Reversible Variable Length Codes Research Articles

Reversible data hiding in JPEG bitstream using optimal VLC mapping

The traditional RDH method for JPEG bitstream is conducted by building the mapping between the variable length codes (VLC). However, the capacity is limited, and the file size may not be well preserved as the capacity is increased. This is because that the trade-off between the capacity and the file size has not been deeply investigated, neither explicitly formulated nor appropriately optimized. In this paper, we propose to take the file size preservation into consideration and minimize the file size increase for a given capacity. We use the value transfer matrix to simulate a theoretical model and then design some optimization rules to reach the reversible solution. Consequently, a better reversible VLC mapping can be obtained in terms of both the capacity and the file size preservation. The experimental results show that the proposed method can increase the capacity with a relatively low cost of file size increase.

A Simplified Joint Source and Channel Coding System for Data Transmission over Fading Channel

The major challenge with multimedia communication lies in the demand for higher data rates with better quality of service and lower latency over the wireless channel. Multimedia content is usually source encoded with variable length codes (VLCs) for optimizing bandwidth utilization. VLCs, even though uniquely decodable, suffer from the problem of error propagation. A single bit error can cause an entire block of data to be decoded wrongly, because the ending of a codeword and the beginning of the next can no longer be determined correctly. Several joint source-channel coding (JSCC) techniques are studied in literature to have efficient source coding with resilience to channel errors, but such methods pose a prohibitively high computational complexity. A variant of JSCC for efficient transmission of information is presented in this paper. The information text is encoded by reversible VLC (RVLC) and corresponding to it, a header sequence is generated. Since the headers are critical in decoding a block, they are channel coded with convolution code to protect from errors. Orthogonal frequency division multiplexing is used to provide high data rate communication and robustness to multipath fading. The performance of the system is analysed over Rayleigh fading channel in terms letter error rate (LER) and computational complexity. The proposed method is seen to provide a good LER performance at moderate to high signal to noise ratio, along with minimal computational complexity, when compared with the contemporary JSCC based schemes. Theoretical performance bounds for the error rate of the proposed system are also derived.

The Most Likely Optimal Symmetric RVLC

For each alphabet size up to 30, a symmetric reversible variable length code (RVLC) is determined which is most likely to be optimal in average codeword length. It is shown that these codes are optimal for more than half of all the possible sources.

Sequentially-Constructible Reversible Variable Length Codes

Dominant codelength sequences for reversible variable length codes (RVLCs) have been recently introduced and studied as a means to looking into optimal RVLCs. However, obtaining the dominant sequences for RVLCs is computationally challenging. In this paper, we consider a special subset of all RVLCs, namely, the sequentially-constructible (SC) RVLCs, for which the dominant sequences can be obtained with less computational complexity. Of course, this time saving is achieved at the cost of losing the optimality. However, it is shown that the dominant sequences for SC RVLCs provide acceptable performance in terms of the redundancy. Specifically, it is seen that the worst case penalty in using the optimal SC RVLCs with respect to the optimal RVLCs is at most 2/9 bit per symbol for alphabet size of up to 16. While obtaining the dominant sequences of SC RVLCs is relatively faster, it will still become challenging as the search space of the relevant branch-and-bound algorithm gets larger, when the source alphabet size increases. In order to further reduce the time complexity, we propose an alternative approach to a table of SC RVL codelength sequences, which avoids the branch-and-bound algorithm. It is shown that the codes obtained by this approach perform almost as well as the SC dominant sequences. Specifically, for an alphabet size of up to 21, the redundancy of this approach is, at most, 2/19 bit more than the optimal SC RVLCs.

Innovations in Video Error Resilience and Concealment

Router buffer overflow and random bit errors have always been a problem in the Internet. The growth in multimedia applications in mobile extensions of the Internet has increased the threat from error bursts, random errors, and packet erasures that are a manifestation of wireless channels. Source-coded error resilience has come to prominence in the H.264/AVC codec standard, and this paper reviews such innovations surrounding this codec. Some innovations are new variants of an existing technique such as datapartitioning and some are entirely new such as the powerful dispersed-mode flexible macroblock ordering. Other techniques, such as reversible variable length coding, were not be transferred to H.264 from earlier codecs and, hence, innovations are proposed to still provide robust entropy coding. Other variants such as adaptive intra-refresh are still being experimented with. When error resilience or other protection methods fail to present an adequate video frame then error concealment can be brought to bear. This paper reviews error concealment which is important to commercial companies as they are able to distinguish their codec from others. The paper considers spatial, temporal and hybrid error concealment methods. Though this paper contains over one hundred references it can only provide a slice through this rich field.

Using reversible variable length codes for JPEG image transmission in a noisy channel

JPEG coder is still the most attractive compression scheme for still image. Using Huffman coding makes the JPEG coder very sensitive to communication error. In this paper we propose a simple modification to JPEG coder by using reversible variable length code designed for the DC coefficients of each block. The results show great improvement in error resilience in a binary symmetric channel transmission with an average reduction of 5---10% in compression ratio.

Innovations in Video Error Resilience and Concealment

Router buffer overflow and random bit errors have always been a problem in the Internet. The growth in multimedia applications in mobile extensions of the Internet has increased the threat from error bursts, random errors, and packet erasures that are a manifestation of wireless channels. Source-coded error resilience has come to prominence in the H.264/AVC codec standard, and this paper reviews such innovations surrounding this codec. Some innovations are new variants of an existing technique such as data-partitioning and some are entirely new such as the powerful dispersed-mode flexible macroblock ordering. Other techniques, such as reversible variable length coding, were not transferred to H.264/AVC from earlier codecs and, hence, innovations are proposed to still provide robust entropy coding. Other variants such as adaptive intra-refresh are still being experimented with. When error resilience or other protection methods fail to present an adequate video frame then error concealment can be brought to bear. This paper reviews error concealment which is important to commercial companies as they are able to distinguish their codec from others. The paper considers spatial, temporal and hybrid error concealment methods. Though this paper contains over one hundred references and relevant patents have been discussed, it can only provide a slice through this rich field.

Digital signal processor-based three-dimensional wavelet error-resilient lossless compression of high-resolution spectrometer data

Ultraspectral sounders revolutionize the way remote sensing data are collected, retrieved, and assimilated to provide better weather, climate, and environmental prediction and monitoring. This unprecedented amount of ultraspectral data increases the burden of data bandwidth and the chance of transmission noise and error contamination. It is desired that source coding of ultraspectral data also have some error-resilient capability, in addition to the error-correcting channel coding. Earlier, we developed three-dimensional wavelet reversible variable-length coding (3DWT-RVLC) for lossless compression of ultraspectral sounder data, which has significantly better error resilience than JPEG2000 Part 2 at only a small reduction in compression gain. The reversible variable-length codes allow instantaneous decoding in both directions, which affords better detection of bit errors due to synchronization losses over a noisy channel. To explore the feasibility of 3DWT-RVLC for real-time ultraspectral data processing, we implement a memory-limited digital signal processor (DSP) version of 3DWT-RVLC. Compression experiments on 10 ultraspectral test granules obtained from the NASA Atmospheric Infrared Sounder show that the memory-limited DSP-based 3DWT-RVLC is able to perform high-speed data processing at only a small reduction in compression ratio as compared to the original 3DWT-RVLC.

An A*-Based Algorithm for Constructing Reversible Variable Length Codes with Minimum Average Codeword Length

Variable length codes (VLCs) are widely adopted in many compression standards due to their good coding efficiency on average codeword length. However, an inherent problem with a VLC is that an error of even one bit can cause serious error propagation and thus loss of synchronization at the receiver, which would lead to a series of non-correctly decoded symbols. Reversible variable length codes (RVLCs) were introduced to significantly mitigate this phenomenon. In this work, a method to find an optimal RVLC in terms of the minimum average codeword length is first formulated as a tree-searching problem, and then, instead of performing an exhaustive search, an A*-based construction algorithm is proposed to find an optimal RVLC. The proposed algorithm has been applied to several benchmarks for sources and has found respective optimal symmetric and asymmetric RVLCs.

Joint source-channel codes based on irregular turbo codes and variable length codes

Variable length codes (VLCs), used in data compression, are very sensitive to error propagation in the presence of noisy channels. To address this problem, several joint source channel turbo techniques have been proposed in the literature. In this paper, we focus on pairs of source/VLC of low redundancy, i.e., when there is a good match between the source statistics and the length distribution of the VLC. It is a case not considered extensively in the literature so far and the classical concatenation of a VLC and a convolutional code is not satisfying. Through EXIT chart and interleaving gain analysis, we show that the introduction of a repetition code between the VLC and the convolutional code considerably improves global performance. In particular, excellent symbol error rates are obtained with reversible VLCs which are used in recent source codecs.

Joint source channel decoding and iterative symbol combining with turbo trellis-coded modulation

A new joint source channel decoding (JSCD) scheme for turbo trellis-coded modulation is proposed which exploits symbol-a-priori probabilities to improve decoding performance. To obtain symbol-a-priori probabilities, we propose a new method which uses a time-stretched bit-level trellis of a variable length code (VLC) decoder alongside a symbol level trellis. Iterative symbol combining (ISC) is also integrated with the proposed JSCD scheme so that multiple transmissions of the same data packet can be combined to improve decoding. Essentially JSCD with ISC (JSCD-ISC) exploits two types of a-priori information. The first one being the symbol-a-priori probabilities derived from source statistics, and the second one is obtained from the saved extrinsic information of previously transmitted copies of the data. Several simulations with different VLC sources like Huffman and reversible variable length codes (RVLC), and for different number of retransmissions have been performed. The most striking result is obtained with RVLC, whereby using only two retransmissions, the JSCD-ISC scheme outperforms a conventional scheme using three retransmissions by 0.2 dB.

Performance of joint source–channel decoding with iterative bit combining and detection

A joint source–channel decoding scheme (JSCD) with iterative bit combining (IBC) is proposed, which exploits two types of a priori information. The first one is the a priori bit probabilities obtained from source statistics, and the second is the channel a priori probabilities obtained from saved extrinsic information of previous transmissions. The JSCD-IBC scheme also incorporates iterative detection as both a stopping criteria and mechanism for triggering retransmissions. This adds an implicit adaptivity to the system and prevents excess iterations/retransmissions from being effected. The performance of the JSCD-IBC scheme is evaluated with four different iterative detection schemes and also two different types of variable length codes, Huffman and reversible variable length codes. Simulation results show that a significant performance gain in terms of bit error rate, throughput, and number of iterations can be achieved with the JSCD-IBC scheme as compared to a separate decoding scheme.

Joint Source and Space Time Decoding over Fading Channels

For high data rate communications, variable length codes (VLC) and multiple input multiple output (MIMO) techniques are required in the application layer and the physical layer, respectively. In this paper, we study the joint decoding for systems that consist of reversible VLC (RVLC) as the source codes and recursive space time trellis codes (STTC) as the coded modulation. The maximum a posteriori probability (MAP) decoding algorithm is modified to accommodate issues including the inseparable systematic information, the unsymmetric trellis structure, and information in both bit and symbol domains. Further, by converting extrinsic information based on the modulation mode and the mapping method, iterative information exchange can be performed so as to fully utilize the redundancy in both RVLC and recursive STTC. The performance of the proposed joint decoding is evaluated over both rapid fading and quasi- static flat fading channels, which shows significant improvement in coding gain in comparison with the non-iterative receiver.

Two algorithms for constructing efficient huffman-code based reversible variable length codes

In this paper, Huffman-code-based reversible variable length code (RVLC) construction algorithms are studied. We use graph models to represent the prefix, suffix, and Hamming distance relationships among RVLC candidate code words. The properties of the so-obtained graphs are investigated in detail, based on which we present two efficient RVLC construction algorithms: Algorithm 1 aims at minimizing the average code word length while Algorithm 2 jointly minimizes the average code word length and maximizes the error-detection probability at the same time.

Two Algorithms for Constructing Efficient Huffman-Code-Based Reversible Variable Length Codes

In this paper, Huffman-code-based reversible variable length code (RVLC) construction algorithms are studied. We use graph models to represent the prefix, suffix, and Hamming distance relationships among RVLC candidate code words. The properties of the so-obtained graphs are investigated in detail, based on which we present two efficient RVLC construction algorithms: Algorithm 1 aims at minimizing the average code word length while Algorithm 2 jointly minimizes the average code word length and maximizes the error-detection probability at the same time.

A New Soft Variable Length Decoder for Wireless Video Transmission

In this paper, we propose an adaptive and scalable soft variable length code (VLC) decoder to greatly reduce overall design complexity. Generally, a soft VLC decoder needs to maintain many states for the correct decoding when the sequence length or table size grows. We propose an adaptive sorting scheme to reduce the memory accesses and design complexity. We reduce the table size by using symbol-merging and table-merging schemes. In addition, the proposed Black-Box model improves the accuracy of performance estimation by a novel measurement of symbol-alias and also achieves a better tradeoff between performance and complexity. Further, no side information is transmitted and the proposed soft VLC decoder is bandwidth-efficient. The proposed design is evaluated using the model of MPEG-4/UDP-Lite/UEP/AWGN, and hence it is standard-compliant. We averagely improve the peak signal-to-noise ratio by 0.4~2.9 dB as compared with traditional VLC decoding and standard-support reversible VLC decoding schemes

New iterative super-trellis decoding with source a priori information for VLCs with turbo codes

A novel Joint Source and Channel Decoding (JSCD) scheme for Variable Length Codes (VLCs) concatenated with turbo codes utilizing a new super-trellis decoding algorithm is presented in this letter. The basic idea of our decoding algorithm is that source a priori information with the form of bit transition probabilities corresponding to the VLC tree can be derived directly from sub-state transitions in new composite-state represented super-trellis. A Maximum Likelihood (ML) decoding algorithm for VLC sequence estimations based on the proposed super-trellis is also described. Simulation results show that the new iterative decoding scheme can obtain obvious encoding gain especially for Reversible Variable Length Codes (RVLCs), when compared with the classical separated turbo decoding and the previous joint decoding not considering source statistical characteristics.

Error resiliency measure for RVLC codes

Video signals transmitted over error-prone wireless channels are often corrupted by bit errors. Due to their superior data recovery performance, the reversible variable length coding (RVLC) has been used as an error resiliency scheme in the MPEG-4 and H.263 video coding standards. In order to evaluate and compare the error resiliency performance of RVLC codes, we develop an error resiliency measure in this letter. Using this measure, different RVLC schemes are compared for MPEG-4 video sequences. The effects of propagating and nonpropagating errors are discussed as well.

On constructing symmetrical reversible variable-length codes independent of the Huffman code

Reversible variable length codes (RVLCs) have received much attention due to their excellent error resilient capabilities. In this paper, a novel construction algorithm for symmetrical RVLC is proposed which is independent of the Huffman code. The proposed algorithm’s codeword assignment is only based on symbol occurrence probability. It has many advantages over symmetrical construction algorithms available for easy realization and better code performance. In addition, the proposed algorithm simplifies the codeword selection mechanism dramatically.

Using CSP to model the synchronisation process of variable length codes

Variable length codes (VLC) have found widespread use for efficient encoding of symbols with unequal probabilities in many practical situations. However, bit errors can cause a loss of decoder synchronism that often leads to error propagation. Recent advances in the development of VLC that limit the effect of error propagation, such as reversible VLC and self-synchronising VLC, contribute further to their popularity. However, it is still important to model the performance of various VLC code sets so that comparisons can be made between different coding schemes and for different applications. Communicating sequential processes (CSP) is a well-established formal description technique that allows one to analyse the behaviour of concurrently evolving processes. It has been successfully applied to industrial-scale problems. The paper describes how CSP can be applied to the modelling of the resync process of VLC. This approach offers three main advantages. First, a complete model comprises processes and events as basic building blocks, making this approach highly scalable. Second, different semantic models provide different level of abstraction. Third, tools are available for automatic generation of sync sequences, which also provide a measure of sync performance. This facilitates comparisons of different VLC schemes in addition to code sets obtained using a given coding scheme.