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Context dependent prediction and category encoding for DPCM image compression

Efficient compression of image data requires the understanding of the noise characteristics of sensors as well as the redundancy expected in imagery. Herein, the techniques of Differential Pulse Code Modulation (DPCM) are reviewed and modified for information-preserving data compression. The modifications include: mapping from intensity to an equal variance space; context dependent one and two dimensional predictors; rationale for nonlinear DPCM encoding based upon an image quality model; context dependent variable length encoding of 2x2 data blocks; and feedback control for constant output rate systems. Examples are presented at compression rates between 1.3 and 2.8 bits per pixel. The need for larger block sizes, 2D context dependent predictors, and the hope for sub-bits-per-pixel compression which maintains spacial resolution (information preserving) are discussed.

Beaudet, Paul R.

Constructing LDPC Codes from Loop-Free Encoding Modules

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Divsalar, Dariush

Finite-State Codes

New class of codes with desirable properties constructed from block codes. Finite-state encoder is machine that has finite number of internal states. Receives k parallel information symbols and transmits n parallel code symbols at each clock pulse. Finite-state codes include both block and convolutional codes. Theory of finite-state codes used to study properties of error-correcting codes in general and to design new codes to various specifications.

Pollara, F.

dc-free coset codes

A class of block coset codes with disparity and run-length constraints are studied. They are particularly well suited for high-speed optical fiber links and similar channels, where dc-free pulse formats, channel error control, and low-complexity encoder-decoder implementations are required. The codes are derived by partitioning linear block codes. The encoder and decoder structures are the same as those of linear block codes with only slight modifications. A special class of dc-free coset block codes are derived from BCH codes with specified bounds on minimum distance, disparity, and run length. The codes have low disparity levels (a small running digital sum) and good error-correcting capabilities.

Deng, Robert H.

Permutation codes for sources.

Source encoding techniques based on permutation codes are investigated. For a broad class of distortion measures it is shown that optimum encoding of a source permutation code is easy to instrument even for very long block lengths. Also, the nonparametric nature of permutation encoding is well suited to situations involving unknown source statistics. For the squared-error distortion measure a procedure for generating good permutation codes of a given rate and block length is described. The performance of such codes for a memoryless Gaussian source is compared both with the rate-distortion function bound and with the performance of various quantization schemes. The comparison reveals that permutation codes are asymptotically ideal for small rates and perform as well as the best entropy-coded quantizers presently known for intermediate rates. They can be made to compare favorably at high rates, too, provided the coding delay associated with extremely long block lengths is tolerable.

Berger, T.

Dynamic models for simulation of the 70-M antenna axis servos

Dynamic models for the various functional elements of the 70 m antenna axis servos are described. The model representing the digital position controller, the linear and nonlinear properties of the physical hardware, and the dynamics of the flexible antenna structure are encoded in six major function blocks. The general modular structure of the function blocks facilitates their adaptation to a variety of dynamic simulation studies. Model parameter values were calculated from component specifications and design data. A simulation using the models to predict limit cycle behavior produced results in excellent agreement with field test data from the DSS 14 70-m antenna.

Hill, R. E.

Trellis-coded multidimensional phase modulation

A 2L-dimensional multiple phase-shift keyed (MPSK) (L x MPSK) signal set is obtained by forming the Cartesian product of L two-dimensional MPSK signal sets. A systematic approach to partitioning L x MPSK signal sets that is based on block coding is used. An encoder system approach is developed. It incorporates the design of a differential precoder, a systematic convolutional encoder, and a signal set mapper. Trellis-coded L x 4PSK, L x 8PSK, and L x 16PSK modulation schemes are found for L = 1-4 and a variety of code rates and decoder complexities, many of which are fully transparent to discrete phase rotations of the signal set. The new codes achieve asymptotic coding gains up to 5.85 dB.

Pietrobon, Steven S.

Encoding of linear kinetic plasma problems in quantum circuits via data compression

We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation Aψ = b to be solved by using the quantum signal processing algorithm. The latter requires encoding of matrix A in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode A in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

LLNL FESP Theory Highlights: October 2024

I. Novikau, I. Y. Dodin, E. A. Startsev, I. Joseph, Quantum algorithms for simulating dissipative linear and nonlinear dynamics of plasmas. Invited talk at the 66th Annual Meeting of the APS Division of Plasma Physics, Atlanta, Georgia. Novikau I., Dodin I.Y., Startsev E.A., Encoding of linear kinetic plasma problems in quantum circuits via data compression, Journal of Plasma Physics. 2024;90(4):805900401, doi:10.1017/S0022377824000795. We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation to be solved by using the quantum signal processing algorithm. The latter requires encoding of a matrix in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes

In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.

Lin, Shu

Radiation-Hard SpaceWire/Gigabit Ethernet-Compatible Transponder

A radiation-hard transponder was developed utilizing submicron/nanotechnology from IBM. The device consumes low power and has a low fabrication cost. This device utilizes a Plug-and-Play concept, and can be integrated into intra-satellite networks, supporting SpaceWire and Gigabit Ethernet I/O. A space-qualified, 100-pin package also was developed, allowing space-qualified (class K) transponders to be delivered within a six-month time frame. The novel, optical, radiation-tolerant transponder was implemented as a standalone board, containing the transponder ASIC (application specific integrated circuit) and optical module, with an FPGA (field-programmable gate array) friendly parallel interface. It features improved radiation tolerance; high-data-rate, low-power consumption; and advanced functionality. The transponder utilizes a patented current mode logic library of radiation-hardened-by-architecture cells. The transponder was developed, fabricated, and radhard tested up to 1 MRad. It was fabricated using 90-nm CMOS (complementary metal oxide semiconductor) 9 SF process from IBM, and incorporates full BIT circuitry, allowing a loop back test. The low-speed parallel LVCMOS (lowvoltage complementary metal oxide semiconductor) bus is compatible with Actel FPGA. The output LVDS (low-voltage differential signaling) interface operates up to 1.5 Gb/s. Built-in CDR (clock-data recovery) circuitry provides robust synchronization and incorporates two alarm signals such as synch loss and signal loss. The ultra-linear peak detector scheme allows on-line control of the amplitude of the input signal. Power consumption is less than 300 mW. The developed transponder with a 1.25 Gb/s serial data rate incorporates a 10-to-1 serializer with an internal clock multiplication unit and a 10-1 deserializer with internal clock and data recovery block, which can operate with 8B10B encoded signals. Three loop-back test modes are provided to facilitate the built-in-test functionality. The design is based on a proprietary library of differential current switching logic cells implemented in the standard 90-nm CMOS 9SF technology from IBM. The proprietary low-power LVDS physical interface is fully compatible with the SpaceWire standard, and can be directly connected to the SFP MSA (small form factor pluggable Multiple Source Agreement) optical transponder. The low-speed parallel interfaces are fully compatible with the standard 1.8 V CMOS input/output devices. The utilized proprietary annular CMOS layout structures provide TID tolerance above 1.2 MRad. The complete chip consumes less than 150 mW of power from a single 1.8-V positive supply source.

Katzman, Vladimir

Encoding of symbols for a computer interconnect based on frequency of symbol values

Data are serially communicated over an interconnect between an encoder and a decoder. The encoder includes a first training unit to count a frequency of symbol values in symbol blocks of a set of N number of symbol blocks in an epoch. A circular shift unit of the encoder stores a set of most-recently-used (MRU) amplitude values. An XOR unit is coupled to the first training unit and the first circular shift unit as inputs and to the interconnect as output. A transmitter is coupled to the encoder XOR unit and the interconnect and thereby contemporaneously sends symbols and trains on the symbols. In a system, a device includes a receiver and decoder that receive, from the encoder, symbols over the interconnect. The decoder includes its own training unit for decoding the transmitted symbols.

SeyedzadehDelcheh, SeyedMohammad

Prioritized LT Codes

The original Luby Transform (LT) coding scheme is extended to account for data transmissions where some information symbols in a message block are more important than others. Prioritized LT codes provide unequal error protection (UEP) of data on an erasure channel by modifying the original LT encoder. The prioritized algorithm improves high-priority data protection without penalizing low-priority data recovery. Moreover, low-latency decoding is also obtained for high-priority data due to fast encoding. Prioritized LT codes only require a slight change in the original encoding algorithm, and no changes at all at the decoder. Hence, with a small complexity increase in the LT encoder, an improved UEP and low-decoding latency performance for high-priority data can be achieved. LT encoding partitions a data stream into fixed-sized message blocks each with a constant number of information symbols. To generate a code symbol from the information symbols in a message, the Robust-Soliton probability distribution is first applied in order to determine the number of information symbols to be used to compute the code symbol. Then, the specific information symbols are chosen uniform randomly from the message block. Finally, the selected information symbols are XORed to form the code symbol. The Prioritized LT code construction includes an additional restriction that code symbols formed by a relatively small number of XORed information symbols select some of these information symbols from the pool of high-priority data. Once high-priority data are fully covered, encoding continues with the conventional LT approach where code symbols are generated by selecting information symbols from the entire message block including all different priorities. Therefore, if code symbols derived from high-priority data experience an unusual high number of erasures, Prioritized LT codes can still reliably recover both high- and low-priority data. This hybrid approach decides not only "how to encode" but also "what to encode" to achieve UEP. Another advantage of the priority encoding process is that the majority of high-priority data can be decoded sooner since only a small number of code symbols are required to reconstruct high-priority data. This approach increases the likelihood that high-priority data is decoded first over low-priority data. The Prioritized LT code scheme achieves an improvement in high-priority data decoding performance as well as overall information recovery without penalizing the decoding of low-priority data, assuming high-priority data is no more than half of a message block. The cost is in the additional complexity required in the encoder. If extra computation resource is available at the transmitter, image, voice, and video transmission quality in terrestrial and space communications can benefit from accurate use of redundancy in protecting data with varying priorities.

Woo, Simon S.

Convolutional Encoding of Self-Dual Codes

Self-dual block codes of rate 1/2 are constructed here, The codes are of length 8m with weights w, w = 0 mod 4. The codes have a convolutional portion of length 8m-2 and non-systematic information length 4m-1.

self

A neural net based architecture for the segmentation of mixed gray-level and binary pictures

A neural-net-based architecture is proposed to perform segmentation in real time for mixed gray-level and binary pictures. In this approach, the composite picture is divided into 16 x 16 pixel blocks, which are identified as character blocks or image blocks on the basis of a dichotomy measure computed by an adaptive 16 x 16 neural net. For compression purposes, each image block is further divided into 4 x 4 subblocks; a one-bit nonparametric quantizer is used to encode 16 x 16 character and 4 x 4 image blocks; and the binary map and quantizer levels are obtained through a neural net segmentor over each block. The efficiency of the neural segmentation in terms of computational speed, data compression, and quality of the compressed picture is demonstrated. The effect of weight quantization is also discussed. VLSI implementations of such adaptive neural nets in CMOS technology are described and simulated in real time for a maximum block size of 256 pixels.

Tabatabai, Ali

Constructions for finite-state codes

A class of codes called finite-state (FS) codes is defined and investigated. These codes, which generalize both block and convolutional codes, are defined by their encoders, which are finite-state machines with parallel inputs and outputs. A family of upper bounds on the free distance of a given FS code is derived from known upper bounds on the minimum distance of block codes. A general construction for FS codes is then given, based on the idea of partitioning a given linear block into cosets of one of its subcodes, and it is shown that in many cases the FS codes constructed in this way have a d sub free which is as large as possible. These codes are found without the need for lengthy computer searches, and have potential applications for future deep-space coding systems. The issue of catastropic error propagation (CEP) for FS codes is also investigated.

Pollara, F.