DC- and Nyquist-free error correcting convolutional codes

A class of DC- and Nyquist-free codes with error correcting capability is proposed. These codes are minimum-bandwidth codes because they have spectral null at Nyquist frequency. They also have a good error correcting capability because they are constructed from binary convolutional codes     

Performance of ultrawideband SSMA using time hopping and M-ary PPM

Wireless spread spectrum multiple access (SSMA) using time hopping and block waveform encoded (M-ary) pulse position modulated (PPM) signals is analyzed. For different M-ary PPM signal designs, the multiple-access performance in free-space propagation renditions is analyzed in terms of the number of users supported by the system for a given bit error rate, signal-to-noise ratio, bit transmission rate, and number of signals in the M-ary set. The processing gain and number of simultaneous users are described in terms of system parameters. Tradeoffs between performance and receiver complexity are discussed. Upper bounds on both the maximum number of users and the total combined bit transmission rate are investigated. This analysis is applied to ultrawideband impulse radio modulation. In this modulation, the communications waveforms are practically realized using subnanosecond impulse technology. A numerical example is given that shows that impulse radio modulation is theoretically able to provide multiple-access communications with a combined transmission capacity of hundreds of megabits per second at bit error rates in the range 10^-4 to 10^-7 using receivers of moderate complexity     

Multiple-word correcting convolutional codes

Two classes of multiple-word correcting convolutional encoders are defined and analyzed. We obtain some conditions for these encoders to be noncatastrophic, and we describe ways to check the (word) minimum distance of the generated codes. The first class can easily be analyzed by algebraic means, but the redundancy of the corresponding codes is not arbitrarily iow. The codes generated by the second class of encoders may have a lower redundancy, but their analysis requires the use of a computer program.     

Parallel error correcting codes

We introduce the concept of "parallel error correcting" codes, the error correcting codes for parallel channels. Here, a parallel channel is a set of channels such that the additive error over a finite field occurs in one of its members at time T if the same error occurs in all members at the same time. The set of codewords of a parallel error correcting code has to be a product set, if the messages transmitted are from independent information sources. We present a simple construction of optimal parallel error correcting codes based on ordinary optimal error correcting codes and a construction of optimal linear parallel codes for independent sources based on optimal ordinary linear error correcting codes. The decoding algorithms for these codes are provided as well     

On ternary error correcting line codes

The authors present Markov diagrams and tables with the capacities in bits/symbol for input restricted ternary channels with various restrictions on maximum runlengths, digital sum variation, and transitions between extreme signal levels. They derive Gilbert-type lower bounds on the minimum Hamming and Euclidean distances achievable with ternary line codes of rates lower than the capacity of the corresponding input restricted channel. They present some single-symbol-error-correcting ternary line codes, found by computer search methods     

High-throughput error correcting space-time block codes

This letter investigates using an error correction code (ECC) to construct the space-time block code (STBC). Block ECCs over several Galois fields are considered. The resulting STBCs have significantly higher throughput and better performance than orthogonal STBCs, at the cost of increased decoding complexity.     

Construction of error correcting codes by interpolation

A generalized and unified method of interpolation and transformation is used to generate all known maximal distance codes and important subfield subcodes. Some powerful tools for the analysis and synthesis of maximal distance codes are presented, as well as a generalization of the Mattson-Solomon polynomial and Lagrange and Fourier transforms to more general functions. In certain cases new codes can be obtained by differentiating a kernel function. Some further generalizations of Srivastava codes are constructed. A general method of decoding is given which can be used for complete decoding of ali coset leaders.     

Unequal error protection for convolutional codes

In this correspondence, unequal error-correcting capabilities of convolutional codes are studied. For errors in the information symbols and code symbols, the free input- and output-distances, respectively, serve as "unequal" counterparts to the free distance. When communication takes place close to or above the channel capacity the error bursts tend to be long and the free distance is not any longer useful as the measure of the error correcting capability. Thus, the active burst distance for a given output and the active burst distance for a given input are introduced as "unequal" counterparts to the active burst distance and improved estimates of the unequal error-correcting capabilities of convolutional codes are obtained and illustrated by examples. Finally, it is shown how to obtain unequal error protection for both information and code symbols using woven convolutional codes.     

Reed-Solomon codes for correcting phased error bursts

A code structure is introduced that represents a Reed-Solomon (RS) code in two-dimensional format. Based on this structure, a novel approach to multiple error burst correction using RS codes is proposed. For a model of phased error bursts, where each burst can affect one of the columns in a two-dimensional transmitted word, it is shown that the bursts can be corrected using a known multisequence shift-register synthesis algorithm. It is further shown that the resulting codes posses nearly optimal burst correction capability, under certain probability of decoding failure. Finally, low-complexity systematic encoding and syndrome computation algorithms for these codes are discussed. The proposed scheme may also find use in decoding of different coding schemes based on RS codes, such as product or concatenated codes.     

Critical lengths of error events in convolutional codes

If the calculation of the critical length is based on the expurgated exponent, the length becomes nonzero for low error probabilities. This result applies to typical long codes, but it may also be useful for modeling error events in specific codes     

Optimum mean-square error use of convolutional codes

Thekinput and output digits of a rate(k/n)linear convolutional code over a finite field GF(q)are related to a finite set of integers by aq-ary expansion. The mean-square error criterion is used to simultaneously select the optimum encoder and decoder rules. This optimization is performed over all one-to-one generalized encoding rules and all decoding functions that map into the real numbers. The optimal design procedure relies upon generalized Fourier transforms, and it is shown that the encoder part of the optimum pair of rules can be taken as a linear function when the input space of symbols is viewed in a natural algebraic setting. The decoder part is a conditional mean estimator coupled with a rounding operation. One method of implementing the decoder uses the nonlinear combination of filter functions defined in the generalized frequency domain.     

The burst error correcting power of m-sequence codes

Linear maximum length sequence codes are shown to be asymptotically efficient burst error correcting codes. These codes are essentially single burst correctors and for binary alphabets have the following parameters : block length, n = 2^m ? 1 ; number of information digits, k = m; and burst error correcting capability, b≥2^m?1 ? m, m ≥ 2 ; where m is an integer. A generalization to multilevel alphabets is also presented.     

Forward error correcting codes in synchronous fiber optictransmission systems

This paper proposes forward error correcting (FEC) code for synchronous digital hierarchy (SDH) fiber optical transmission systems. They are (18880, 18865) and (2370, 2358) shortened Hamming codes and are encoded at the multiplex-section layer; the check bits are embedded in auxiliary multiplex-section overhead (MSOH) bytes. The codes realize general circuit configurations regardless of the transmission speed or path-size, perfect compatibility with SDH format, suppressed processing delay accumulation, and decrease the chance of line-switching in the case of signal degradation. To ensure that the various requirements of each network-provider such as customized usage of SOH bytes and affordable circuit scale could be satisfied, a trial circuit board was constructed on the programmable hardware called PROTEUS, which enables flexible operation in terms of code-selection and check bit area. We actually confirm error-correcting capability through the first STM-64 FEC-coded-optical transmission experiment. The statistics of error occurrence in the optical transmission line are also studied. The result indicates that the proposed codes are effective in optical transmission systems if the BER is limited by optical noise and dispersion     

Block error correcting codes using finite-field wavelet transforms

This paper extends the popular wavelet framework for signal representation to error control coding. The primary goal of the paper is to use cyclic finite-field wavelets and filter banks to study arbitrary-rate L-circulant codes. It is shown that the wavelet representation leads to an efficient implementation of the block code encoder and the syndrome generator. A formulation is then given for constructing maximum-distance separable (MDS) wavelet codes using frequency-domain constraints. This paper also studies the possibility of finding a wavelet code whose tail-biting trellis is efficient for soft-decision decoding. The wavelet method may provide an easy way to look for such codes.     

纠错码性能仿真中的误码率估计

在纠错码性能仿真中,一般是给定信噪比后,由实测的错误信息比特数与发达信息比特总数相比来估计误码率的,这种方法在大码长或者极低误码率情况下。可信程度不高。本文提出用仿真数据计算后验概率分布参数的方法来直接估计纠错误码率及其置信区间,给出了误码率的上界,由少量测试数据仍然可以获得比较可靠的误码率估计,由于这种后验估计考虑了信道特性,所以适用于任意广义信道模型。     

N-modular redundancy using the theory of error correcting codes

Using redundancy is basic to fault-tolerant computing. N-modular redundancy (NMR) is in some ways analogous to the use of a repetition code where an information symbol is replicated as parity symbols in a codeword. Linear error-correcting codes (ECC) use linear combinations of information symbols as parity symbols to generate syndromes for error patterns. In this paper, ECC theory has been applied to derive redundant circuits that tolerate faults in both the modules and checkers. Circuits using comparators for diagnosis are derived with a non-graph-theoretic approach. Coding theoretic principles are applied directly to NMR, so that extensive diagnosis of the fault-tolerant system is achieved.     

Binary multilevel convolutional codes with unequal error protectioncapabilities

Binary multilevel convolutional codes (CCs) with unequal error protection (UEP) capabilities are studied. These codes belong to the class of generalized concatenated (GC) codes. Binary CCs are used as outer codes. Binary linear block codes of short length, and selected subcodes in their two-way subcode partition chain, are used as inner codes. Multistage decodings are presented that use Viterbi decoders operating on trellises with similar structure to that of the constituent binary CCs. Simulation results of example binary two-level CC's are also reported     

Single error correcting and multiple unidirectional error detecting cyclic an arithmetic codes

We present cyclic AN arithmetic codes capable of single error correction and multiple unidirectional error detection. These codes can be used throughout a fault-tolerant computer, and they eliminate the need for encoding/decoding circuits and code translation circuits. We use criteria for the determination of the unidirectional error detection capability for a given AN code, and we present a new error correction/detection scheme.