Non-uniform Quantization Scheme Research Articles

멀티 레벨 셀 낸드 플래시 메모리용 적응적 양자화기 설계

An adaptive non-uniform quantization scheme is proposed for soft-decision error correction in NAND flash memory. Even though the conventional maximizing mutual information (MMI) quantizer shows the optimal post-FEC (forward error correction) bit error rate (BER) performance, this quantization scheme demands heavy computational overheads due to the exhaustive search to find the optimal parameter values. The proposed quantization scheme has a simple structure that is constructed by only six parameters, and the optimal values of them are found by maximizing the mutual information between the input and the output symbols. It is demonstrated that the proposed quantization scheme improves the BER performance of soft-decision decoding with only small computational overheads.

A memory efficient parallel layered QC-LDPC decoder for CMMB systems

This paper presents a memory efficient architecture of layered decoder for the dual-rate LDPC codes in the China Multimedia Mobile Broadcasting (CMMB) system. An efficient scheme for reducing the memory block number is proposed to increase the memory usage efficiency, so that the quantity of memory bits, decoder area and power consumption is significantly reduced. At the same time, the memory structure keeps the “one cycle one layer access” timing schedule to achieve high decoding throughput. Furthermore, the early termination strategy is employed to further increase the throughput; a non-uniform quantization scheme and an area efficient calculation module are developed to further improve the memory efficiency and hardware resource efficiency, respectively. By using SMIC 130nm 1P7M CMOS process, the decoder is implemented and the core area is 5.29mm2. The total memory bits consumption is only 130.5K which consumes 2.53mm2 memory area.

Design of Fixed-Width Multipliers With Linear Compensation Function

This paper focuses on fixed-width multipliers with linear compensation function by investigating in detail the effect of coefficients quantization. New fixed-width multiplier topologies, with different accuracy versus hardware complexity trade-off, are obtained by varying the quantization scheme. Two topologies are in particular selected as the most effective ones. The first one is based on a uniform coefficient quantization, while the second topology uses a nonuniform quantization scheme. The novel fixed-width multiplier topologies exhibit better accuracy with respect to previous solutions, close to the theoretical lower bound.

Min-Sum Decoder Architectures With Reduced Word Length for LDPC Codes

In this paper, we propose an improvement of the normalized min-sum (MS) decoding algorithm and novel MS decoder architectures with reduced word length using nonuniform quantization schemes for low-density parity-check (LDPC) codes. The proposed normalized MS algorithm introduces a more exact adjustment with two optimized correction factors for check-node-updating computations, while the conventional normalized MS algorithm applies only one correction factor. The proposed algorithm provides a significant performance gain without any additional computation or hardware complexity. The finite word-length analysis in implementing an LDPC decoder is a very important factor since it directly impacts the size of memory to store the intrinsic and extrinsic messages and the overall hardware area in the partially parallel LDPC decoder. The proposed nonuniform quantization scheme can reduce the finite word length while achieving similar performances compared to a conventional quantization scheme. From simulation results, it is shown that the proposed 4-bit nonuniform quantization scheme achieves an acceptable decoding performance, unlike the conventional 4-bit uniform quantization scheme. Finally, the proposed MS decoder architectures by the nonuniform quantization scheme provide significant reductions of 20% and up to 8% for the memory area and combinational logic area, respectively, compared to the conventional 5-bit ones.

Flexible LDPC Decoder Design for Multigigabit-per-Second Applications

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Low-density parity-check (LDPC) codes are one of the most promising error-correcting codes approaching Shannon capacity and have been adopted in many applications. However, the efficient implementation of high-throughput LDPC decoders adaptable for various channel conditions still remains challenging. In this paper, a low-complexity reconfigurable VLSI architecture for high-speed LDPC decoders is presented. Shift-LDPC codes are incorporated within the design and have shown not only comparable decoding performance to computer-generated random codes but also high hardware efficiency in high-speed applications. The single-minimum Min-Sum decoding scheme and the nonuniform quantization scheme are explored to reduce the complexity of computing core and the memory requirement. The well-known Benes network is employed to construct the configurable permutation network to support multiple shift-LDPC codes with various code parameters. The ASIC implementation results of an (8192, 7168) (4, 32)-regular shift-LDPC decoder demonstrate a maximum decoding throughput of 3.6 Gbits/s at 16 iterations, which outperforms the state-of-the-art design for high-speed flexible LDPC decoders by many times with even less hardware. </para>

Variable non-uniform quantized belief propagation algorithm for LDPC decoding

Non-uniform quantization for messages in Low-Density Parity-Check (LDPC) decoding can reduce implementation complexity and mitigate performance loss. But the distribution of messages varies in the iterative decoding. This letter proposes a variable non-uniform quantized Belief Propagation (BP) algorithm. The BP decoding is analyzed by density evolution with Gaussian approximation. Since the probability density of messages can be well approximated by Gaussian distribution, by the unbiased estimation of variance, the distribution of messages can be tracked during the iteration. Thus the non-uniform quantization scheme can be optimized to minimize the distortion. Simulation results show that the variable non-uniform quantization scheme can achieve better error rate performance and faster decoding convergence than the conventional non-uniform quantization and uniform quantization schemes.

Low-Complexity High-Speed Decoder Design for Quasi-Cyclic LDPC Codes

This paper studies low-complexity high-speed decoder architectures for quasi-cyclic low density parity check (QC-LDPC) codes. Algorithmic transformation and architectural level optimization are incorporated to reduce the critical path. Enhanced partially parallel decoding architectures are proposed to linearly increase the throughput of conventional partially parallel decoders through introducing a small percentage of extra hardware. Based on the proposed architectures, a (8176, 7154) Euclidian geometry-based QC-LDPC code decoder is implemented on Xilinx field programmable gate array (FPGA) Virtex-II 6000, where an efficient nonuniform quantization scheme is employed to reduce the size of memories storing soft messages. FPGA implementation results show that the proposed decoder can achieve a maximum (source data) decoding throughput of 172 Mb/s at 15 iterations

New method for reducing GOP-boundary artifacts in wavelet-based video coding

The conventional motion-compensated temporal wavelet transform using the 5/3 filter produces GOP-boundary artifacts, i.e., a drop in picture quality at the boundaries of groups of pictures (GOP). A simple and efficient method is proposed in this paper to reduce the GOP-boundary artifacts and improve the overall performance of the transform. With this method, a group of pictures to be temporally transformed is extended by boundary repetition to one side and by symmetrical extension to the other side. The sub-sampling rule changes from one level to another during the multi-level transform. In addition, a non-uniform quantization scheme is employed. This method does not require any additional computation or memory. Experimental results of video coding with six test sequences show that this method outperforms the conventional method, providing a coding gain of 0.27 dB in terms of average PSNR and up to 1.95 dB in terms of minimum PSNR

Capacity Analysis for Finite-State Markov Mapping of Flat-Fading Channels

In this paper, time-varying flat-fading channels are modeled as first-order finite-state Markov channels (FSMC). The effect of this modeling on the channel information capacity is addressed. The approximation accuracy of the first-order memory assumption in the Markov model is validated by comparing the FSMC capacity with the channel capacity assuming perfect state information at the receiver side. The results indicate that the first-order Markovian assumption is accurate for normalized Doppler frequencies f/sub d/T /spl lsim/ 0.01, in amplitude-only quantization of the channel gain for noncoherent binary signaling. In phase-only and joint phase and amplitude quantization of the channel gain for coherent binary signaling, the first-order Markovian assumption is accurate for f/sub d/T /spl lsim/ 0.001. Furthermore, the effect of channel quantization thresholds on the FSMC capacity is studied. In high signal-to-noise ratio (SNR) conditions, nonuniform two-level amplitude quantization scheme outperforms equiprobable quantization method by 0.8-1.5 dB.

DOA estimation based on the database retrieval technique with nonuniform quantization and clustering

A direction-of-arrival (DOA) estimation method using an array antenna has been developed based on a database retrieval technique. This method uses a database consisting of a set of correlation matrices of the array output vectors for various combinations of the quantized angles and signal powers. When a correlation matrix is estimated from an observed output vector, several correlation matrices close to the estimated one are searched out from the database, and the DOA is estimated based on the retrieved data. This method gives an accurate estimation, but the use of uniform quantization step size requires a large amount of storage space. In this paper, the relation between the quantization step size and the estimation accuracy is analyzed, and a nonuniform quantization scheme is developed to reduce the database size without sacrificing the estimation accuracy. A clustering technique is also introduced to alleviate the performance degradation caused by the retrieval of data which have similar correlation matrices but have much different angles. We show by simulations that the nonuniform quantization reduces the database size and the clustering improves the estimation accuracy, and that the proposed method is applicable to the array of three elements at the present.

In-loop atom modulus quantization for matching pursuit and its application to video coding

This paper provides a precise analytical study of the selection and modulus quantization of matching pursuit (MP) coefficients. We demonstrate that an optimal rate-distortion trade-off is achieved by selecting the atoms up to a quality-dependent threshold, and by defining the modulus quantizer in terms of that threshold. In doing so, we take into account quantization error re-injection resulting from inserting the modulus quantizer inside the MP atom computation loop. In-loop quantization not only improves coding performance, but also affects the optimal quantizer design for both uniform and nonuniform quantization. We measure the impact of our work in the context of video coding. For both uniform and nonuniform quantization, the precise understanding of the relation between atom selection and quantization results in significant improvements in terms of coding efficiency. At high bitrates, the proposed nonuniform quantization scheme results in 0.5 to 2 dB improvement over the previous method.

Efficient dynamic focus control for three-dimensional imaging using two-dimensional arrays.

Dynamic receive focusing in ultrasonic array imaging involves extensive real-time computations and data communication. Particularly for three-dimensional imaging, using fully sampled, two-dimensional arrays, implementation of dynamic focusing can be extremely complicated because of the large channel count. In this paper, an efficient dynamic focus control scheme for a delay-and-sum-based beamformer is proposed. The scheme simplifies dynamic focus control by exploiting the range-dependent characteristics of the focusing delay. Specifically, the overall delay is divided into a range-independent steering term and a range-dependent focusing term. Because the focusing term is inversely proportional to range, approximation can be made to simplify dynamic focus control significantly at the price of minimal degradation in focusing quality at shallow depths. In addition, the aperture growth controlled by a constant f/number can also be utilized to devise a non-uniform quantization scheme for the focusing delay values. Efficacy of the proposed scheme is demonstrated using simulated beam plots of a fully sampled, two-dimensional array. Design procedures are also described in detail in this paper. One design example shows that, with the proposed dynamic focus control scheme, a 4096-element array only requires 227 independent controllers for the range-dependent focusing term. Moreover, only 28 non-uniform quantization levels are required to achieve the same focusing quality as that of a conventional scheme with 784 uniform quantization levels. The beam plots of a fully sampled array show that sidelobes are slightly increased below the -30 dB level for imaging depths less than 3 cm. At greater depths, there is no observable degradation.