Turbo Product Codes Research Articles

Quantum turbo product codes

Quantum communication is a growing interdisciplinary field which combines classical communications and quantum mechanics. Quantum error correction coding is one of the key techniques in quantum communication. Nearly all of the classical error correction coding schemes have been transplanted to the domain of quantum communication, and the quantum counterparts of classical error correction coding techniques have been found. Based on the classical turbo product codes (TPCs) which is one of the most outstanding schemes in classical coding region, a new structure of the CSS-type quantum convolutional codes (QCC) as stabilizer sub-code of the quantum turbo product codes (QTPC) is presented. Firstly, CSS-type QCC stabilizer generator is constructed with the help of group theory and the basic principle of stabilizer coders, and the corresponding networks are described. Secondly, the interleaved coded matrix of the QTPC is obtained by quantum permutation SWAP gate definition. Finally, the corresponding relation between the quantum trace distance of QTPC decoding and the distance of classical TPCs decoding is obtained, and the scheme of QTPCs coding and decoding is completed. The coding and decoding of QTPCs have a highly regular structure and a simple design idea, and the networks are easy to realize.

Design of Shortened Turbo Product Codes And Their Improved Decoding

In this paper, a general matrix structure for shortened turbo product codes (TPC) and an improved decoding algorithm based on Chase decoder are presented. In the proposed algorithm, the decoding complexity is decreased by reducing the number of candidate codewords and, an efficient method to estimate the extrinsic information without competing codeword is designed, too. Compared with the conventional algorithm, simulation results show that considerable coding gains can be obtained by the proposed decoding algorithm with decreasing decoding complexity.

Theoretical and experimental studies of turbo product code with time diversity in free space optical communication

In free space optical communication (FSOC) systems, channel fading caused by atmospheric turbulence degrades the system performance seriously. However, channel coding combined with diversity techniques can be exploited to mitigate channel fading. In this paper, based on the experimental study of the channel fading effects, we propose to use turbo product code (TPC) as the channel coding scheme, which features good resistance to burst errors and no error floor. However, only channel coding cannot cope with burst errors caused by channel fading, interleaving is also used. We investigate the efficiency of interleaving for different interleaving depths, and then the optimum interleaving depth for TPC is also determined. Finally, an experimental study of TPC with interleaving is demonstrated, and we show that TPC with interleaving can significantly mitigate channel fading in FSOC systems.

Iterative decoding algorithm of TPC based on correlation computation

Chase-Pyndiah algorithm is one of the decoding algorithms of Turbo Product Code(TPC).Based on that,an iterative decoding algorithm involved with correlation was introduced.This algorithm avoids the computation of Euclidean distance due to the use of correlation as the metric;and uses a comparative method in the choice of the concurrent codewords,which prevents the search of competition codeword.On the basis of this study,further simplification was presented,which decreased the complexity and the latency of the decoder.Both analysis and simulation result show the advantage of the proposed algorithm over conventional algorithm in speed and performance.

Turbo Product Code Decoder Without Interleaving Resource: From Parallelism Exploration to High Efficiency Architecture

This article proposes to explore parallelism in Turbo-Product Code (TPC) decoding through a parallelism level classification and characterization. From this design space exploration, an innovative TPC decoder architecture without any interleaving resource is presented. This architecture includes a fully-parallel SISO decoder capable of processing n symbols in one clock period. Syntheses results show the better efficiency of such an architecture compared with existing solutions. Considering a six-iteration turbo decoder of a BCH(32,26)2 product code, synthesized in 90 nm CMOS technology, 10 Gb/s can be achieved with an area of 600 Kgates. Moreover, a second architecture enhancing parallelism rate is described. The throughput is 50 Gb/s while an area estimation gives 2.2 Mgates. Finally, comparisons with existing TPC decoders and existing LDPC decoders are performed. They validate the potential of proposed TPC decoder for Gb/s optical fiber transmission systems.

Soft Information Relaying for Distributed Turbo Product Codes (SIR-DTPC)

In this letter, we propose a distributed turbo product code (DTPC) with soft information relaying over cooperative network using block extended Bose Chaudhuri Hochquenghem (EBCH) codes as component codes. The source broadcasts extended EBCH coded frames to the destination and to a preassigned relay. After soft-decoding, the received sequences and obtaining the log-likelihood ratio (LLR) values, the relay constructs a product code by arranging the decoded bit sequences in rows and re-encoding them along the columns using a novel soft block encoding technique to obtain soft parity bits with different reliabilities that can be used as soft incremental redundancy (IR) that is forwarded to the destination. We compared the simulation results in additive white Gaussian noise (AWGN) channel with our previous work for decode-and-forward (DF) DTPC and with noncooperative case. The proposed system shows better bit error rate (BER) performance and less sensitivity to the relay's position.

Decoding algorithms for shortened-extended turbo product codes in WiMAX systems

The component codes of turbo product codes inWiMAX systems are extended Hamming codes and single parity check codes as well as their shortened forms. In this paper, three novel iterative decoding algorithms based on Chase, MAP algorithms and their combination are proposed for shortened-extended turbo product codes. The iterative decoding algorithm based on Chase algorithm is proposed to reduce the decoding complexity without any performance loss. An efficient MAP algorithm is then proposed to decode the component codes of shortened single parity check codes and shortened-extended Hamming codes. A comprehensive performance comparison of the proposed decoding schemes is conducted for three typical classes of turbo product codes in WiMAX OFDMA systems. The suitable decoding algorithms are recommended for different classes based on the simulation results.

Approximate performance analysis of coded OSTBC-OFDM systems over arbitrary correlated generalized ricean fading channels

A framework for analyzing the performance of coded OSTBC-OFDM systems over arbitrary correlated generalized Ricean fading channels is established. The moment generating function of the signal-to-noise ratio at the input to the channel decoder is derived assuming correlated transmitter and receiver antennas and correlated paths in frequency selective channels. The probability of outage, the pairwise error probability, and the bit error rate are then evaluated. Bit-interleaved and iteratively decoded turbo product codes, Gray encoded M-ary quadrature amplitude modulation, and other parameters of the IEEE 802.16 Standard are used to illustrate numerical results.

Non-sequential decoding algorithm for hard iterative turbo product codes - [transactions letters

In this letter, we propose a new decoding algorithm to improve the bit error rate performance of the hard-input hard-output (HIHO) turbo product codes (TPC) with hard iterative decoding. The proposed algorithm iteratively, but not sequentially, decodes the received TPC blocks based on the reliability of the constituent codes. Simulation results confirm a noticeable coding gain improvement using the proposed decoding process with respect to standard HIHO TPC decoding. An efficient implementation of the new technique offers a negligible additional complexity when the channel-bit error probability is less than 10-2.

Optical LDPC decoders for beyond 100 Gbits/s optical transmission

We present an optical low-density parity-check (LDPC) decoder suitable for implementation above 100 Gbits/s, which provides large coding gains when based on large-girth LDPC codes. We show that a basic building block, the probabilities multiplier circuit, can be implemented using a Mach-Zehnder interferometer, and we propose corresponding probabilistic-domain sum-product algorithm (SPA). We perform simulations of a fully parallel implementation employing girth-10 LDPC codes and proposed SPA. The girth-10 LDPC(24015,19212) code of the rate of 0.8 outperforms the BCH(128,113)xBCH(256,239) turbo-product code of the rate of 0.82 by 0.91 dB (for binary phase-shift keying at 100 Gbits/s and a bit error rate of 10(-9)), and provides a net effective coding gain of 10.09 dB.

Adaptive coding for frequency-hop transmission in mobile ad hoc networks with partial-band interference

Alternative protocols are presented for adapting the code from packet to packet in a mobile, wireless, ad hoc network that employs frequency hopping, coherent or noncoherent demodulation, and soft-decision decoding on channels with time-varying propagation loss and time-varying partial-band interference. The protocols can be employed with a wide range of codes and decoding algorithms. No channel measurements are needed, and no external side information is supplied to the receiver. Performance results are provided for packet transmissions that employ turbo product codes. The protocol performance results are compared with capacity limits and with the performance for hypothetical ideal protocols that use perfect channel-state information to select the codes that maximize the expected throughput.

Test-pattern-reduced decoding for turbo product codes with multi-error-correcting eBCH codes

We present a method to reduce the number of test patterns (TPs) decoded in the Chase-II algorithm for turbo product codes (TPCs) constructed with multi-error-correcting extended Bose-Chaudhuri-Hocquengem (eBCH) codes. We classify TPs into different conditions based on the relationship between syndromes and the number of errors so that TPs with the same codeword are not decoded except the one with the least number of errors. For eBCH with code length of 64, simulation results show that over 50% of TPs need not to be decoded without any performance degradation.

Enhanced Message Passing in Turbo Product Code

Turbo product code with single parity check (TPC/SPC) has demonstrated superior error correction capability over the conventional PRML channel. However, the performance usually suffers at higher code rate. A scheme to improve BER of TPC/SPC at higher code rate is proposed. By adding cyclic redundancy check (CRC) to TPC/SPC, a sub-block can be ensured error free after passing both the parity check and CRC. At the completion of each iteration, the messages from the error free sub-blocks are modified to greatly increase their confidence levels. The artificially high confidence level from those error free sub-block bits results in much more efficient iterations subsequently and greatly lowers the ultimate BER. It is found that enhanced message passing combined with noise prediction maximum likelihood (NPML) detection in the soft output Viterbi algorithm (SOVA) gives the best performance. Spinstand head/media signals passed through software channel are used to validate the channel performance.

Iterative reduced-search decoding for coded partial-response channels

The full-complexity soft-input/soft-output (SISO) detector based on the BCJR algorithm for coded partial-response channels has a computational complexity growing exponentially with channel memory length. In this letter, we propose a low complexity soft-output channel detector based on the Chase decoding algorithm, which was previously applied to decode turbo product codes. At each iteration, the proposed detector forms a candidate list using all possible combinations of bit patterns in the weakest indices based on tentative hard estimates and a priori information fed back from the outer decoder. To demonstrate the performance/complexity tradeoff of the proposed detector, simulation results over rate-8/9 turbo-coded EPR4 and ME/sup 2/PR4 channels are presented, respectively. It is shown that the proposed detector can significantly reduce the computational complexity with only a small performance loss compared to the BCJR algorithm.

Reed-Solomon Turbo Product Codes for Optical Communications: From Code Optimization to Decoder Design

Turbo product codes (TPCs) are an attractive solution to improve link budgets and reduce systems costs by relaxing the requirements on expensive optical devices in high capacity optical transport systems. In this paper, we investigate the use of Reed-Solomon (RS) turbo product codes for 40Gbps transmission over optical transport networks and 10Gbps transmission over passive optical networks. An algorithmic study is first performed in order to design RS TPCs that are compatible with the performance requirements imposed by the two applications. Then, a novel ultrahigh-speed parallel architecture for turbo decoding of product codes is described. A comparison with binary Bose-Chaudhuri-Hocquenghem (BCH) TPCs is performed. The results show that high-rate RS TPCs offer a better complexity/performance tradeoff than BCH TPCs for low-cost Gbps fiber optic communications.

Antenna selection for MIMO-OFDM systems

In this paper, a new subcarrier-by-subcarrier antenna selection scheme for a multiple input multiple output (MIMO) space–frequency block coded (SFBC) orthogonal frequency division multiplexing (OFDM) system concatenated with a turbo product code is presented. We examine the coding and diversity advantage of the SFBC-OFDM system with antenna selection using average SNR gain, outage probability and BER analysis validated by numerical simulation. The system performance of different forms of the proposed scheme is evaluated and compared. It is shown that the proposed scheme can greatly improve the performance of the conventional SFBC-OFDM systems.

A low complexity decoding algorithm for extended turbo product codes

In this letter, we propose a low complexity algorithm for extended turbo product codes by considering both the encoding and decoding aspects. For the encoding part, a new encoding scheme is presented for which the operations of looking up and fetching error patterns are no longer necessary, and thus the lookup table can be omitted. For the decoder, a new algorithm is proposed to extract the extrinsic information and reduce the redundancy. This new algorithm can reduce decoding complexity greatly and enhance the performance of the decoder. Simulation results are presented to show the effectiveness of the proposed scheme.

Shortened Turbo Product Codes: Encoding Design and Decoding Algorithm

Shortened turbo product codes (TPCs) have already been adopted in many standards. In this paper, we study shortened TPCs from two aspects, namely encoding design and decoding algorithm. To obtain different encoding block sizes, shortened-extended Hamming codes are used as the component codes of product codes in the IEEE 802.16 standard. To design a good structure for the shortened TPC, we compute the undetected error probability of its corresponding component codes. The component codes are shortened-extended Hamming codes, and their optimal generator polynomials are selected in terms of their undetected error probability. For the decoding algorithm, we present an efficient Chase decoding algorithm for shortened TPCs in flat fading channels. In the proposed scheme, the reliability factor used in Pyndiah's scheme is not needed; thus, the decoding complexity is greatly reduced by avoiding the normalization operation of the whole code word at each iteration. Simulation results are also presented to verify the performance of the proposed algorithm.

Performance characteristics and weight distribution analysis of turbo product code with Reed–Muller component codes

In this paper, we present simulation results for Reed–Muller (RM) turbo codes over AWGN and Rayleigh fading channels. We also compare the simulation results of turbo product codes and block turbo codes with RM component codes over an AWGN channel. We show that minimum distance is not important as far as the BER performance of long codes is concerned. The weight distribution of RM codes of different lengths and turbo product codes with first-order RM component codes are obtained and analyzed for their good performance. We show that the weight distribution asymptotically approaches that of random coding as the code length increases.

An Efficient Stopping Criterion for Turbo Product Codes

In this letter, a stopping criterion using the error- detecting capability of linear block codes is proposed for the decoding of turbo product codes. The iterative decoding is stopped when the outputs from the Chase decoder are valid codewords for all rows and columns simultaneously. Simulation shows that the proposed method can reduce about one and half iterations compared with an existing stopping method, without noticeable BER performance loss. Some modification has also been discussed which may further reduce the decoding complexity.