Haruo Ogiwara

Iterative decoding of serially concatenated punctured trellis-coded modulation

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 a BER of 10/sup -6/ at E/sub b//N/sub 0/=4.43 dB even with a small interleaver of size 2047.

Sum-product decoding of convolutional codes

This article proposes two methods to improve the sum-product soft-in/soft-out decoding performance of convolutional codes. The first method is to transform a parity check equation in such a way as to remove cycles of length four in a Tanner graph of a convolutional code, and performs sum-product algorithm (SPA) with the transformed parity check equation. This method improves the performance of (7,5)8 convolutional code (CC1). However, for (45,73)8 convolutional code (CC2), the method does not effect. The second proposed method is to use a higher order parity check equation in comparison with a normal parity check equation for SPA decoding. This method improves the performance for both convolutional codes (CC1, CC2). The performance is close to that by BCJR algorithm and it is less complex than BCJR algorithm.

Optimal design of trellis coded quantization based on reliability information of turbo trellis coded modulation

Turbo trellis-coded modulation (TCM) with code matched interleaver (CMI) is applied to develop a trellis coded quantization (TCQ). It can been shown that TCQ of memoryless Gaussian sources results in substantial improvement of performance with iterative decoding of turbo TCM and iterative optimization of minimum overall distortion between the source input and decoding output. Numerical results indicate substantial improvement of performance because optimal TCQ based on turbo TCM can be achieved at moderate to high signal-to-noise ratio (SNR) on an additive white Gaussian noise (AWGN) channel for a memoryless Gaussian source and a memoryless uniform source.

Sum-Product Decoding of BCH Codes

This paper proposes methods to improve soft-input and soft-output decoding performance of BCH codes by sum-product algorithm (SPA). A method to remove cycles of length four (RmFC) in the Tanner graph has been proposed. However, the RmFC can not realize good decoding performance for BCH codes which have more than one error correcting capability. To overcome this problem, this paper proposes two methods. One is to use a parity check matrix of the echelon canonical form as the starting check matrix of RmFC. The other is to use a parity check matrix that is concatenation (ConC) of multiple parity check matrices. For BCH(31,11,11) code, SPA with ConC realizes Eb/N0 3.8 dB better than the original SPA, and 3.1 dB better than the SPA with only RmFC at bit error rate 10-5. The decoding complexity is 0.08 times of that of Chase-2 decoding.

Sum-product decoding of BCH codes

This paper proposes methods to improve soft-input and soft-output decoding performance of BCH codes by sum-product algorithm (SPA). A method to remove cycles of length four (RmFC) in the Tanner graph has been proposed. However, the RmFC can not realize good decoding performance for BCH codes which have more than one error correcting capability. To overcome this problem, this paper proposes two methods. One is to use a parity check matrix of the echelon canonical form as the starting check matrix of RmFC. The other is to use a parity check matrix that is concatenation (ConC) of multiple parity check matrices. For BCH(31,11,11) code, SPA with ConC realizes Eb/N0 3.8 dB better than the original SPA, and 3.1 dB better than the SPA with only RmFC at bit error rate 10-5. The decoding complexity is 0.08 times of that of Chase-2 decoding.

Sum-Product decoding of convolutional code for wireless LAN standard

This paper proposes decoding methods for the convolutional code for the wireless Local Area Network (LAN) standard by using sum-product algorithm (SPA). The code is non-systematic. For this code, the conventional SPA decoding cannot provide good decoding performance. This paper shows the reason. The reason is that the conventional SPA uses a Tanner graph including information bits, however, no received signals for information bits are available for the code. This paper proposes two-step SPA decoding method (Proposed Method 1: PM1). The PM1 is as follows. (1) Only parity bits are decoded by SPA. (2) With decoded parity bits, information bits are decoded by SPA. The PM1 can provide much better decoding performance in comparison to the conventional SPA. Furthermore, this paper proposes the combined use of PM1 and method of [4] (Proposed Method 2: PM2). The PM2 provides good performance near BCJR performance. At BER=10−5, PM2 performance is only 0.7[dB] inferior to BCJR performance.

Performance improvement with increasing interleaver length for serially concatenated trellis coded modulation

This paper shows new results on the dependency of the performance on the interleaver size for multilevel serially concatenated trellis coded modulation. The dependency of bit error rate on interleaver size for multilevel SCTCM and optimum code are also discussed.

Importance sampling for TCM scheme on additive non-Gaussian noise channel

Some error probability estimation methods of a trellis-coded modulation (TCM) scheme using importance sampling have been previously proposed (Sadowsky, 1990). However, these methods are not suitable for an additive non-Gaussian noise channel case. The main problem is how to design the probability density function in importance sampling. We propose a new design method of the probability density function related to the Bhattacharyya bound.

Turbo like multi-stage threshold decoding for self-orthogonal convolutional codes

This paper presents a new dimension of soft decoding turbo-like multi-stage threshold decoding (TLMTD) for self-orthogonal convolutional codes (SOCCs). The TLMTD uses comparatively shorter constraint length conventional code of multi-stage threshold decoding (MTD) system. The bit error performance is considered for several types of soft decoding algorithms on the additive white Gaussian noise (AWGN) channel. When threshold value used as a priori threshold value for other decoding stage, TLMTD realizes better performance in waterfall and error floor regions. Moreover, the TLMTD gives 0.20 dB more coding gain compared to MTD for equivalent SOCCs at the bit error rate less than 104.

Performance analysis of threshold decoder with feedback for self-orthogonal convolutional codes

Bit error performance of a threshold decoder with feedback for self-orthogonal convolutional codes are analyzed. The difference triangle method is applied to determine the effect of feedback for consecutive decoded symbols. Instead of stochastic method proposed by Morrissey, the difference triangle method is faster, easier and implementable for any constraint length convolutional codes with large correcting capability. The analytical results show more closer estimation of error probability than that of Genie and definite decoder for same codes at high Eb/N0 region.