Small Block Size Research Articles

An Arithmetic over GF (2^5) Tt Implement in ECC

The potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized by Diffe and Hellman in 1976. Although the discrete logarithm problem as first employed by them was defined explicitly as the problem of finding logarithms with respect to a generator in the multiplicative group of the integers module a prime, this idea can be extended to arbitrary groups and in particular, to elliptic curve groups. The resulting public – key systems provide relatively small block size, high speed, and high security. In this paper an efficient arithmetic for operations over elements of GF(2 5 ) represented in normal basis is presented. The arithmetic is applicable in public-key cryptography.

A Low-Complexity Solution to Decode Diversity-Oriented Block Codes in MIMO Systems with Inter-Symbol Interference

In this paper we first propose a block-code based general model to combat the Inter-Symbol Interference (ISI) caused by frequency selective channels in a Multi-Input Multi-Output (MIMO) system and/or by asynchronous cooperative transmissions. The general model is not only exemplified by the Time-Reversed Space-Time Block Code (TR-STBC) scheme, but also by the Asynchronous Cooperative Liner Dispersion Codes (ACLDC) scheme. In these schemes a guard interval has to be inserted between adjacent transmission blocks to mitigate the effect of ISI. Consequently, this could degrade the effective symbol rate for a small block size. A larger block size would enhance the effective symbol rate and also substantially increase the decoding complexity. In the general model proposed in this paper, we further present a novel low-complexity breadth-adjustable tree-search algorithm and compare it with Sphere-Decoding (SD) based algorithms. With simulation results we will illustrate that our algorithm is able to achieve the optimal performance in terms of Bit Error Rate (BER) with a complexity much lower than the SD-based algorithms, whether the ACLDC or TR-STBC scheme is employed. Through simulations we further demonstrate that when the block size of the ACLDC is equivalent to 20, the complexity of the proposed algorithm is only a fraction of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> that of the Maximum Likelihood (ML) algorithm. This would allow us to practically enhance the effective symbol rate without any performance degradation.

An orthogonal polynomials transform-based variable block size adaptive vector quantisation for colour image coding

In this paper, a new adaptive vector quantisation with variable block size based on orthogonal polynomials is proposed for colour image coding. The input colour image is partitioned into fixed larger block sizes and the homogeneity/complexity of the local region is tested with the mean-normalised variance classifier. The homogeneous regions are encoded with fixed larger blocks and the complex regions are further divided into smaller block sizes for encoding as it gives the wealth of low-level information such as the high detail and high number of contrast edges. The integer-based orthogonal polynomials transform is then applied on the variable block sizes utilising the inter-correlation property of individual colour planes and interactions among the colour planes so as to reduce the vector dimension and hence the less computational cost. The proposed technique generates two dynamic codebooks and two backup codebooks adaptively and use rate-distortion cost criteria to encode both the homogeneous and complex regions separately. Since the proposed method encodes all the three colour components in single pass, the colour image encoding time is slightly higher than that of grey scale image coding but in contrast to three times in the existing colour image coding techniques.

Distributed source coding using chaos-based cryptosystem

A distributed source coding scheme is proposed by incorporating a chaos-based cryptosystem in the Slepian–Wolf coding. The punctured codeword generated by the chaos-based cryptosystem results in ambiguity at the decoder side. This ambiguity can be removed by the maximum a posteriori decoding with the help of side information. In this way, encryption and source coding are performed simultaneously. This leads to a simple encoder structure with low implementation complexity. Simulation results show that the encoder complexity is lower than that of existing distributed source coding schemes. Moreover, at small block size, the proposed scheme has a performance comparable to existing distributed source coding schemes.

Relative SAD-based Inter Mode Decision Algorithm for H.264/AVC Video Standard

In this paper, a new relative sum of absolute difference (RSAD) based inter mode decision algorithm is proposed for H.264/AVC video standard. The main idea is to determine the best inter mode based on RSAD cost instead of the rate-distortion cost. This approach can avoid most of the computationally intensive processes in the H.264/AVC mode decision, such as integer transform, quantization, variable length coding and pixelreconstruction. Besides, it can solve the problem of SADbased cost function for H.264/AVC mode decision in biasing to the smaller block size modes, as they are normally achieving higher prediction accuracy. It is demonstrated by experimental results that the proposed RSAD-based mode decision algorithm can reduce 60% to 68% of the H.264/AVC total encoding time with negligible degradation in the rate-distortion performance. The proposed algorithm is also combined with SKIP mode early termination algorithm for further time saving and computation reduction. The enhanced algorithm with SKIP mode early termination technique could save up to 10% of the encoding time with only a little rate-distortion degradation.

THE M/G/1-TYPE MARKOV CHAIN WITH RESTRICTED TRANSITIONS AND ITS APPLICATION TO QUEUES WITH BATCH ARRIVALS

We consider M/G/1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure—referred to as restricted downward transitions—can be exploited to speed up the computation of the stationary probability vector of the chain. To this end we define a new M/G/1-type Markov chain with a smaller block size, the G matrix of which is used to find the original chain's G matrix. This approach is then used to analyze the BMAP/PH/1 queue and the BMAP[2]/PH[2]/1 preemptive priority queue, yielding significant reductions in computation time.

Focusing on the Flood

Focusing on the Flood

Motion Refinement Based Progressive Side-Information Estimation for Wyner-Ziv Video Coding

During the past ten years, Wyner-Ziv video coding (WZVC) has gained a lot of research interests because of its unique characteristics of "simple encoding, complex de coding." However, the performance gap between WZVC and conventional video coding has never been closed to the point promised by the information theory. In this paper, we illustrate the chicken-and-egg dilemma encountered in WZVC: high efficiency WZVC requires good estimation of side information (SI); however, good SI estimation is not possible for the decoder without access to the decoded current frame. To resolve such a dilemma, we present and advocate a framework that explores an important concept of decoder-side progressive-learning. More specifically, a decoder-side multi-resolution motion refinement (MRMR) scheme is proposed, where the decoder is able to learn from the already-decoded lower-resolution data to refine the motion estimation (ME), which in turn greatly improves the SI quality as well as the coding efficiency for the higher resolution data. Theoretical analysis shows that at high rates, decoder-side MRMR outperforms motion extrapolation by as much as 5 dB, while falling behind conventional encoder-side inter-frame ME by only about 1.5 dB. In addition, since decoder-side ME does not suffer from the bit-rate overhead in transmitting the motion information, further performance gain can be achieved for decoder-side MRMR by incorporating fractional-pel motion search, block matching with smaller block sizes, and multiple hypothesis prediction. We also present a practical WZVC implementation with MRMR, which shows comparable coding performance as H.264 at very high bit rates.

H.264/AVC에서 성능 향상을 위한 단방향의 4X4 인트라 예측 모드

본 논문에서는 H.264/AVC의 성능향상을 위해 단방향 예측에 의한 <TEX>$4{\times}4$</TEX> 인트라 부호화 방법을 제안한다. 최신의 동영상 압축 표준인 H.264/AVC에서는 <TEX>$16{\times}16$</TEX>과 <TEX>$4{\times}4$</TEX> 인트라 예측 방법을 사용하고 있다. <TEX>$4{\times}4$</TEX> 인트라 예측 방법은 예측 블록의 크기가 작기 때문에 <TEX>$16{\times}16$</TEX> 예측 방법과 비교하여 상대적으로 복잡한 영역에서 보다 정밀한 예측이 가능하고, <TEX>$16{\times}16$</TEX> 인트라 예측 방법은 <TEX>$4{\times}4$</TEX> 예측 방법에 비해 상대적으로 큰 예측 블록을 사용하여 예측 방향정보를 적게 전송함으로써 평편한 영역에서 보다 높은 효율로 부호화할 수 있는 특징이 있다. 제안하는 방법은 매크로블록(Macroblock)을 부호화하기 위해 <TEX>$4{\times}4$</TEX> 블록 단위로 예측하여 예측블록의 정밀도를 높이고, 동시에 모두 같은 방향으로 예측하여 예측 방향 정보를 줄임으로써 부호화 효율을 높이는 효과가 있다. 실험 결과, 제안하는 단방향의 <TEX>$4{\times}4$</TEX> 인트라 예측 방법은 기존 H.264/AVC의 <TEX>$16{\times}16$</TEX> 예측 방법과의 툴 단위 성능 비교에서 약 10.47% 정도의 비트 감소를 보인다. 또한, <TEX>$16{\times}16$</TEX> 및 <TEX>$4{\times}4$</TEX> 예측 방법을 모두 적용한 것과 두 가지 방법에 제안한 방법을 추가로 적용했을 때의 성능 비교에서는 평균적으로 약 1.57% 정도의 비트 감소가 있음을 확인할 수 있다. In this paper, we propose a new <TEX>$4{\times}4$</TEX> intra coding method by unidirectional prediction for improvement of intra-frame coding efficiency of H.264/AVC. There are <TEX>$4{\times}4$</TEX>, <TEX>$8{\times}8$</TEX>, and <TEX>$16{\times}16$</TEX> intra prediction modes in the current H.264/AVC. For the <TEX>$4{\times}4$</TEX> intra prediction, coding efficiency is achieved by accurate prediction with small block size in relatively complicated regions, and the <TEX>$16{\times}16$</TEX> intra prediction method can predict more accurately compared to <TEX>$4{\times}4$</TEX> intra prediction with only one directional information in relatively homogeneous regions. We propose a unidirectional <TEX>$4{\times}4$</TEX> intra prediction method adopting a small-size prediction and one directional prediction approaches. In order to improve coding efficiency, the proposed method is conducted by <TEX>$4{\times}4$</TEX> block and their prediction directions are all the same, resulting that we need to send only one directional information for each macroblock. For intra-frame coding setting, we achieve 10.47% and 1.57% coding efficiency in BD-bitrate for only <TEX>$16{\times}16$</TEX> intra mode and <TEX>$4{\times}4$</TEX>, <TEX>$16{\times}16$</TEX> intra mode, respectively.

Phase-coherent communications without explicit phase tracking

Phase-coherent communications typically requires a reliable phase-tracking algorithm. An initial phase estimate with training symbols allows a receiver to compensate for a motion-induced Doppler shift. Following the training period, however, explicit phase tracking can be avoided in time reversal communications that has been implemented on a block-by-block basis to accommodate time-varying channels. This is accomplished by a smaller block size and adaptive channel estimation using previously detected symbols on a symbol-by-symbol basis. The proposed time reversal approach without explicit phase tracking is demonstrated using experimental data (12-20 kHz) in shallow water.

Achieving a near‐optimum erasure correction performance with low‐complexity LDPC codes

AbstractLow‐density parity‐check (LDPC) codes are shown to tightly approach the performance of idealized maximum distance separable (MDS) codes over memoryless erasure channels, under maximum likelihood (ML) decoding. This is possible down to low error rates and even for small and moderate block sizes. The decoding complexity of ML decoding is kept low thanks to a class of decoding algorithms, which exploit the sparseness of the parity‐check matrix to reduce the complexity of Gaussian elimination. ML decoding of LDPC codes is reviewed at first. A performance comparison among various classes of LDPC codes is then carried out, including a comparison with fixed‐rate Raptor codes for the same parameters. The results confirm that a judicious LDPC code design allows achieving a near‐optimum performance over the erasure channel, with very low error floors. Furthermore, it is shown that LDPC and Raptor codes, under ML decoding, provide almost identical performance in terms of decoding failure probability vs. overhead. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Multibit Error-Correction Methods for Latency-Constrained Flash Memory Systems

This paper presents multibit error-correction schemes for nor Flash used specifically for execute-in-place applications. As architectures advance to accommodate more bits/cell and geometries decrease to structures that are smaller than 32 nm, single-bit error-correction codes (ECCs) are unable to compensate for the increasing array bit error rates, making it imperative to use 2-b ECC. However, 2-b ECC algorithms are complex and add a timing overhead on the memory read access time. This paper proposes low-latency multibit ECC schemes. Starting with the binary Bose-Chaudhuri-Hocquenghem (BCH) codes, an optimized scheme is introduced which combines a multibit error-correcting BCH code with Hamming codes in a hierarchical manner to give an average latency as low as that of the single-bit correcting Hamming decoder. A Hamming algorithm with 2-b error-correcting capacity for very small block sizes (< 1 B) is another low-latency multibit ECC algorithm that is discussed. The viability of these methods and algorithms with respect to latency and die area is proved vis-a¿-vis software and hardware implementations.

Performance versus overhead for fountain codes over Fq

Fountain codes for packet erasure recovery are investigated over Galois fields of order q ? 2. It is shown through development of tight upper and lower bounds on the decoding failure probability under maximum likelihood decoding, that the adoption of higher order Galois fields is beneficial, in terms of performance, for linear random fountain codes. Moreover, it is illustrated how Raptor codes can provide performances very close to those of random fountain codes, with an affordable encoding and decoding complexity. Non-binary Raptor codes turn out to represent an appealing option for applications requiring severe constraints in terms of performance versus overhead, especially for small source block sizes.

Interleaver optimization of convolutional turbo code for 802.16 systems

Convolutional turbo code (CTC) has been adopted as an optional channel coding scheme for wireless metropolitan area networks (WMAN) and digital video broadcasting (DVB) owing to its powerful error correction capability and flexibility. In spite of the fact that the internal interleaver of CTC mainly affects the characteristics of the code, interleaving parameters, especially for small and moderate block sizes, have not been fully optimized in terms of performance. In this paper, we investigate structural behavior of interleaving parameters and suggest several optimization methodologies for the CTC interleaver of 802.16 systems. Simulation shows that power gains up to 0.7 dB can be acquired at a target frame error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> by only substituting the newly optimized parameters for the current ones.

내장형 시스템을 위한 선택적 뱅크 알고리즘을 이용한 데이터 캐쉬 시스템

One of the most effective way to improve cache performance is to exploit both temporal and spatial locality given by any program executive characteristics. In this paper we present a high performance and low power cache structure with a bank selection mechanism that enhances exploitation of spatial and temporal locality. The proposed cache system consists of two parts, i.e., a main direct-mapped cache with a small block size and a fully associative buffer with a large block size as a multiple of the small block size. Especially, the main direct-mapped cache is constructed as two banks for low power consumption and stores a small block which is selected from fully associative buffer by the proposed bank selection algorithm. By using the bank selection algorithm and three state bits, We selectively extend the lifetime of those small blocks with high temporal locality by storing them in the main direct-mapped caches. This approach effectively reduces conflict misses and cache pollution at the same time. According to the simulation results, the average miss ratio, compared with the Victim and STAS caches with the same size, is improved by about 23% and 32% for Mibench applications respectively. The average memory access time is reduced by about 14% and 18% compared with the he victim and STAS caches respectively. It is also shown that energy consumption of the proposed cache is around 10% lower than other cache systems that we examine.

Fast motion estimation for H.264

Several specific features have been incorporated into Motion estimation (ME) in H.264 coding standard to improve its coding efficiency. However, they result in very high computational load. In this paper, a fast ME algorithm is proposed to reduce the computational complexity. First, a mode discriminant method is used to free the encoder from checking the small block size modes in homogeneous regions. Second, a condensed hierarchical block matching method and a spatial neighbor searching scheme are employed to find the best full-pixel motion vector. Finally, direction-based selection rule is utilized to reduce the searching range in sub-pixel ME process. Experimental results on commonly used QCIF and CIF format test sequences have shown that the proposed algorithm achieves a reduction of 88% ME process time on average, while incurring only 0.033 dB loss in PSNR and 0.50% increment on the total bit rate compared with that of exhaustive ME process, which is a default approach adopted in the JM reference software.

An Opportunistic Error Correction Layer for OFDM Systems

We propose a novel cross layer scheme to reduce the power consumption of ADCs in OFDM systems. The ADCs in a receiver can consume up to 50% of the total baseband energy. Our scheme is based on resolution-adaptive ADCs and Fountain codes. In a wireless frequency-selective channel some subcarriers have good channel conditions and others are attenuated. The key part of the proposed system is that the dynamic range of ADCs can be reduced by discarding subcarriers that are attenuated by the channel. Correspondingly, the power consumption in ADCs can be decreased. In our approach, each subcarrier carries a Fountain-encoded packet. To protect Fountain-encoded packets against bit errors, an LDPC code has been used. The receiver only decodes subcarriers (i.e., Fountain-encoded packets) with the highest SNR. Others are discarded. For that reason a LDPC code with a relatively high code rate can be used. The new error correction layer does not require perfect channel knowledge, so it can be used in a realistic system where the channel is estimated. With our approach, more than 70% of the energy consumption in the ADCs can be saved compared with the conventional IEEE 802.11a WLAN system under the same channel conditions and throughput. In addition, it requires 7.5 dB less SNR than the 802.11a system. To reduce the overhead of Fountain codes, we apply message passing and Gaussian elimination in the decoder. In this way, the overhead is 3% for a small block size (i.e., 500 packets). Using both methods results in an efficient system with low delay.

다차원 DCT를 이용한 비디오 부호화기 설계

본 논문은 H.264/AVC가 이전의 비디오 코덱에서 사용하는 8<TEX>$\times$</TEX>8 변환이 아닌 4<TEX>$\times$</TEX>4 변환을 도입하면서 인트라 및 인터 예측 성능을 높인 반면 공간적 압축도가 낮은 점을 개선하기 위한 다차원 변환 방법을 제안한다. 다차원 변환 방법은 H.264/AVC가 갖는 시간적 예측의 장점과 공간적 압축도를 동시에 충족시킬 수 있는 방법이다. 먼저 실험을 통해 다차원 DCT가 H.264/AVC의 2차원 정수 변환(Integer Transform)보다 에너지 압축율이 높다는 것을 보였다. 다차원 DCT를 위한 정수형 변환과 양자화기를 설계하였으며, H.264에서 사용하는 컨텍스트 기반 적응 가변 길이 코딩 (CAVLC)을 엔트로피 코더로 사용하여 다차원 부호화기를 설계하였다. 다차원 부호화기에는 다차원 변환에 따른 블록 주사 방식과 파라미터 갱신, 다차원 변환 모드 선택 등의 도구가 적용되었다. 실험 결과, 다차원 부호화기는 낮은 비트율에서 H.264/AVC와 유사한 압축 효율을 보였지만, 엔트로피와 0이 아닌 계수를 계산하여 비교한 통계적 성능 비교에서는 높은 성능을 보였다. 따라서, 다차원 부호화에 대한 추가적인 연구가 진행된다면 기존의 H.264/AVC의 성능을 보완할 수 있는 부호화 알고리즘으로서 발전할 수 있을 것이다. In H.264/AVC, 4<TEX>$\times$</TEX>4 block transform is used for intra and inter prediction instead of 8<TEX>$\times$</TEX>8 block transform. Using small block size coding, H.264/AVC obtains high temporal prediction efficiency, however, it has limitation in utilizing spatial redundancy. Motivated on these points, we propose a multi-dimensional transform which achieves both the accuracy of temporal prediction as well as effective use of spatial redundancy. From preliminary experiments, the proposed multi-dimensional transform achieves higher energy compaction than 2-D DCT used in H.264. We designed an integer-based transform and quantization coder for multi-dimensional coder. Moreover, several additional methods for multi-dimensional coder are proposed, which are cube forming, scan order, mode decision and updating parameters. The Context-based Adaptive Variable-Length Coding (CAVLC) used in H.264 was employed for the entropy coder. Simulation results show that the performance of the multi-dimensional codec appears similar to that of H.264 in lower bit rates although the rate-distortion curves of the multi-dimensional DCT measured by entropy and the number of non-zero coefficients show remarkably higher performance than those of H.264/AVC. This implies that more efficient entropy coder optimized to the statistics of multi-dimensional DCT coefficients and rate-distortion operation are needed to take full advantage of the multi-dimensional DCT. There remains many issues and future works about multi-dimensional coder to improve coding efficiency over H.264/AVC.

고성능 데이터 캐시 메모리 구조

In this paper, a new high performance data cache scheme that improves exploitation of both the spatial and temporal locality is proposed. The proposed data cache consists of a hardware prefetch unit and two sub-caches such as a direct-mapped (DM) cache with a large block size and a fully associative buffer with a small block size. Spatial locality is exploited by fetching and storing large blocks into a direct mapped cache, and is enhanced by prefetching a neighboring block when a DM cache hit occurs. Temporal locality is exploited by storing small blocks from the DM cache in the fully associative buffer according to their activity in the DM cache when they are replaced. Experimental results on Spec2000 programs show that the proposed scheme can reduce the average miss ratio by and the AMAT by compared to the previous schemes such as direct mapped cache, 4-way set associative cache and SMI(selective mode intelligent) cache[8].

A Multi-Pass True Motion Estimation Scheme With Motion Vector Propagation for Frame Rate Up-Conversion Applications

This paper presents a robust true motion estimation algorithm, designated as MPMVP (Multi-pass and Motion Vector Propagation), to enhance the accuracy of the motion vector fields in frame rate up-conversion applications. The MPMVP uses a multi-pass scheme to progressively refine approximate motion vectors to true motion vectors based upon the motion information acquired in previous passes. The multi-pass motion estimation process uses a large block size to detect the motion vectors within the objects themselves and small block sizes to detect the motion vectors along the object boundaries. Actually, the block size is progressively reduced during the search process. When the motion vector of a block is considered to be sufficiently accurate for motion estimation purposes, the block is said to be converged and the local motion vector search process terminates. A novel technique, referred to as motion vector propagation, is then applied to propagate the motion vector of the converged block to its neighboring blocks. This technique not only ensures that neighboring motion vectors within the same object have a high degree of spatial correlation, but also accelerates the convergence of the motion vectors in the neighboring blocks and therefore reduces the overall computational time and expense of the multi-pass motion vector search procedure. A novel distortion criterion is proposed to enhance the tolerance of the traditional sum-of-absolute-difference measurement technique applied in the motion estimation scheme to noise and shadow effects. The experimental results demonstrate that the proposed true motion estimation algorithm outperforms the traditional full search, 3DRS and TCSBP algorithms in terms of both the smoothness of the generated motion vector fields and the visual quality of the up-converted frames.