4ML systems at a normalized linear density of 3.

Simple computation method of soft value, that is used in iterative soft decision decoding, is proposed. For the product code composed of BCH(63, 57) and that composed of BCH(63, 45), computation time with the proposed method is 1/15-1/6 as that with a method based on the Chase algorithm. Bit error rate (BER) performance with the proposed method is within 0.8 [dB] inferior to that with the method based on the Chase algorithm at BER=10-5.