A class of binary burst error-correcting quasi-cyclic codes

A class of binary quasi-cyclic burst error-correcting codes based upon product codes is studied. An expression for the maximum burst error-correcting capability for each code in the class is given. In certain cases, the codes exist in the class which have the same block length and number of check bits as the Gilbert codes, but correct longer bursts of errors than Gilbert codes. By shortening the codes, it is possible to design codes which achieve the Reiger bound     

A class of high-speed decoders for linear cyclic binary codes

A general method is proposed for decoding any cyclic binary code at extremely high speed using only modulo2adders and threshold elements, and the decoders may be designed for maximum-likelihood decoding. The number of decoding cycles is a fraction of the number of digits in the code word.     

On the undetected error probability for binary codes

In this paper, the undetected error probability for binary codes is studied. First complementary codes are studied. Next, a new proof of Abdel-Ghaffar's (1997) lower bound on the undetected error probability is presented and some generalizations are given. Further, upper and lower bounds on the undetected error probability for binary constant weight codes are given, and asymptotic versions are studied.     

Runlength limited codes for random and burst error correction

A product code approach to the design of multiple error correcting runlength limited codes is presented. In contrast to recent coding schemes of this type they are based entirely on binary coding operations and are therefore relatively simple to realise in hardware. A table of some illustrative codes is presented.<>     

The simplex codes and other even-weight binary linear codes for error correction

The probability of correct decoding on the binary-symmetric channel is studied. In particular, a class of codes with the same lengths and dimensions as the linear simplex codes, but with larger probability of correct decoding for all parameters p, 0 < p < 1/2, is given.     

A class of QC-LDPC codes with low encoding complexity and good error performance

We propose a novel approximate lower triangular structure for the parity part of the parity-check matrix of QC-LDPC codes. About half of the non-zero elements in the parity part are set to locate on the upper diagonal while the remaining non-zero elements can be located almost anywhere within the lower triangular area, provided certain rules are observed. Compared with the typical dual-diagonal structure, the proposed structure requires very similar encoding complexity and produces lower error rates over an AWGN channel.     

一种低差错平底线性复杂度的QC-LDPC码构造方法

本文给出了一种低差错平底QC-LDPC码构造方法.首先,提出了扩展近似下三角阵eALT( extern Approximate Lower Triangular)的全局矩阵构造法,通过对改进后的全局矩阵M进行矩阵置换,生成LDPC码的校验矩阵H以达 到减少小停止集( Stopping Set)数量,降低差错平台(Er...     

New class of nonlinear systematic error detecting codes

A code C detects error e with probability 1-Q(e),ifQ(e) is a fraction of codewords y such that y, y+e/spl isin/C. We present a class of optimal nonlinear q-ary systematic (n, q/sup k/)-codes (robust codes) minimizing over all (n, q/sup k/)-codes the maximum of Q(e) for nonzero e. We also show that any linear (n, q/sup k/)-code V with n /spl les/2k can be modified into a nonlinear (n, q/sup k/)-code C/sub v/ with simple encoding and decoding procedures, such that the set E={e|Q(e)=1} of undetected errors for C/sub v/ is a (k-r)-dimensional subspace of V (|E|=q/sup k-r/ instead of q/sup k/ for V). For the remaining q/sup n/-q/sup k-r/ nonzero errors, Q(e)/spl les/q/sup -r/for q/spl ges/3 and Q(e)/spl les/ 2/sup -r+1/ for q=2.     

Undetected error probabilities of binary primitive BCH codes forboth error correction and detection

We investigate the undetected error probabilities for bounded-distance decoding of binary primitive BCH codes when they are used for both error correction and detection on a binary symmetric channel. We show that the undetected error probability of binary linear codes can be simplified and quantified if the weight distribution of the code is binomial-like. We obtain bounds on the undetected error probability of binary primitive BCH codes by applying the result to the code and show that the bounds are quantified by the deviation factor of the true weight distribution from the binomial-like weight distribution     

A union bound on the error probability of binary codes over block-fading channels

Block-fading is a popular channel model that approximates the behavior of different wireless communication systems. In this paper, a union bound on the error probability of binary-coded systems over block-fading channels is proposed. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. The distribution of error bits over the fading blocks is computed. For a specific distribution pattern, the pairwise error probability is derived. Block-fading channels modeled as Rician and Nakagami distributions are studied. We consider coherent receivers with perfect and imperfect channel side information (SI) as well as noncoherent receivers employing square-law combining. Throughout the paper, imperfect SI is obtained using pilot-aided estimation. A lower bound on the performance of iterative receivers that perform joint decoding and channel estimation is obtained assuming the receiver knows the correct data and uses them as pilots. From this, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Furthermore, the optimal energy allocation for pilot signals is found for different channel memory lengths.     

A class of irregular LDPC codes with low error floor and low encoding complexity

In this letter, we propose a class of irregular structured low-density parity-check (LDPC) codes with low error floor and low encoding complexity by designing the parity check matrix in a triangular plus dual-diagonal form. The proposed irregular codes clearly lower the error floor and dramatically improve the performance in the waterfall region of error-rate curves. Being characterized by linear encoding complexity, the encoders of the proposed codes attain throughputs over 10 Gbit/s.     

A new class of binary codes constructed on the basis of BCH codes (Corresp.)

In this correspondence, we present a new class of binary codes that are constructed on the basis of BCH codes. Some examples of these codes are given, having more codewords than the best codes previously known (to the authors) with the same minimum distance and number of check symbols. A decoding algorithm for the codes is also described.     

On the undetected error probability of nonlinear binary constantweight codes

The undetected error probability (UEP) of binary (n, 2δ, m) nonlinear constant weight codes over the binary symmetric channel (BSC) is investigated, where n is the blocklength, m is the weight of codeword and 2δ is the minimum distance of the codes. The distance distribution of the (n, 2, m) nonlinear constant weight codes is evaluated. It is proven in this paper that the (5, 2, 2) code, (5, 2, 3) code, (6, 2, 3) code, (7, 2, 4) code, (7, 2, 3) code and (8, 2, 4) code are the only proper error-detecting codes in the (n, 2, m) nonlinear constant weight codes for n⩾5, in the sense that their UEP is increased monotonically with the channel error rate p, of course all these proper codes are m-out-of-n codes. Furthermore, it is conjectured that except for the cases of n⩽4δ, there are no proper error-detecting binary (n, 2δ, m) nonlinear constant weight codes, for n>8 and δ⩾1     

The single burst error detection performance of binary cyclic codes

Using a new statistical model for burst errors, the authors calculate the conditional probability of undetected error for CRC codes with generator polynomials of the form g(x)=(1+x)p(x), p(x) a primitive polynomial. They show that the choice of p(x) affects the performance of these codes     

MIMO-DFE based space-time receiver over frequency selective channels with limited error propagation

MIMO-DFE(Multiple-Input-Multiple-Output Decision Feedback Equalizer) based receiver architectures are researched recently to detect signals in BLAST(Bell laboratories LAyered Space-Time) over frequency-selective channels. Due to their recursive structure, these receivers may suffer from error propagation which results in an overall mean square error degradation. An MIMO-DFE based BLAST receiver with limited error propagation to combat frequencyselective channel is proposed, which employs both norm constraint on feedback filter taps and soft decision device. Simulation results show that the proposed receiver outperforms conventional ones in various frequency selective channels.     

Weight distribution of a class of binary block codes formed from RCPC codes

In this paper, we study the weight enumerator and the numerical performance of a class of binary linear block codes formed from a family of rate-compatible punctured convolutional (RCPC) codes. Also, we present useful numerical results for a well-known family of RCPC codes.     

Distance distribution of binary codes and the error probability of decoding

We address the problem of bounding below the probability of error under maximum-likelihood decoding of a binary code with a known distance distribution used on a binary-symmetric channel (BSC). An improved upper bound is given for the maximum attainable exponent of this probability (the reliability function of the channel). In particular, we prove that the "random coding exponent" is the true value of the channel reliability for codes rate R in some interval immediately below the critical rate of the channel. An analogous result is obtained for the Gaussian channel.     

New class of codes suitable for computer error control

A new concept of generalised orthogonality is proposed and a class of generalised orthogonal codes based on SBIBD theory is developed     

The average binary weight-enumerator for a class of generalizedReed-Solomon codes

An explicit weight-enumerator for the set of binary expansions of a class of generalized Reed-Solomon codes is derived. This enumerator is then used to show that most of these binary codes are asymptotically good, and to bound the rates of self-intersecting codes     

Bounds on the decoding error probability of binary linear codes viatheir spectra

Bounds on the error probability of maximum likelihood decoding of a binary linear code are considered. The bounds derived use the weight spectrum of the code and they are tighter than the conventional union bound in the case of large noise in the channel. The bounds derived are applied to a code with an average spectrum, and the result is compared to the random coding exponent. The author shows that the bound considered for the binary symmetrical channel case coincides asymptotically with the random coding bound. For the case of AWGN channel the author shows that Berlekamp's (1980) tangential bound can be improved, but even this improved bound does not coincide with the random coding bound, although it can be very close to it