High Coding Research Articles

A Repair-Efficient Coding for Distributed Storage Systems Under Piggybacking Framework

Piggybacking is an efficient framework to reduce the repair bandwidth of distributed storage systems, especially, when the systems meet the settings–maximum distance separable (MDS), high code rate, and a small number of substripes. Through an analysis on the repair ratio of a piggybacking construction, this paper reveals that the proportion $p_{p}$ of piggybacking protected stripes is the key to significantly decrease the repair bandwidth. Based on this analysis, this paper proposes a repair efficient coding under piggybacking framework (REPB) by considering various piggybacking protected stripes and MDS only protected stripes. The repair ratio of REPB tends to 0 and is close to theoretical cut-set bound, as the proportion $p_{p}$ is no longer fixed at 1/2. Furthermore, the proposed REPB codes enjoy low computational complexity in repair operation.

Mixed-resolution HEVC based multiview video codec for low bitrate transmission

There has been increasing demand for multiview video transmission over band limited channel over past years and various techniques have been proposed to fulfil this need. In this paper, a High Efficiency Video Codec (HEVC) based spatial resolution scaling type of mixed resolution coding model, MRHEVC-MVC, for frame interleaved multiview videos is presented. However, enabling the HEVC to encode video with different frame resolutions is a challenge due to the coding tree partitioning used by the codec. This has been overcome by super-imposing the low resolution replica of each full resolution frame on their respective decoded picture buffer and setting the remaining space of the frame buffer to zero. The codec’s reference frames structure is designed to efficiently encode frame interleaved multiview videos using a HEVC based mixed resolution codec. The proposed MRHEVC-MVC codec has been tested against the standard multiview extension of high efficiency video codec (MV-HEVC) for “Balloon”, “Newspaper1”, “Undo_Dancer”, “Kendo” and ““Poznan_Street” standard multiview video sequences. Results show that the proposed codec gives significantly higher coding performance to that of the MV-HEVC codec at low bitrate both subjectively and objectively.

A Flexible and Energy-Efficient Convolutional Neural Network Acceleration With Dedicated ISA and Accelerator

State-of-the-art convolutional neural networks (CNNs) usually have a large number of layers and filter weights which bring huge computation and communication overheads. A general purpose instruction set architecture (ISA) is flexible but has low code density and high power consumption. The existing CNN-specific accelerators are much more efficient but usually are inflexible or require a complex controller to handle the computation and data transfer of different CNNs. In this brief, we propose a new CNN-specific ISA which embeds the parallel computation and data reuse parameters in the instructions. An instruction generator deploys the instruction parameters according to the feature of CNNs and hardware’s computation and storage resources. In addition, a reconfigurable accelerator with 225 multipliers and 24 adder trees is realized to obtain efficient parallel computation and data transfer. Compared with x86 processors, our design has 392 times better energy efficiency and 16 times higher code density. Compared with other state-of-the-art accelerators, our solution has a higher flexibility to support all popular CNNs and a higher energy efficiency.

Reduced decoding time of LDPC code using convolutional code with Vitrebi decoding in Underwater Communication

Low Density Parity Check code is the more efficient technique to attain the minimal error rate in the underwater channel. To reduce the processing delay in the LDPC decoding, convolutional code with high code rate is used. The result showed that the BER of 10-4 can be obtained with Eb/No value of 20 for code rate of ½ and 12 for code rate of 1/8. It is also showed in result that the decoding time is reduced one-third for data size of 500 and one-tenth for the data size of 1500 bits.

A 9.52 dB NCG FEC Scheme and 162 b/Cycle Low-Complexity Product Decoder Architecture

Powerful Forward Error Correction (FEC) schemes are used in optical communications to achieve bit-error rates below $10^{-15}$. These FECs follow one of two approaches: concatenation of simpler hard-decision codes or usage of inherently powerful soft-decision codes. The first approach yields lower Net Coding Gains (NCGs), but can usually work at higher code rates and have lower complexity decoders. In this work, we propose a novel FEC scheme based on a product code and a post-processing technique. It can achieve an NCG of 9.52~dB at a BER of $10^{-15}$ and 9.96~dB at a BER of $10^{-18}$, an error-correction performance that sits between that of current hard-decision and soft-decision FECs. A decoder architecture is designed, tested on FPGA and synthesized in 65 nm CMOS technology: its 164 bits/cycle worst-case information throughput can reach 100 Gb/s at the achieved frequency of 609~MHz. Its complexity is shown to be lower than that of hard-decision decoders in literature, and an order of magnitude lower than the estimated complexity of soft-decision decoders.

Linear-time list recovery of high-rate expander codes

We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have applications to constructing efficiently list-decodable codes, as well as in compressed sensing and group testing. Previous list recoverable codes with linear-time decoding algorithms have all had rate at most 1/2; in contrast, our codes can have rate 1−ε for any ε>0. We can plug our high-rate codes into a construction of Alon and Luby (1996), recently highlighted by Meir (2014) to obtain linear-time list recoverable codes of arbitrary rates R, which approach the optimal trade-off between the number of non-trivial lists provided and the rate of the code.A slight strengthening of our result would imply linear-time and optimally list-decodable codes for all rates. Thus, our result is a step in the direction of solving this important problem.

Ultra-Light Decoder for Turbo Product Codes

This letter presents a novel low-complexity decoder for turbo product codes (TPCs). The new decoder, denoted as ultra-light decoder (ULD), can perform soft-decision decoding without an algebraic hard decision decoder, which is the core of conventional soft-decision decoders of block codes. Moreover, the unique structure of the ULD enables the design of a new approach to compute the minimum Euclidean distance at each decoding iteration. Therefore, the ULD offers significant complexity and delay reduction as compared with the conventional TPC decoders. Reducing the complexity and delay will enable using codes with high code rates to improve the system spectral efficiency or use powerful codes with low code rates to reduce the transmission power. The system bit-error rate is presented for binary and $M$ -ary modulation schemes over additive white Gaussian noise channels, and the coding gain is given for Rayleigh fading channels. The obtained numerical results show that the ULD offers coding gain that is comparable to the conventional TPC decoders under various system and channel conditions but with significantly lower complexity.

On the Girth of Tanner (3, 13) Quasi-Cyclic LDPC Codes

Girth is an important structural property of low-density parity-check (LDPC) codes. Motivated by the works on the girth of Tanner (3, 5), (3, 7), (3, 11), and (5, 7) quasi-cyclic (QC) LDPC codes, we, in this paper, study the girth of Tanner (3, 13) QC-LDPC codes of length $13p$ for $p$ being a prime of the form $(39m+1)$ . First, the cycle structure of Tanner (3, 13) QC-LDPC codes is analyzed, and the cycles of length lesser than 12 are divided into five equivalent classes. Based on each equivalent class, the existence of the cycles is equivalent to the solution of polynomial equations in a 39th unit root in the prime filed $\mathbb {F}_{p}$ . By solving these polynomial equations over $\mathbb {F}_{p}$ and summarizing the resulting candidate prime values, the girth of Tanner (3, 13) QC-LDPC codes is obtained. As an advantage, Tanner (3, 13) QC-LDPC codes have much higher code rates than Tanner (3, 5), (3, 7), (3, 11), and (5, 7) QC-LDPC codes, and provide a promising coding scheme for the data storage systems and optical communications.

Construction and Decoding of Rate‐Compatible Globally Coupled LDPC Codes

This paper presents a family of rate‐compatible (RC) globally coupled low‐density parity‐check (GC‐LDPC) codes, which is constructed by combining algebraic construction method and graph extension. Specifically, the highest rate code is constructed using the algebraic method and the codes of lower rates are formed by successively extending the graph of the higher rate codes. The proposed rate‐compatible codes provide more flexibility in code rate and guarantee the structural property of algebraic construction. It is confirmed, by numerical simulations over the AWGN channel, that the proposed codes have better performances than their counterpart GC‐LDPC codes formed by the classical method and exhibit an approximately uniform gap to the capacity over a wide range of rates. Furthermore, a modified two-phase local/global iterative decoding scheme for GC‐LDPC codes is proposed. Numerical results show that the proposed decoding scheme can reduce the unnecessary cost of local decoder at low and moderate SNRs, without any increase in the number of decoding iterations in the global decoder at high SNRs.

Explicit Constructions of High-Rate MSR Codes with Optimal Access Property over Small Finite Fields

Up to now, many $(k+r,k,N)$ minimum-storage regenerating (MSR) codes with $k$ information nodes, $r$ parity nodes, and node capacity $N$ have been proposed. However, most of them are constructed over a relatively large finite field. In this paper, we propose three high-rate MSR codes over small finite fields. First, the new MSR code $\mathcal {C}_{1}$ with the optimal access property for all nodes is constructed over small finite field $\mathbb {F}_{q}$ , for example $q=3$ for even $r$ or $q\ge r+1$ for odd $r$ , which is much smaller than that of the known one given by Ye and Barg. Further, considering to reduce the node capacity, another new MSR code $\mathcal {C}_{2}$ over $\mathbb {F}_{q}$ with $q\ge r+2$ is generated based on $\mathcal {C}_{1}$ , which can effectively reduce the node capacity of $\mathcal {C}_{1}$ by a factor of $r^{r-1}$ . However, only the first $k$ nodes of $\mathcal {C}_{2}$ have the optimal access property. Therefore, the new MSR code $\mathcal {C}_{3}$ over $\mathbb {F}_{q}$ with $q\ge r+2$ which has the optimal access property for all nodes is proposed by modifying $\mathcal {C}_{2}$ . Notably, in contrast to $\mathcal {C}_{1}$ , the node capacity of $\mathcal {C}_{3}$ is decreased by a factor of $r^{r-2}$ .

Low-Latency CRC Calculation in Turbo-Code Decoding

Design of Turbo-Code decoders for the 3GPP LTE/LTE-A standard focuses on achieving a high-throughput of up to 1 Gbps with low decoding latencies at very high code rates. At code rates close to one, as specified in LTE/LTE-A, the decoding process can oscillate. Although the decoder converges to a valid code word after half-iteration i, after half-iteration \(i+1\) the decoded code word is invalid again. To circumvent this, the CRC that is attached to each code word must be evaluated after each half-iteration. We present a generalized architecture for calculating the CRC On-the-fly during both non-interleaved and interleaved half-iterations and thus explicitly taking into account the requirements for low-latency Turbo-Code decoding. Further, we investigate the latency-, and energy savings provided by employing this calculation scheme. Lastly, we give post layout synthesis results for a case study implementation in state-of-the-art 28 nm FDSOI technology.

An Expurgating-Based Method for Constructing Multi-Rate Non-Binary Quasi-Cyclic LDPC Codes

This letter presents a new method for constructing the multi-rate non-binary quasi-cyclic low-density parity-check codes by expurgating a high-rate mother code. A matrix-theoretic approach is applied to design the parity-check matrices of the proposed codes. The resulting codes possess a quasi-cyclic structure, which is desirable for hardware implementations of the encoder and decoder. The codes can also be encoded directly with parity-check matrices due to the block dual-diagonal structure. Simulation results show that the codes can achieve good performance within a wide range of code rates both in the waterfall region and in the error-floor region.

Information rates of probabilistically shaped coded modulation for a multi-span fiber-optic communication system with 64QAM

This paper studies probabilistic shaping in a multi-span wavelength-division multiplexing optical fiber system with 64-ary quadrature amplitude modulation (QAM) input. In split-step fiber simulations and via an enhanced Gaussian noise model, three figures of merit are investigated, which are signal-to-noise ratio (SNR), achievable information rate (AIR) for capacity-achieving forward error correction (FEC) with bit-metric decoding, and the information rate achieved with low-density parity-check (LDPC) FEC. For the considered system parameters and different shaped input distributions, shaping is found to decrease the SNR by 0.3 dB yet simultaneously increases the AIR by up to 0.4 bit per 4D-symbol. The information rates of LDPC-coded modulation with shaped 64QAM input are improved by up to 0.74 bit per 4D-symbol, which is larger than the shaping gain when considering AIRs. This increase is attributed to the reduced coding gap of the higher-rate code that is used for decoding the nonuniform QAM input.

위성 방송 시스템에서 최적의 고전송 효율 기법 연구

차세대 위성 방송 시스템에서는 빠른 전송 효율과 신뢰도 있는 통신에 대한 요구가 지속적으로 증가하고 있다. 전송 효율을 높이고 성능을 향상시키기 위해 새로운 위성 표준 인 DVB-S3 (Digital Video Broadcasting - Satellite - Third Generation) 시스템에서는 Nyquist 전송률 보다 빠르게 전송하는 FTN (Faster Than Nyquist) 방식이 대두되고 있다. 이러한 요구에 맞춰 본 논문에서는 전송 효율 향상을 위한 세 가지 방식에 대한 성능을 비교 분석하였다. 기존의 LDPC 부호기에서 고 부호화율 방식과 LDPC 복호화 과정에서 생선된 check node를 이용하여 bit node를 puncturing시켜 부호화율 증가 시키는 punctured LDPC 방식, 그리고 Nyquist 속도보다 빠르게 전송하는 FTN 방식이 고려된다. 시뮬레이션을 통해, 세 가지 방식을 동일 전송률 관점에서 성능을 비교한 결과 FTN 방식은 동일한 전송 효율을 유지하면서 성능 면에서 가장 효율적임을 확인하였다. In next generation satellite broadcasting system, requirement of high throughput efficiency has been increasing continuously. To increase throughput efficiency and improve bit error performance simultaneously, FTN method and LDPC codes are employed in new sattelite standard, DVB-S3 system. This paper considered three kinds of methods for increase throughput efficiency. Firstly, as conventional one, high coding rate parity matrix in LDPC encoder is considered. Secondly, punctured coding scheme which delete the coded symbols according to appropriate rules is considered. Lastly, FTN method which transmit fater than Nyquist rate is considered. Among of three kinds of methods, FTN method is most efficient in aspect to performance while maintain same throughput efficiency.

Code-Aided DOA Estimation From Turbo-Coded QAM Transmissions: Analytical CRLBs and Maximum Likelihood Estimator

In this paper, we address the problem of direction of arrival (DOA) estimation from turbo-coded square-QAM-modulated transmissions. We devise a new code-aware direction finding concept, derived from maximum likelihood (ML) theory, wherein the soft information provided by the soft-input soft-output decoder, in the form of log-likelihood ratios, is exploited to assist the estimation process. At each turbo iteration, the decoder output is used to refine the ML DOA estimate. The latter is in turn used to perform a more focused receiving beamforming thereby providing more reliable information-bearing sequences for the next turbo iteration. In order to benchmark the new estimator, we also derive the analytical expressions for the exact Cramer-Rao lower bounds (CRLBs) of code-aided (CA) DOA estimates. Simulation results will show that the new CA direction finding scheme lies between the two traditional schemes of completely non-data-aided and data-aided (DA) estimations. Huge performance improvements are achieved by embedding the direction finding and receive beamforming tasks into the turbo iteration loop. Moreover, the new CA DOA estimator reaches the new CA CRLBs over a wide range of practical SNRs thereby confirming its statistical efficiency. As expected intuitively, its performance further improves at higher coding rates and/or lower modulation orders.

Efficiently Decoding Reed–Muller Codes From Random Errors

Reed–Muller (RM) codes encode an $m$ -variate polynomial of degree at most $r$ by evaluating it on all points in $\{0,1\}^{m}$ . We denote this code by $RM(r,m)$ . The minimum distance of $RM(r,m)$ is $2^{m-r}$ and so it cannot correct more than half that number of errors in the worst case. For random errors one may hope for a better result. In this paper we give an efficient algorithm (in the block length $n=2^{m}$ ) for decoding random errors in RM codes far beyond the minimum distance. Specifically, for low-rate codes (of degree $r=o(\sqrt {m})$ ), we can correct a random set of $(1/2-o(1))n$ errors with high probability. For high rate codes (of degree $m-r$ for $r=o(\sqrt {m/\log m})$ ), we can correct roughly $m^{r/2}$ errors. More generally, for any integer $r$ , our algorithm can correct any error pattern in $RM(m-(2r+2),m)$ , for which the same erasure pattern can be corrected in $RM(m-(r+1),m)$ . The results above are obtained by applying recent results of Abbe, Shpilka, and Wigderson (STOC, 2015) and Kudekar et al. (STOC, 2016) regarding the ability of RM codes to correct random erasures. The algorithm is based on solving a carefully defined set of linear equations and thus it is significantly different than other algorithms for decoding RM codes that are based on the recursive structure of the code. It can be seen as a more explicit proof of a result of Abbe et al. that shows a reduction from correcting erasures to correcting errors, and it also bares some similarities with the error-locating pair method of Pellikaan, Duursma, and Kotter that generalizes the Berlekamp–Welch algorithm for decoding Reed–Solomon codes.

Integer codes correcting single errors and burst asymmetric errors within a byte

In this paper we present a class of integer codes that are suitable for use in optical networks without optical amplifiers. The presented codes can correct all single errors and all burst asymmetric errors within a b-bit byte. Compared to other classes of integer codes, these codes have two advantages: first, they are less demanding in terms of memory needs, and second, they have higher code rates. Thanks to these features, the proposed codes are faster to decode, and thus simpler to implement.

On Constructions of a Class of Binary Locally Repairable Codes With Multiple Repair Groups

Recently, Hao and Xia noted a connection between a class of binary locally repairable codes (LRCs) with multiple repair groups and binary low-density parity-check (LDPC) codes, and proposed a framework for constructing binary LRCs from LDPC codes as well as three specific constructions of binary LRCs that can achieve a distance bound. The connection between binary LRCs and LDPC codes, however, has not yet been fully disclosed and constructions of binary LRCs that can achieve the distance bound remain largely unknown. Accordingly, this paper comments on the connection and presents two infinite families of binary LRCs that can achieve the distance bound, based on circulant permutation matrices and affine permutation matrices. The proposed LRCs generalize the promising construction of high-rate codes proposed by Hao and Xia, and offer larger relative distances with the same or higher code rates when compared with other competitive codes.

Association between Health Information Technology and Case Mix Index.

ObjectivesHealth information technology (IT) can assist healthcare providers in ordering medication and adhering to guidelines while improving communication among providers and the quality of care. However, the relationship between health IT and Case Mix Index (CMI) has not been thoroughly investigated; therefore, this study aimed to clarify this relationship.MethodsTo examine the effect of health IT on CMI, a generalized estimation equation (GEE) was applied to two years of California hospital data.ResultsWe found that IT was positively associated with CMI, indicating that increased IT adoption could lead to a higher CMI or billing though DRG up-coding. This implies that hospitals' revenue could increase around $40,000 by increasing IT investment by 10%.ConclusionsThe positive association between IT and CMI implies that IT adoption itself could lead to higher patient billings. Generally, a higher CMI in a hospital indicates that the hospital provides expensive services with higher coding and therefore receives more money from patients. Therefore, measures to prevent upcoding through IT systems should be implemented.

Double-pulse pair Brillouin optical correlation-domain analysis.

Brillouin optical correlation-domain analysis (B-OCDA) allows for distributed measurements of strain and temperature with sub-cm resolution. Time-multiplexing techniques have previously extended B-OCDA to the monitoring of many km of fiber and two million resolution points. Thus far, however, the number of scans of correlation peaks positions, necessary to cover the fiber under test, was restricted to the order of 100 or more. In this work we report a B-OCDA protocol that is able to address an entire fiber using only 11 pairs of position scans per choice of frequency. The measurements protocol relies on a merger between B-OCDA principles and double-pulse-pair analysis, previously incorporated in time-domain Brillouin sensors. Phase coding of the pump and signal waves with a repeating, short and high-rate code stimulates Brillouin interactions in a large number of narrow correlation peaks, with substantial temporal overlap. Unambiguous measurements are achieved by repeating each experiment twice, using a pair of pump pulses of different durations, and subtracting the two output traces. The principle is demonstrated in the analysis of a 43 m-long fiber with 2.7 cm resolution. Several local hot-spots are properly identified in the measurements. The experimental uncertainty in the measurement of the local Brillouin frequency shift is estimated as ± 1.9 MHz. The proposed method requires broader detection bandwidth and a larger number of averages than those of previous time-gated B-OCDA setups. Hence the overall number of measurements is similar to that of previous setups.