Forbidden Symbol Research Articles

Source Symbol Purging-Based Distributed Conditional Arithmetic Coding.

A distributed arithmetic coding algorithm based on source symbol purging and using the context model is proposed to solve the asymmetric Slepian–Wolf problem. The proposed scheme is to make better use of both the correlation between adjacent symbols in the source sequence and the correlation between the corresponding symbols of the source and the side information sequences to improve the coding performance of the source. Since the encoder purges a part of symbols from the source sequence, a shorter codeword length can be obtained. Those purged symbols are still used as the context of the subsequent symbols to be encoded. An improved calculation method for the posterior probability is also proposed based on the purging feature, such that the decoder can utilize the correlation within the source sequence to improve the decoding performance. In addition, this scheme achieves better error performance at the decoder by adding a forbidden symbol in the encoding process. The simulation results show that the encoding complexity and the minimum code rate required for lossless decoding are lower than that of the traditional distributed arithmetic coding. When the internal correlation strength of the source is strong, compared with other DSC schemes, the proposed scheme exhibits a better decoding performance under the same code rate.

Singular integrals in quantum Euclidean spaces

We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes’ pseudodifferential calculus for rotation algebras, thanks to a new form of Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduceLpL_p-boundedness and Sobolevpp-estimates for regular, exotic and forbidden symbols in the expected ranks. In theL2L_2level both Calderón-Vaillancourt and Bourdaud theorems for exotic and forbidden symbols are also generalized to the quantum setting. As a basic application of our methods, we proveLpL_p-regularity of solutions for elliptic PDEs.

Mapping properties of operator-valued pseudo-differential operators

In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. We prove the boundedness of regular symbols on Sobolev spaces H2α(Rd;L2(M)) and Besov spaces Bp,qα(Rd;Lp(M)) for α∈R and 1≤p,q≤∞, as well as the boundedness of forbidden symbols on H2α(Rd;L2(M)) and Bp,qα(Rd;Lp(M)) for α>0 and 1≤p,q≤∞. Thanks to the smooth atomic decomposition of the operator-valued Triebel-Lizorkin spaces F1α,c(Rd,M) obtained in our previous paper, we establish the F1α,c-regularity of regular symbols for every α∈R, and the F1α,c-regularity of forbidden symbols for α>0. As applications, we obtain the same results on the usual and quantum tori.

An Effective Error Correction Scheme for Arithmetic Coding

We propose an effective error correction technique for arithmetic coding with forbidden symbol. By predicting the occurrence of the subsequent forbidden symbols, the forbidden region is actually expanded and theoretically, a better error correction performance can be achieved. Moreover, a generalized stack algorithm is exploited to detect the forbidden symbol beforehand. The proposed approach is combined with themaximum a posteriori(MAP) metric to keep the highly probable decoding paths in the stack. Simulation results justify that our scheme performs better than the existing MAP methods on the error correction performance, especially at a low coding rate.

Secure Arithmetic Coding with Error Detection Capability

Recently, arithmetic coding has attracted the attention of many scholars because of its high compression capability. Accordingly, this paper proposed a Joint Source-Cryptographic-Channel Coding (JSCC) based on Arithmetic Coding (AC). For this purpose, embedded error detection arithmetic coding, which is known as continuous error detection (CED), is used. In our proposed method, a random length of forbidden symbol which is produced with a key is used in each recursion. The dummy symbol is divided into two dummy symbols with a key and then is placed in random positions in order to provide security. Finally, in addition to producing secure codes, the suggested method reduced the added redundancy to half of the total redundancy added by CED. It has less complexity than cascades source, channel coding, and encryption while its key space in comparison to other joint methods has enlarged. Moreover, the coder provides a flexible switch between a standard compression model and a joint model.

A New Model for the Error Detection Delay of Finite Precision Binary Arithmetic Codes with a Forbidden Symbol

In this paper, the statistical characteristic of the Error Detection Delay (EDD) of Finite Precision Binary Arithmetic Codes (FPBAC) is discussed. It is observed that, apart from the probability of the Forbidden Symbol (FS) inserted into the list of the source symbols, the probability of the source sequence and the operation precision as well as the position of the FS in the coding interval can affect the statistical characteristic of the EDD. Experiments demonstrate that the actual distribution of the EDD of FPBAC is quite different from the geometric distribution of infinite precision arithmetic codes. This phenomenon is researched deeply, and a new statistical model (gamma distribution) of the actual distribution of the EDD is proposed, which can make a more precise prediction of the EDD. Finally, the relation expressions between the parameters of gamma distribution and the related factors affecting the distribution are given.

Joint distortion model for progressive image transmission using error correcting arithmetic codes

A novel joint source channel distortion model was proposed, which can essentially estimate the average distortion in progressive image transmission. To improve the precision of the model, the redundancy generated by a forbidden symbol in the arithmetic codes is used to distinguish the quantization distortion and the channel distortion, all the coefficients from the first error one to the end of the sequence are set to be a value within the variance range of the coefficients instead of zero, then the error propagation coming from the entropy coding can be essentially estimated, which is disregarded in the most conventional joint source channel coding (JSCC) systems. The precision of the model in terms of average peak-signal-to-noise has been improved about 0.5 dB compared to classical works. An efficient unequal error protection system based on the model is developed, and can be used in the wireless communication systems.

Error Recovery Properties and Soft Decoding of Quasi-Arithmetic Codes

This paper first introduces a new set of aggregated state models for soft-input decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding performance and complexity. It is shown that close-to-optimal decoding performance can be obtained with low values of the aggregation parameter, that is, with a complexity which is significantly reduced with respect to optimal QA bit/symbol models. The choice of the aggregation parameter depends on the synchronization recovery properties of the QA codes. This paper thus describes a method to estimate the probability mass function (PMF) of the gain/loss of symbols following a single bit error (i.e., of the difference between the number of encoded and decoded symbols). The entropy of the gain/loss turns out to be the average amount of information conveyed by a length constraint on both the optimal and aggregated state models. This quantity allows us to choose the value of the aggregation parameter that will lead to close-to-optimal decoding performance. It is shown that the optimum position for the length constraint is not the last time instant of the decoding process. This observation leads to the introduction of a new technique for robust decoding of QA codes with redundancy which turns out to outperform techniques based on the concept of forbidden symbol.

Iterative Decoding of Serially Concatenated Arithmetic and Channel Codes With JPEG 2000 Applications

In this paper, an innovative joint-source channel coding scheme is presented. The proposed approach enables iterative soft decoding of arithmetic codes by means of a soft-in soft- out decoder based on suboptimal search and pruning of a binary tree. An error-resilient arithmetic coder with a forbidden symbol is used in order to improve the performance of the joint source/channel scheme. The performance in the case of transmission across the AWGN channel is evaluated in terms of word error probability and compared to a traditional separated approach. The interleaver gain, the convergence property of the system, and the optimal source/channel rate allocation are investigated. Finally, the practical relevance of the proposed joint decoding approach is demonstrated within the JPEG 2000 coding standard. In particular, an iterative channel and JPEG 2000 decoder is designed and tested in the case of image transmission across the AWGN channel.

A syntax-preserving error resilience tool for JPEG 2000 based on error correcting arithmetic coding

JPEG 2000 is the novel ISO standard for image and video coding. Besides its improved coding efficiency, it also provides a few error resilience tools in order to limit the effect of errors in the codestream, which can occur when the compressed image or video data are transmitted over an error-prone channel, as typically occurs in wireless communication scenarios. However, for very harsh channels, these tools often do not provide an adequate degree of error protection. In this paper, we propose a novel error-resilience tool for JPEG 2000, based on the concept of ternary arithmetic coders employing a forbidden symbol. Such coders introduce a controlled degree of redundancy during the encoding process, which can be exploited at the decoder side in order to detect and correct errors. We propose a maximum likelihood and a maximum a posteriori context-based decoder, specifically tailored to the JPEG 2000 arithmetic coder, which are able to carry out both hard and soft decoding of a corrupted code-stream. The proposed decoder extends the JPEG 2000 capabilities in error-prone scenarios, without violating the standard syntax. Extensive simulations on video sequences show that the proposed decoders largely outperform the standard in terms of PSNR and visual quality.

Joint Source/Channel Coding and MAP Decoding of Arithmetic Codes

In this paper, a novel maximum a posteriori (MAP) estimation approach is employed for error correction of arithmetic codes with a forbidden symbol. The system is founded on the principle of joint source channel coding, which allows one to unify the arithmetic decoding and error correction tasks into a single process, with superior performance compared to traditional separated techniques. The proposed system improves the performance in terms of error correction with respect to a separated source and channel coding approach based on convolutional codes, with the additional great advantage of allowing complete flexibility in adjusting the coding rate. The proposed MAP decoder is tested in the case of image transmission across the additive white Gaussian noise channel and compared against standard forward error correction techniques in terms of performance and complexity. Both hard and soft decoding are taken into account, and excellent results in terms of packet error rate and decoded image quality are obtained.

Robust video transmission over error-prone channels via error correcting arithmetic codes

We propose arithmetic codes (ACs) with a forbidden symbol as a joint entropy coding and error protection tool for robust video transmission over error-prone channels. In particular, we introduce a MAP decoder of ACs, and apply it to the transmission of 3-D SPIHT coded video and RTP/UDP/IP H.264 video with data partitioning. Experimental results show that the proposed system exhibits several advantages with respect to other schemes, and outperforms rate-compatible punctured convolutional (RCPC) codes in the applications considered.

Bilinear pseudodifferential operators with forbidden symbols on Lipschitz and Besov spaces

We show that bilinear pseudodifferential operators with symbols in the forbidden class are bounded on products of Lipschitz and Besov spaces.

L2 Estimates for Weyl Quantization

Sharp L2 estimates for Weyl quantized pseudodifferential operators are established in the framework of Hörmander's classes of symbols Smϱ, δ. In particular, the case of forbidden symbols is discussed.