Degenerate asymmetric quantum concatenated codes for correcting biased quantum errors

In most practical quantum mechanical systems,quantum noise due to decoherence is highly biased towards dephasing.The quantum state suffers from phase flip noise much more seriously than from the bit flip noise.In this work,we construct new families of asymmetric quantum concatenated codes(AQCCs)to deal with such biased quantum noise.Our construction is based on a novel concatenation scheme for constructing AQCCs with large asymmetries,in which classical tensor product codes and concatenated codes are utilized to correct phase flip noise and bit flip noise,respectively.We generalize the original concatenation scheme to a more general case for better correcting degenerate errors.Moreover,we focus on constructing nonbinary AQCCs that are highly degenerate.Compared to previous literatures,AQCCs constructed in this paper show much better parameter performance than existed ones.Furthermore,we design the specific encoding circuit of the AQCCs.It is shown that our codes can be encoded more efficiently than standard quantum codes.

Improved Belief Propagation Decoder for LDPC-CRC-Polar Codes with Bit-Freezing

Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.

Iterative Decoding of Parallel Concatenated Block Codes and Coset Based MAP Decoding Algorithm for F24 Code

A multi dimensional concatenation scheme for block codes is introduced, in which information symbols are interleaved and re encoded for more than once. It provides a convenient platform to design high performance codes with flexible interleaver size. Coset based MAP soft in/soft out decoding algorithms are presented for the F24 code. Simulation results show that the proposed coding scheme can achieve high coding gain with flexible interleaver length and very low decoding complexity.

Decoding Technique of Concatenated HadamardCodes and Its Performance

The decoding technique of concatenated Hadamard codes and its performance are studied. Efficient soft in soft out decoding algorithms based on the fast Hadamard transform are developed. Performance required by CDMA mobile or PCS speech services, e.g. , BER=10 -3 , can be achieved at Eb/No =0.9 dB using short interleaving length of 192 bits.

Improved Design and SOVA Algorithm for Serial Concatenated Convolutional Code

To improve the performance of the short interleaved serial concatenated convolutional code(SCCC) with low decoding iterative times, the structure of Log MAP algorithm is introduced into the conventional SOVA decoder to improve its performance at short interleaving delay. The combination of Log MAP and SOVA avoids updating the matrices of the maximum path, and also makes a contribution to the requirement of short delay. The simulation results of several SCCCs show that the improved decoder can obtain satisfied performance with short frame interleaver and it is suitable to the high bit rate low delay communication systems.

SERIALLY CONCATENATED CONTINUOUS PHASE MODULATION WITH REDUCED ITERATIVE DEMODULATION AND DETECTION

A reduced state Soft Input Soft Output (SISO) a posteriori probability algorithm for Seri-ally Concatenated Continuous Phase Modulation (SCCPM) is proposed in this paper. Based on the Reduced State Sequence Detection (RSSD),it has more general form compared with other reduced state SISO algorithms. The proposed algorithm can greatly reduce the state number,thus leads to the computation complexity reduction. It also minimizes the degradation in Euclidean distance with decision feedback in the reduced state trellis. Analysis and simulation results show that the perform-ance degradation is little with proper reduction scheme.

Improved FEC Code Based on Concatenated Code for Optical Transmission Systems

The improved three novel schemes of the super forward error correction （super-FEC） concatenated codes are proposed after the development trend of long-haul optical transmission systems and the defects of the existing FEC codes have been analyzed. The performance simulation of the Reed-Solomon（RS）＋ Bose-Chaudhuri-Hocguenghem（BCH） inner-outer serial concatenated code is implemented and the conceptions of encoding/decoding the parallel-concatenated code are presented. Furthermore, the simulation results for the RS（255,239） ＋RS（255,239） code and the RS（255,239） ＋RS（255,223） code show that the two consecutive concatenated codes are a superior coding scheme with such advantages as the better error correction, moderate redundancy and easy realization compared to the classic RS（255,239） code and other codes, and their signal to noise ratio gains are respectively 2-3 dB more than that of the RS（255,239）code at the bit error rate of 1 × 10^-13. Finally, the frame structure of the novel consecutive concatenated code is arranged to lay a firm foundation in designing its hardware.

Study on New Concatenated Code in WDM Optical Transmission Systems

A new concatenated code of RS（255,239）＋BCH（2 040,1 930） code to he suitable for WDM optical transmission systems is proposed. The simulation resuhs show that this new concatenated code. compared with the RS（255,239）4-CSOC（k0/n0=6/7, J= 8） code in ITU-TG. 75.1, has a lower redundancy and better error-correction performance, furthermore, its net coding gain（NCG） is respectively 0. 46 dB, 0.43 dB morethanthatofRS（255,239）＋CSOC（k0/n0= 6/7, J= 8） code and BCH（3860,3824）＋BCH （2 040,1 930） code in ITU TG. 75. 1 at the third iteration for the bit error rate（BER） of 10^-12. Therefore, the new super forward error correction（Super-FEC） concatenated code can be better used in ultra long-haul, ultra large-capacity and ultra high-speed WDM optical communication systems.

A Theoretical Method for Estimating Performance of Reed-Solomon Codes Concatenated with Orthogonal Space-Time Block Codes

Based on the studies of Reed-Solomon codes and orthogonalspace-time block codes over Rayleigh fading channel, a theoreticalmethod for estimating performance of Reed-Solomon codes concatenatedwith orthogonal space- time block codes is presented in this paper.And an upper bound of the bit error rate is also obtained. It isshown through computer simulations that the signal-to-noise ratioreduces about 15 dB or more after orthogonal space-time block codesare concatenate with Reed-Solomon(15,6)codes over Rayleigh fadingchannel, when the bit error rate is 10^-4.

Multiple accumulated-crossover parallel concatenated SPC codes

By constructing an accumulated-crossover relationship in multiple parallel concatenated single parity check （M-PC-SPC） codes, a class of error-correcting codes, termed multiple accumulated-crossover parallel concatenated single parity check （M-ACPC-SPC） codes, is proposed. M-ACPC-SPC codes possess linear encoding complexity and can be decoded iteratively with low complexity by the sum-product algorithm （SPA）. Simulation results show that M-ACPC-SPC codes have lower error floors than M-PCSPC codes with the same dimension, and when the dimension is 5, M-ACPC-SPC codes achieve bit error rate （BER） better than （3, 6） regular low density parity check （LDPC） codes.

Improved iterative breadth-first detection algorithms for MIMO wireless systems

A reduced-complexity detection algorithm is proposed, which is applied to iterative receivers for multiple-input multiple-output （MIMO） systems. Unlike the exhaustive search over all the possible trans-mitted symbol vectors of the optimum maximum a posteriori probability （MAP） detector, the new algo-rithm evaluates only the symbol vectors that contribute significantly to the soft output of the detector. The algorithm is facilitated by carrying out the breadth-first search on a reconfigurable tree, constructed by computing the symbol reliability of each layer based on zero-forcing criterion and reordering the symbols according to the symbol reliabilities. Simulations are presented and the good performance of the new algo-rithm over a quasi-static Rayleigh channel even for relatively small list sizes are proved.

Optimum of Interleaving Schemes over Combined Channels

The optimum choice of key parameters in the interleaving schemes used in RS codes/Viterbi-decoded convolutional codes concatenated coding systems is discussed. At the same time the simulation results and other optional interleaving schemes are given.

A reduced state SISO iterative decoding algorithm for serially concatenated continuous phase modulation

In this paper, serially concatenated continuous phase modulation （SCCPM） system is analyzed and a reduced state soft input soft output （SlSO） a posteriori probability algorithm is proposed. Based on the reduced state sequence detection （RSSD）, it has the more general form compared with other reduced state SISO algorithms. The proposed algorithm can greatly reduce the state number, thus leads to the computation complexity reduction. It also minimizes the degradation in Euclidean distance with decision feedback in the reduced state trellis. Analysis and simulation results show that the performance degradation is little with proper reduction scheme.

Asymptotic bound on binary self-orthogonal codes

We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the in-formation rate R = 1/2, by our constructive lower bound, the relative minimum distance δ≈ 0.0595 (for GV bound, δ≈ 0.110). Moreover, we have proved that the binary self-orthogonal codes asymptotically achieve the Gilbert-Varshamov bound.

Improving the Structure of Multiple Dimension Turbo Codes Using Multiple Identical Component Encoders

In this paper,we propose an improved structure for M-dimension ( M ≥ 2)turbo codes using M identical component encoders. The presented structure only applies single recursive convolutional encoder to encode M interleaved versions of infor-mation sequence and single tail sequence to operate termination. For the commonly used two-dimension (M = 2) turbo codes,two cascade soft input soft output (SISO) decoders are detailed to de-code the corresponding codes. With the two cascade SISO decod-ers,this coding structure obviously outperforms traditional turbo codes at high code rates,especially,about 0.3 dB gain can be ob-tained at code rate 0.9 in additive white Gaussian noise channel with quadrature phase shift keying modulation. This makes the proposed coding structure very attractive for future radio commu-nication systems with high throughput requirements.

How to apply polar codes in high throughput space communications

This paper describes how to apply polar codes in high-throughput space communications.The high throughput space communications can enable terabit data rate capacity wideband wireless transmissions,and offer service availability of anywhere and anytime.The paper investigates the channel characteristics in space communications.The channels are lossy,time-varying,intermittent,long-latency,and with imperfect channel state information(CSI).In order to make the polar codes suitable for the space channel,some improvements and designs on the polar codes are provided in this paper.The encoding and decoding methods of polar codes are discussed,which are the key to determine the performance.We describe some rateless polar coding schemes that can guide the construction of suitable codes for time-varying channels with no-CSI in long-haul transmissions.Then,a high-rate parallel concatenation scheme of polar codes is introduced,which can improve the anti-interrupt ability of polar codes.Moreover,in order to support the massive connectivity requirements of future space communication networks,polar-coded sparse-code-multiple-access(SCMA)schemes are investigated.

SPC-APPM coded modulation for deep-space optical communications

A coded modulation scheme for deep-space optical communications is proposed, which is composed of an outer single- parity-check （SPC）-based product code, an interleaver, a bit-accumulator and a pulse-position modulation （PPM）. It is referred as SPC-APPM code, which is decoded with an iterativc demodulator-decoder using standard turbo-decoding techniques. Investigations show that the scheme has the advantages of low encoding and decoding complexities, good performance and flexible code rate for all rates above I/2. Meanwhile, simulation results demonstrate that the SPC-APPM provides the performance similar to the low-density parity-check-APPM （LDPC-APPM）, superior to the LDPC-PPM and product accumulate code-PPM （PA-PPM）, although inferior to serially concatenated PPM （SCPPM）. At the bit error rate （BER） of 105, the performance of SPC-APPM is about 0.7 dB better than LDPC-PPM and 1.2 dB better than PA-PPM.