Subspace-based error and erasure correction with DFT codes for wireless channels

This paper deals with the decoding of lowpass discrete Fourier transform (DFT) codes in the presence of both errors and erasures. We propose a subspace-based approach for the error localization that is similar to the subspace approaches followed in the array signal processing for direction-of-arrival (DOA) estimation. The basic idea is to divide a vector space into two orthogonal subspaces of which one is spanned by the error locator vectors. The locations of the errors are estimated from the spanning eigenvectors of the complement subspace. However, unlike the subspace approach in DOA estimation, which is similar to estimating the subspaces from the syndrome covariance matrix after a projection, in the proposed approach, the subspaces are estimated from the modified syndrome covariance matrix after a whitening transform. Simulation results with a Gauss-Markov source reveal that the proposed algorithm is more efficient than the coding theoretic approach on impulsive channels as well as the subspace approach with projection on lossy channels.     

A permutation decoding of the (24, 12, 8) Golay code (Corresp.)

We give a minimal set consisting of14permutations to decode the(24,12,8)Golay code using a permutation decoding method.     

On forward error correction with adaptive decoding (Corresp.)

A method is proposed that utilizes punctured Reed-Solomon (RS) block codes for adaptive coding. Part of the redundancy of the RS codewords is used in a convolutional coding framework. This enables some codewords to use more redundancy for correcting errors, while other adjacent codewords use less redundancy.     

双二元Turbo码的译码算法研究

双二元Turbo码（double-binary Turbo code）是支持无线城域网（WMAN）802．16d标准中多载波OFDM系统物理层采用的前向纠错码方案之一。相对于经典Turbo码，它具有编码效率高，相同复杂度译码器下纠错性能好以及译码时延小等优点。现介绍了双二元Turbo码的编码器结构特点，并且详细推导了双二元Turbo码的两种译码算法，同时给出了仿真性能曲线。     

部分正交空时块编码(POSTBC)及其解码算法

提出一种三发射天线的部分正交空时编码(POSTBC)结构.发送天线被分成两组,第一组采用Alamouti STBC编码,第二组则直接采用QPSK调制 .和Alamouti STBC 分组码相比它的优点是不需要偶数根发射天线. 由于各组发送的数据流相互独立,针对这一系统框架,采用了最优排序串行干扰消除(OSIC)译码算法和一种新的译码算法.计算机仿真结果表明,这种空时编码(MIMO)结构在等数据率的情况下能获得比相应的V-BLAST系统更优的性能.     

Fast ML decoding algorithm for the Nordstrom - Robinson code (Corresp.)

The extended Nordstrom-Robinson code is an optimum nonlinear double-error-correcting code of length16with considerable practical importance. This code is also useful as a rate1/2vector quantizer for random waveforms such as speech linear-predictive-coding (LPC) residual. A fast decoding algorithm is described for maximum likelihood decoding (or nearest neighbor search in the squared-error sense) with304additions and128comparisons.     

A 12-bit successive-approximation-type ADC with digital error correction

A correction algorithm has been implemented that gives an almost twofold improvement in conversion speed without loss of accuracy or changes to the analog circuitry of a slower design. The design of a smart successive-approximation register chip, which has been fabricated in a double poly CMOS process and takes up 18 mil/SUP 2/ in die area, is described. The area is 13% larger than that of an A/D converter utilizing the same analog chip but a conventional digital chip without error correction. A speed improvement from 12 to 7 /spl mu/s was obtained with digital error correction.     

A new high rate code scheme with highly parallel and low complexity decoding algorithm

A new high rate code scheme is proposed in this paper. It consists of serial concatenated recursive systematic ordinary (nonpunctured) convolutional codes with only 8 states in the trellis of the corresponding reciprocal dual codes. With a low complexity and highly parallel decoding algorithm, over additive white Gaussian noise channels, the proposed codes can achieve good bit error rate (BER) performance comparable to that of turbo codes and low density parity check (LDPC) codes. At code rate R=16/17, the overall decoding complexity of the proposed code scheme is almost half that of the LDPC codes.     

The probability of undetected error when a code is used for error correction and detection (Corresp.)

We study the probability of having an undetected error when a linear block code is used to correct up toterrors on a symmetric channel, and the remaining power of the code is used for error detection.     

On high-speed decoding of the (23,12,7) Golay code

An algebraic decoding method for triple-error-correcting binary BCH codes applicable to complete decoding of the (23,12,7) Golay code has been proved by M. Elia (see ibid., vol.IT-33, p.150-1, 1987). A modified step-by-step complete decoding algorithm of this Golay code is introduced which needs fewer shift operations than Kasami's error-trapping decoder. Based on the algorithm, a high-speed hardware decoder of this code is proposed     

Algebraic decoding of the (32, 16, 8) quadratic residue code

An algebraic decoding algorithm for the 1/2-rate (32, 16, 8) quadratic residue (QR) code is found. The key idea of this algorithm is to find the error locator polynomial by a systematic use of the Newton identities associated with the code syndromes. The techniques developed extend the algebraic decoding algorithm found recently for the (32, 16, 8) QR code. It is expected that the algebraic approach developed here and by M. Elia (1987) applies also to longer QR codes and other BCH-type codes that are not fully decoded by the standard BCH decoding algorithm     

A novel approach for evaluating the performance of SPC productcodes under erasure decoding

Product codes are powerful codes that can be used to correct errors or recover erasures. The simplest form of a product code is that where every row and every column is terminated by a single parity bit, referred to as single parity check (SPC) product code. This code has a minimum distance of four and is thus guaranteed to recover all single, double, and triple erasure patterns. Judging the code performance based on its minimum distance is very pessimistic because the code is actually capable of recovering many higher erasure patterns. This paper develops a novel approach for deriving an upper bound on the post-decoding erasure rate for the SPC product code with iterative decoding. Simulation shows that the derived bound is very tight     

Cover positions and decoding complexity of the Golay code, using anextended Kasami algorithm

This paper compares the complexity of an extended Kasami (1964) algorithm with three other algorithms for the Golay code. A nonmathematical method is described to determine the best cover positions. This leads to a result different from the Kasami algorithm and significantly reduces the decoding complexity     

Estimation of the exponent of the decoding error probability for a special generalized LDPC code

A special construction of a generalized low-density parity-check (LDPC) code and a low-complexity algorithm for his code decoding are proposed. A lower estimate of the exponent of the decoding error probability is obtained for the considered code and the decoding algorithm. This estimate leads the conclusion that, in an ensemble of considered LDPC codes, there are codes with rates as high as the code capacity and the exponent of the decoding error probability exceeds zero.     

Soft-decision and erasure decoding in fast frequency-hoppingsystems with convolutional, turbo, and Reed-Solomon codes

In this contribution we present an exhaustive treatment of various coding and decoding techniques for use in fast frequency-hopping/multiple frequency shift keying multiple-access systems. One of the main goals is to show how reliability information on each received bit can be derived to enable soft-decision decoding. Convolutional codes as well as turbo codes are considered applying soft-decision, erasure, and hard-decision decoding. Their performance is compared to that of previously proposed Reed-Solomon with either errors-only or errors-and-erasures decoding. A mobile radio environment yielding a frequency-selective fading channel is assumed. It is shown that the application of turbo codes and convolutional codes with soft decision decoding can allow for a comparable number of simultaneously transmitting users to Reed-Solomon codes with errors-and-erasures decoding. Furthermore, the advantage of soft decisions is shown, which can be applied to a widely and growing range of channel codes. The pertinent technique of calculating soft decisions is described in the paper     

A decoding algorithm with restrictions for array codes

We present a simple and efficient error correction scheme for array-like data structures. We assume that the channel behaves such that each row of a received array is either error-free or corrupted by many symbol errors. Provided that row error vectors are linearly independent, the proposed decoding algorithm can correct asymptotically one erroneous row per redundant row, even without having reliability information from the channel output. This efficient decoding algorithm can be used for correction of error clusters and for decoding of concatenated codes. We also derive a random access scheme that has many similarities with the Aloha system     

Joint iterative decoding of LDPC codes for channels with memory and erasure noise

This paper investigates the joint iterative decoding of low-density parity-check (LDPC) codes and channels with memory. Sequences of irregular LDPC codes are presented that achieve, under joint iterative decoding, the symmetric information rate of a class of channels with memory and erasure noise. This gives proof, for the first time, that joint iterative decoding can be information rate lossless with respect to maximum-likelihood decoding. These results build on previous capacity-achieving code constructions for the binary erasure channel. A two state intersymbol-interference channel with erasure noise, known as the dicode erasure channel, is used as a concrete example throughout the paper.     

Algebraic decoding of the (23,12,7) Golay code (Corresp.)

It is shown that the algebraic method for decoding three-error-correcting BCH codes is also applicable to complete decoding of the(23,12,7)Golay code.     

Exponential error bounds for erasure, list, and decision feedback schemes

By an extension of Gallager's bounding methods, exponential error bounds applicable to coding schemes involving erasures, variable-size lists, and decision feedback are obtained. The bounds are everywhere the tightest known.