Area efficient parallel lfsr for cyclic redundancy check

Cyclic Redundancy Check (CRC), code for error detection finds many applications in the field of digital communication, data storage, control system and data compression. CRC encoding operation is carried out by using a Linear Feedback Shift Register (LFSR). Serial implementation of CRC requires more clock cycles which is equal to data message length plus generator polynomial degree but in parallel implementation of CRC one clock cycle is required if a whole data message is applied at a time. In previous work related to parallel LFSR, hardware complexity of the architecture reduced using a technique named state space transformation. This paper presents detailed explaination of search algorithm implementation and technique to find number of XOR gates required for different CRC algorithms. This paper presents a searching algorithm and new technique to find the number of XOR gates required for different CRC algorithms. The comparison between proposed and previous architectures shows that the number of XOR gates are reduced for CRC algorithms which improve the hardware efficiency. Searching algorithm and all the matrix computations have been performed using MATLAB simulations

A Flexible BCH decoder for Flash Memory Systems using Cascaded BCH codes

NAND ash memories are widely used in consumer electronics, such as tablets, personal computers, smartphones, and gaming systems. However, unlike other standard storage devices, these ash memories suffer from various random errors. In order to address these reliability issues, various error correction codes (ECC) are employed. Bose-Chaudhuri Hocquenghem (BCH) code is the most common ECC used to address the errors in modern ash memories. Because of the limitation of the realization of the BCH codes for more extensive error correction, the modern ash memory devices use Low-density parity-check (LDPC) codes for error correction scheme. The realization of the LDPC decoders have greater complexity than BCH decoders, so these ECC decoders are implemented within the ash memory device. This thesis analyzes the limitation imposed by the state of the art implementation of BCH decoders and proposes a cascaded BCH code to address these limitations. In order to support a variety of ash memory devices, there are three main challenges to be addressed for BCH decoders. First, the latency of the BCH decoders, in the case of no error scenario, should be less than 100us. Second, there should be flexibility in supporting different ECC block size; more precisely, the solution should be able to support 256, 512, 1024, and 2048 bytes of ECC block. Third, there should be flexibility in supporting different bit errors. A recent development with Graphical Processing Units (GPUs) has attracted many researchers to use GPUs for non-graphical implementation. These GPUs are used in many consumer electronics as part of the system on chip (SOC) configuration. In this thesis we studied the limitation imposed by different implementations (VLSI, GPU, and CPU) of BCH decoders, and we propose a cascaded BCH code implemented using a hybrid approach to overcome the limitations of the BCH codes. By splitting the implementation across VLSI and GPUs, we have shown in this thesis that this method can provide flexibility over the block size and the bit error to be corrected

INTEND AND PROPOSE THE HIGH SPEED LFSR CIRCUIT USING SST METHOD

Linear feedback shift register (LFSR) is an important component of the cyclic redundancy check (CRC) operations and BCH encoders. This thesis presents a mathematical proof of existence of a linear transformation to transform LFSR circuits into equivalent state space formulations. This transformation achieves a full speed-up compared to the serial architecture at the cost of an increase in hardware overhead. This method applies to all irreducible polynomials used in CRC operations and BCH encoders. A new formulation is proposed to modify the LFSR into the form of an CRC filter. We propose a novel high speed parallel LFSR architecture based on parallel Infinite Impulse Response (CRC) filter design, pipelining and retiming algorithms. The advantage of proposed approach over the previous architectures is that it has both feedforward and feedback paths. We further propose to apply combined parallel and pipelining techniques to eliminate the fanout effect in long generator polynomials. The proposed scheme can be applied to any generator polynomial, i.e., any LFSR in general. A comparison between the proposed and previous architectures shows that the proposed parallel architecture achieves the same critical path as that of previous designs with a reduced hardware cost

Hardware Implementations of CCSDS Deep Space LDPC Codes for a Satellite Transponder

Error-correction coding is a technique that adds mathematical structure to a message, allowing corruptions to be detected and corrected when the message is received. This is especially important for deep space satellite communications, since the long distances and low signal power levels often cause message corruption. A very strong type of error-correction coding known as LDPC codes was recently standardized for use with space communications. This project implements the encoding and decoding algorithms required for a small satellite radio to be able to use these LDPC codes. Several decoder architectures are implemented and compared by their performance, speed, and complexity. Using these LDPC decoders requires knowledge of the received signal and noise levels, so an appropriate algorithm for estimating these parameters is developed and implemented. The LDPC encoder is implemented using a flexible architecture that allows the entire standardized family of ten LDPC codes to be encoded using the same hardware

Concatenated Turbo/LDPC codes for deep space communications: performance and implementation

Deep space communications require error correction codes able to reach extremely low bit-error-rates, possibly with a steep waterfall region and without error floor. Several schemes have been proposed in the literature to achieve these goals. Most of them rely on the concatenation of different codes that leads to high hardware implementation complexity and poor resource sharing. This work proposes a scheme based on the concatenation of non-custom LDPC and turbo codes that achieves excellent error correction performance. Moreover, since both LDPC and turbo codes can be decoded with the BCJR algorithm, our preliminary results show that an efficient hardware architecture with high resource reuse can be designe

Polynomials in Error Detection and Correction in Data Communication System

The chapter gives an overview of the various types of errors encountered in a communication system. It discusses the various error detection and error correction codes. The role of polynomials in error detection and error correction is discussed in detail with the architecture for practical implementation of the codes in a communication channel

An Optimization Technique for CRC Generation

Abstract: In networking environments, the cyclic redundancy check (CRC) is widely utilized to determine whether errors have been introduced during transmissions over physical links. In this paper, we present a fast cyclic redundancy check (CRC) algorithm that performs CRC computation for an arbitrary length of message in parallel. This paper proposes 64 bits parallel CRC architecture based on F matrix with order of generator polynomial is 32 and showed CRC-64 is having less latency and high throughput compared to CRC-32 parallel architecture through Xilinx Simulator

2D Parity Product Code for TSV online fault correction and detection

Through-Silicon-Via (TSV) is one of the most promising technologies to realize 3D Integrated Circuits (3D-ICs).  However, the reliability issues due to the low yield rates and the sensitivity to thermal hotspots and stress issues are preventing TSV-based 3D-ICs from being widely and efficiently used. To enhance the reliability of TSV connections, using error correction code to detect and correct faults automatically has been demonstrated as a viable solution.This paper presents a 2D Parity Product Code (2D-PPC) for TSV fault-tolerance with the ability to correct one fault and detect, at least, two faults.  In an implementation of 64-bit data and 81-bit codeword, 2D-PPC can detect over 71 faults, on average. Its encoder and decoder decrease the overall latency by 38.33% when compared to the Single Error Correction Double Error Detection code.  In addition to the high detection rates, the encoder can detect 100% of its gate failures, and the decoder can detect and correct around 40% of its individual gate failures. The squared 2D-PPC could be extended using orthogonal Latin square to support extra bit correction

A VLSI synthesis of a Reed-Solomon processor for digital communication systems

The Reed-Solomon codes have been widely used in digital communication systems such as computer networks, satellites, VCRs, mobile communications and high- definition television (HDTV), in order to protect digital data against erasures, random and burst errors during transmission. Since the encoding and decoding algorithms for such codes are computationally intensive, special purpose hardware implementations are often required to meet the real time requirements. -- One motivation for this thesis is to investigate and introduce reconfigurable Galois field arithmetic structures which exploit the symmetric properties of available architectures. Another is to design and implement an RS encoder/decoder ASIC which can support a wide family of RS codes. -- An m-programmable Galois field multiplier which uses the standard basis representation of the elements is first introduced. It is then demonstrated that the exponentiator can be used to implement a fast inverter which outperforms the available inverters in GF(2m). Using these basic structures, an ASIC design and synthesis of a reconfigurable Reed-Solomon encoder/decoder processor which implements a large family of RS codes is proposed. The design is parameterized in terms of the block length n, Galois field symbol size m, and error correction capability t for the various RS codes. The design has been captured using the VHDL hardware description language and mapped onto CMOS standard cells available in the 0.8-µm BiCMOS design kits for Cadence and Synopsys tools. The experimental chip contains 218,206 logic gates and supports values of the Galois field symbol size m = 3,4,5,6,7,8 and error correction capability t = 1,2,3, ..., 16. Thus, the block length n is variable from 7 to 255. Error correction t and Galois field symbol size m are pin-selectable. -- Since low design complexity and high throughput are desired in the VLSI chip, the algebraic decoding technique has been investigated instead of the time or transform domain. The encoder uses a self-reciprocal generator polynomial which structures the codewords in a systematic form. At the beginning of the decoding process, received words are initially stored in the first-in-first-out (FIFO) buffer as they enter the syndrome module. The Berlekemp-Massey algorithm is used to determine both the error locator and error evaluator polynomials. The Chien Search and Forney's algorithms operate sequentially to solve for the error locations and error values respectively. The error values are exclusive or-ed with the buffered messages in order to correct the errors, as the processed data leave the chip