Systematic Linear Block Codes Research Articles

A Coded Compressed Sensing Scheme for Unsourced Multiple Access

This article introduces a novel scheme, termed coded compressed sensing, for unsourced multiple-access communication. The proposed divide-and-conquer approach leverages recent advances in compressed sensing and forward error correction to produce a novel uncoordinated access paradigm, along with a computationally efficient decoding algorithm. Within this framework, every active device partitions its data into several sub-blocks and, subsequently, adds redundancy using a systematic linear block code. Compressed sensing techniques are then employed to recover sub-blocks up to a permutation of their order, and the original messages are obtained by stitching fragments together using a tree-based algorithm. The error probability and computational complexity of this access paradigm are characterized. An optimization framework, which exploits the tradeoff between performance and computational complexity, is developed to assign parity-check bits to each sub-block. In addition, two emblematic parity bit allocation strategies are examined and their performances are analyzed in the limit as the number of active users and their corresponding payloads tend to infinity. The number of channel uses needed and the computational complexity associated with these allocation strategies are established for various scaling regimes. Numerical results demonstrate that coded compressed sensing outperforms other existing practical access strategies over a range of operational scenarios.

Forward Error Correction For Gigabit Automotive Ethernet using RS(450,406) Encoder

Error correction and detection during data transmission is a major issue. For resolving this, many error correction techniques are available. The Reed-Solomon coding is the most powerful forward error correction technique used in Gigabit Automotive Ethernet to compact channel noise during data transmission. The car becomes more smarter day by day and more new advanced electronics is being used in-vehicle. Gigabit Automotive Ethernet(1000BASE-T1) provide fast bandwidth for many kinds of applications and connect different functional parts in the car. The Reed Solomon(RS) coding is the powerful forward error correction(FEC) technique used in 1000BASE-T1 Automotive Ethernet. RS(450,406) coding is also known as shortened Reed Solomon codes. The Reed Solomon(RS) codes are generally used in communication system due to its ability of correcting both random and burst errors. Reed Solomon codes are no-binary systematic linear block codes. RS coding is widely used in high speed communication system. This RS code is implemented using Galois field(GF). The Automotive Ethernet is encoded using RS(450,406) codes through GF(512) for FEC. This RS codes can corrects the error up to t=22 symbol, while other encoding techniques corrects the error in t bits. In this paper we implemented the RS(Reed Solomon) code in Cadence ncsim Verilog software and used Cadence Simvision for showing timing diagrams. This RS code uses 9-bit based shortened (450,406) code.

Застосування алгоритму bkw для відновлення систематичних лінійних блокових кодів за наборами спотворених кодових слів

Застосування алгоритму bkw для відновлення систематичних лінійних блокових кодів за наборами спотворених кодових слів

A novel rateless codes design scheme based on two‐stage encoding and forward equal probability

SummaryThis paper proposes an ideal rateless codes model to comprehensively describe rateless codes and extends the definition of systematic linear block code to generalized systematic code. Under the proposed model, average delay, maximum disorder, and uniformity recovery entropy are introduced as performance indices to design efficient rateless codes. A novel coding scheme based on two‐stage encoding and forward equal probability is proposed to optimize the proposed indices. In the first stage, the first k symbols are encoded, aiming to improve the performance of order recovery, uniformity recovery, and transmission efficiency as much as possible. In the second stage, the remaining infinite symbols are encoded, where the symbols with high degree are used to compensate the symbols loss in the first stage. Simulation results show that the proposed scheme can achieve generalized systematic rateless codes with high probability and also has less average delay and maximum disorder, better capacity achievability, and uniformity recovery performance than Luby trasform (LT) codes and rateless coded symbol sorting algorithm. Besides, the proposed scheme has the aforementioned advantages compared with expending window fountain codes except for uniformity recovery and maximum disorder performance when the erasure rate is higher than about 0.25. Copyright © 2013 John Wiley & Sons, Ltd.

Near maximum likelihood soft-decision decoding of a particular class of rate-1/2 systematic linear block codes

Presented is a soft-decision decoding algorithm for a particular class of rate-1/2 systematic linear block codes. The proposed algorithm performs successive re-encoding of both the data and parity bits, to produce a list of codewords among which the most likely candidate is chosen. Simulation results show that close to optimal performance can be obtained at reasonable complexity. They validate the potential of the proposed algorithm as a practical approach for soft-decision decoding.

Analysis of Linear Block Codes as Sources with Memory

The linear, binary, block codes with no equally likely probabilities for the binary symbols are analyzed. The encoding graph for systematic linear block codes is proposed. These codes are seen as sources with memory and the information quantities H(S,X), H(S), H(X), H(X|S), H(S|X), I(S,X) are derived. On the base of these quantities, the code performances are analyzed.

Performance of Systematic Distance-4 Binary Linear Block Codes with Continuous Phase Frequency Shift Keying over MIMO Systems

Codes with full information rate (optimal), for example Hamming codes, provide the highest possible code rate R (R = k/n where k and n are the code dimension and length respectively) and it is an important property for a block code. Recently, the Systematic Distance-4 (SD-4) codes are proposed that allows generating all the optimal Hamming distance-4 binary linear block codes. Continuous Phase Frequency Shift Keying (CPFSK) provides low spectral occupancy and is suitable for power and bandwidth-limited channels such as satellite communication channels. MIMO technique is essential for modern wireless communication systems. In this article, we evaluated the error performances of SD-4 codes utilizing CPFSK modulation over MIMO Rician and Rayleigh channels via computer simulations and obtained outstanding results regarding coding gain.

On the Input-Output Weight Enumerators of Product Accumulate Codes

In this letter, a generalized MacWilliams transform that relates the input-redundancy weight enumerator of a systematic binary linear block code to that of its dual code is first presented. Based on this transform, the input-output weight enumerators of direct-product single-parity-check codes and the type-II product-accumulate codes are then derived, and used to analyze the asymptotic bit error performance of these codes.

Event error control codes and their applications

Burst error detection codes and cyclic redundancy check (CRC) codes are generalized to event-error detection codes, which are useful in various noisy channels. A systematic linear block code is constructed that detects any event error from an arbitrary list of event errors. The result is generalized to detection and correction of multiple event errors. Bounds are found on the minimum number of redundant bits needed to construct such codes. It is shown that, under certain conditions, the linear code construction is optimal. Various applications are discussed, where there is a Markov source or a Markov channel. It is argued that the codes described herein can be employed either as error detection codes, or as distance-enhancing codes when complete decoders are applied. Specific examples covered in this correspondence include hybrid automatic repeat request (ARQ) systems, intersymbol interference (ISI) channels, and Gilbert (1958) channels.

Linear block codes

The article discusses systematic cyclic linear block codes. A block code uses an encoder that accepts a block of message symbols, and generates a block of code word symbols at the output. This type is in contrast to a convolutional code when the encoder accepts a continuous stream of symbols and similarly generates a continuous encoded output stream. A code is linear if the addition of any two valid code words results in another valid code word. Similarly, a code is cyclic if a circular shift of any valid code word results in another valid code word. The term systematic is used for codes in which the code word contains the message symbols in an unaltered form. Systematic code words are formed by appending additional symbols to the message. These additional symbols are called redundancy or parity symbols. The term symbols as used in this article denotes the individual elements of a code word. In a binary code, the symbols are bits and in a non-binary code, the symbols are collections of bits (e.g., bytes).

Memory/speed tradeoffs for look-up table decoding of systematic linear block codes

Memory/speed tradeoffs are presented for the implementation of systematic linear block code decoders using lookup tables. Specifically, the authors show how to reduce the size of the lookup table that converts the syndrome into the error pattern. On the basis of such a single-error-correcting decoder they propose a t-stage decoder that can correct up to t errors. It is shown that the proposed scheme actually constitutes a general method for compressing lookup tables.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the complete decoding of binary linear codes (Corresp.)

Complete decoding of systematic linear block codes by standard arrays with coset leaders not necessarily of minimal weight gives, in several interesting cases on the binary symmetric channel with error probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> , a smaller symbol error probability than decoding using the coset leaders of minimum weight. The proposed choice of the coset leaders allows for the classes of uniformly packed and nearly perfect binary codes to achieve a lower information bit error probability, at least for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> sufficiently near zero.

An Efficient Image Watermarking System Based on Error Correcting Codes in DCT Domain

Digital watermarking has drawn extensive attention for copyright protection of multimedia data. This paper proposes a new watermarking system for digital images using efficient systematic linear block codes (SLBC) in discrete cosine transform (DCT) domain. The proposed watermarking system using SLBC generates a code sequence of {0, 1} that provides error correction capabilities and then replaces it with a binary watermark sequence of {-1, 1}. This achieves more robust invisible image watermarks and requires a small storage unit for binary sequence numbers. The generated watermark sequence is then used as an input for our proposed watermarking system which consists of watermark embedding process and watermark detection process. Experimental results indicate that the invisible watermark embedded with the proposed system are very robust against various kinds of attacks such as white Gaussian noise, JPEG compression, median, and mean filtering, by showing similarity values ranging from 0.7 to 0.8. KEY WORDS: Digital Watermarking; Linear Block Code; Copyright Protection. DOI: http://dx.doi.org/10.3329/mist.v3i0.8056