Showing papers on "Forward error correction published in 1989"

A Viterbi algorithm with soft-decision outputs and its applications

Abstract: The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated. >

Bandwidth efficient coding for fading channels: code construction and performance analysis

Abstract: The authors apply a general method of bounding the event error probability of TCM (trellis-coded modulation) schemes to fading channels and use the effective length and the minimum-squared-product distance to replace the minimum-free-squared-Euclidean distance as code design parameters for Rayleigh and Rician fading channels with a substantial multipath component. They present 8-PSK (phase-shift-keying) trellis codes specifically constructed for fading channels that outperform equivalent codes designed for the AWGN (additive white Gaussian noise) channel when v>or=5. For quasiregular trellis codes there exists an efficient algorithm for evaluating event error probability, and numerical results which demonstrate the importance of the effective length as a code design parameter for fading channels with or without side information have been obtained. This is consistent with the case for binary signaling, where the Hamming distance remains the best code design parameter for fading channels. The authors show that the use of Reed-Solomon block codes with expanded signal sets becomes interesting only for large value of E/sub s//N/sub 0/, where they begin to outperform trellis codes. >

On-Chip ECC for Multi-Level Random Access Memories

Abstract: In this talk we investigate a number of on-chip coding techniques for the protection of Random Access Memories which use multi-level as opposed to binary storage cells. The motivation for such RAM cells is of course the storage of several bits per cell as opposed to one bit per cell [l]. Since the typical number of levels which a multi-level RAM can handle is 16 (the cell being based on a standard DRAM cell which has varying amounts of voltage stored on it) there are four bits recorded into each cell [2]. The disadvantage of multi-level RAMs is that they are much more prone to errors, and so on-chip ECC is essential for reliable operation. There are essentially three reasons for error control coding in multi-level RAMs: To correct soft errors, to correct hard errors, and to correct read errors. The source of these errors is, respectively, alpha particle radiation, hardware faults, and data level ambiguities. On-chip error correction can be used to increase the mean life before failure for all three types of errors. Coding schemes can be both bitwise and cellwise. Bitwise schemes include simple parity checks and SEC-DED codes, either by themselves or as product codes [3]. Data organization should allow for burst error correction, since alpha particles can wipe out all four bits in a single cell, and for dense memory chips, data in surrounding cells as well. This latter effect becomes more serious as feature sizes are scaled, and a single alpha particle hit affects many adjacent cells. Burst codes such as those in [4] can be used to correct for these errors. Bitwise coding schemes are more efficient in correcting read errors, since they can correct single bit errors and allow the remaining error correction power to be used elsewhere. Read errors essentially affect one bit only, since the use of Grey codes for encoding the bits into the memory cells ensures that at most one bit is flipped with each successive change in level. Cellwise schemes include Reed-Solomon codes, hexadecimal codes, and product codes. However, simple encoding and decoding algorithms are necessary, since excessive space taken by powerful but complex encoding/decoding circuits can be offset by having more parity cells and using simpler codes. These coding techniques are more useful for correcting hard and soft errors which affect the entire cell. They tend to be more complex, and they are not as efficient in correcting read errors as the bitwise codes. In the talk we will investigate the suitability and performance of various multi-level RAM coding schemes, such as row-column codes, burst codes, hexadecimal codes, Reed-Solomon codes, concatenated codes, and some new majority-logic decodable codes. In particular we investigate their tolerance to soft errors, and to feature size scaling.

Error detecting capabilities of the shortened Hamming codes adopted for error detection in IEEE Standard 802.3

Abstract: Investigates the error detecting capabilities of the shortened hamming codes adopted for error detection in IEEE Standard 802.3. These codes are also used for error detection in the data link layer of the Ethernet, a local area network. The authors compute the weight distributions for various code lengths. From the results, they show the probability of undetectable error and that of detectable error for a binary symmetric channel with bit-error rate 10/sup -5/ >

A general error-correcting code construction for run-length limited binary channels

Abstract: A general method is presented for constructing a single-error-correcting, run-length-limited code for the class of input-restricted, binary symmetric channels described by the parameters (d,k), where d is the minimum and k the maximum number of consecutive zeros in any allowable channel input sequence. Upper and lower bounds on the rates of these codes are derived. >

There are many good periodically time-varying convolutional codes

Abstract: It is shown empirically that the number of good periodically time-varying convolutional codes increases exponentially with the period for any set of parameters. Hence, they can be used to enhance the security of cryptosystems without sacrificing error correction capability. It is shown that some periodically time-varying convolutional codes improve the free distance compared with fixed codes. >

Bi-level image coding with MELCODE-comparison of block type code and arithmetic type code

Abstract: It is shown how to encode and transmit binary Markov sources using a set of block codes called MELCODE. Fill symbol control is used to manage the transmission order of codewords with limitation of memory size. MELCODE is extended to arithmetic-type code, and the calculation accuracy of coding address is clarified. Block codes and arithmetic codes are compared in terms of memory size and coding efficiency through the simulation of bilevel image coding, showing an improvement in coding efficiency. >

Distance preserving run-length limited codes

Abstract: A subset of the RLL (run-length limited) codes called distance preserving RLL codes is introduced. In addition to satisfying a run-length constraint, these codes have the property that the Hamming distance between any two encoder output sequences is at least as large as the Hamming distance between the corresponding encoder input sequences. Thus, when used in combination with a binary ECC code, a distance preserving RL code does not reduce the overall Hamming distance of the ECC/RLL combination to something below the Hamming distance of the ECC code alone. It is shown how distance preserving RLL codes can be used with binary convolutional codes to create combined ECC/RLL codes with the distance properties of the original convolutional code. >

Error control techniques applicable to HF channels

Abstract: Owing to the time-varying nature of the HF channel, error correcting codes of a fixed rate provide unnecessary correction power for much of the time, with consequently low data rates. The purpose of an adaptive coding scheme is to permit only the necessary degree of error correction to be applied to the transmitted information according to the channel conditions. Such a coding scheme, based on product codes, is introduced, and the improvement, compared to similar fixed rate codes, is demonstrated. A method of improving the code rate further is described, and the results of this and an interleaving procedure are also given.

Bounds and constructions for codes correcting unidirectional errors

Abstract: A brief introduction is given on the theory of codes correcting unidirectional errors, in the context of symmetric and asymmetric error-correcting codes. Upper bounds on the size of a code of length n correcting t or fewer unidirectional errors are then derived. Methods in which codes correcting up to t unidirectional errors are constructed by expurgating t-fold asymmetric error-correcting codes or by expurgating and puncturing t-fold symmetric error-correcting codes are also presented. Finally, tables summarizing some results on the size of optimal unidirectional error-correcting codes which follow from these bounds and constructions are given. >

Compact, high-speed and high-coding-gain general purpose FEC encoder/decoder-NUFEC codec

Abstract: A novel universal forward error correction (NUFEC) scheme, comprising direct high-coding-rate convolutional code generators and variable-rate Viterbi decoders, is proposed. To make this NUFEC scheme available in various communication systems, three kinds of CMOS VLSIs have been developed. They can operate up to 25 Mb/s and are easily applicable to various coding-rate convolutional codes. Furthermore, by using these NUFEC VLSIs, a compact, high-speed, and high-coding-gain FEC codec (NUFEC codec) has been developed. Experimental results on the Pe performance of this codec have shown powerful coding gains of 5.5, 4.5, 3.4, and 2.2 dB at Pe=1*10/sup -6/ in coding rates of 1/2, 3/4, 7/8, and 15/16, respectively. >

Performance of a meteor-burst communication system using packet messages with variable data rates

Abstract: The transmitted data rate is a function of the channel state and is varied in such a way as to keep the probability of bit error approximately constant. The performance measure of the system is the probability of successful message completion in a given time span T/sub D/. Optimum operational signal-to-noise ratios are found as well as practical limits on the maximum and minimum transmission data rates. It is shown that the adaptive data rate feature provides a significant improvement in system performance as compared to a system transmitting at a fixed data rate. The performance improvement which can be obtained by the use of forward error correction coding is also analyzed. The codes considered are Reed-Solomon codes with rates of 1/3, 1/2, and 2/3. A much simpler expression for the probability of successful completion of a message is derived and used in the optimization search. >

An application of neural net in decoding error-correcting codes

Abstract: A neural net architecture is implemented as a maximum-likelihood decoder. Any block binary code can be easily decoded. In a von Neumann computer, the computation of all the Hamming distances requires exponential time; however, polynomial-time is needed for the neural net, taking advantage of parallel computation. In fact, picking the maximum is a polynomial-time problem. Since the decoding problem is NP-complete, all other NP-complete problems may be solvable by neural nets. >

Forward error correction in packet switched communications

Abstract: In a packet switched network, information is encoded in accord with a maximum distance separable code and the redundancy forms r packets of length L symbols additional to the K packets of length L symbols comprising the original information, whereby any K packets suffice to reconstruct the original information.

An investigation of ARQ and hybrid FEC-ARQ on an experimental high latitude meteor burst channel

Abstract: A computer investigation of error-control-coding techniques and bit error patterns recorded on an experimental Northern latitude meteor burst link is presented. Automatic repeat request (ARQ) and hybrid forward error correction (FEC) with ARC are examined from the standpoint of probability of message delivery and encountered message delivery delays. It is demonstrated that FEC will yield substantial improvement in the number of messages deliverable within a specified time constraint. Potential gains in extending the usable time duration of a meteor burst channel are on the order of factors of four with successful message delivery percentages increased by factors of 50. >

Performance of convolutional coded SQAM in hardlimited satellite channels

Abstract: The hardware implementation and experimental measurements of a differential encoded superposed quadrature amplitude modulation (SQAM) modem combined with 3/4-rate convolutional encoding and threshold decoding for use in bandwidth and power-limited satellite communications are presented. To avoid error propagation caused by differential encoding/decoding, and also to combat bursty channel noise, a data interleave/deinterleave scheme is integrated into the forward error-code (FEC) codec. Specific signal waveshaping is achieved digitally after FEC encoding to produce signals free of intersymbol interference (ISI) and timing jitter while providing a compact power spectrum. Experimentally measured results including signal waveforms, eye diagrams, power spectrum, and bit error rate (BER) performance in linear and hardlimited transmission channels are reported. The BER results show that the power efficiency of the modem is excellent. Spectral regrowth of the modulated signal is also retained at the minimum to ensure minimum interference to adjacent channels and thus maximize the channel utilization efficiency. >

Algorithms for converting convolutional codes from feedback to feedforward form and vice versa

Abstract: Algorithms for conversion from feedforward (FF) to feedback (FB) codes and vice versa are presented. The former is based on a trellis search and the latter on an algebraic solution. The algorithms work on trellis codes of rate R = k/n.

The Weight Distribution and Randomness of Linear Codes

Abstract: Finding the weight distributions of block codes is a problem of theoretical and practical interest. Yet the weight distributions of most block codes are still unknown except for a few classes of block codes. Here, by using the inclusion and exclusion principle, an explicit formula is derived which enumerates the complete weight distribution of an (n,k,d) linear code using a partially known weight distribution. This expression is analogous to the Pless power-moment identities - a system of equations relating the weight distribution of a linear code to the weight distribution of its dual code. Also, an approximate formula for the weight distribution of most linear (n,k,d) codes is derived. It is shown that for a given linear (n,k,d) code over GF(q), the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q = q(-)(n-k) as u becomes large. A relationship between the randomness of a linear block code and the minimum distance of its dual code is given, and it is shown that most linear block codes with rigid algebraic and combinatorial structure also display certain random properties which make them similar to random codes with no structure at all.

Error control techniques for integrated services packet networks

Abstract: The design of a multiservice packet network must ensure that delays to speech packets are minimized while data and other types of packets are delivered without error. The author suggests some ways in which error detection, forward error correction (FEC), and automatic repeat request (ARQ) schemes may be utilized in integrated services packet networks (ISPNs) to ensure that satisfactory error performance and reliability standards are achieved. The results show that ARQ schemes combined with reliable error detection are the most practical way of achieving reliable error control in integrated services networks. Also, such error control schemes can have performance advantages if applied on a region-by-region basis rather than simple end-to-end. >

Combined coding and modulation using block codes

Abstract: We present the basic idea of a combined coding and modulation scheme which is simple, powerful and easy to synchronise.

Asymptotic performance analysis of hybrid ARQ protocols in slotted direct-sequence code division multiple-access networks

Abstract: The performance of hybrid automatic repeat-request (ARQ) protocols in slotted direct-sequence code-division multiple-access networks is analyzed. A Markov model is used to derive throughput-delay expressions in terms of the channel cutoff rate and capacity. Network design parameters are identified and their dependency on systems parameters is examined in detail. It is shown that, for a given population size, traffic intensity, and ratio of bit energy to background noise, there is an optimal probability of retransmission, code rate, and processing gain that maximizes performance. The stability of the network is also discussed. >

Error control codes for digital recording systems

Abstract: The author considers a concatenated coding scheme for digital recording systems. This concatenated scheme uses an inner code to detect errors during the storage/retrieval process and to erase the corresponding errors. The Reed-Solomon code is used as an outer code to correct the errors (undetected errors) and the erasures (detected errors) generated by the inner code. Several error detecting codes are considered as the inner code, and the corresponding block error probabilities and average net information that can be stored and retrieved without error in a unit time are computed to make performance comparisons. >

Low complexity concatenated coding schemes for digital satellite communications

Abstract: A study of reduced complexity concatenated coding schemes, for commercial digital satellite systems with low-cost earth terminals, is reported. The study explored trade-offs between coding gain, overall rate and decoder complexity, and compared concatenated schemes with single codes. It concentrated on short block and constraint length inner codes, with soft decision decoding, concatenated with a range of Reed-Solomon outer codes. The dimension of the inner code was matched to the outer code symbol size, and appropriate interleaving between the inner and outer codes was used. Very useful coding gains were achieved with relatively high-rate, low-complexity schemes. For example, concatenating the soft decision decoded (9,8) single parity check inner code with the CCSDS recommended standard Reed-Solomon outer code gives a coding gain of 4.8dB at a bit error probability of 10−5, with an overall rate of 0-78.

On renewal inner channels and block code error control outer channels

Abstract: The authors investigate the underlying statistical structure of the block error detection, correction, and misdetection events of a block code on a discrete renewal inner channel, such as a fading RF channel. They show that these events can be represented with outer channel models, i.e. partitioned Markov processes, similar to the inner channel models. Analytical procedures to determine the parameters of these outer channel models are presented. The application of these models in the design of such error-control systems as ARQ (automatic repeat request) systems is investigated. Consideration is also given to the memory-efficient recording of the channel error stream to be recorded or stored, in order to parameterize inner channel models. The results of several simulations to verify the analytical procedures are also presented. >

Adaptive rate error control through the use of diversity combining and majority logic decoding in a hybrid-ARQ protocol

Abstract: The author demonstrates an adaptive rate coding system based on the majority logic decoding of convolutional codes. The proposed system retains the high-data-rate capability of FEC (forward error correction) majority logic decoders while providing an adaptive code rate and a significant improvement in error protection through the incorporation of diversity combining and hybrid-ARQ (automatic repeat request) techniques. It is shown through analysis and simulation that this error control system provides a high level of data reliability at the expense of a minimal reduction in throughput. >

An error control technique for high data rate communication networks

Abstract: A new method is discussed for modifying majority-logic convolutional decoders for use in a type-I hybrid-ARQ protocol. In standard forward error correcting (FEC) operation, these decoders generate reliability information in the form of orthogonal sets of parity check sums. The modified decoder uses this information to identify received packets whose decoded data may be unreliable and to request retransmission of these packets. It is shown through analysis and simulation that the resulting error control system provides substantially higher data reliability than its FEC counterpart at the expense of a very small reduction in data throughput. >

Multilevel codes for high-speed voiceband data modem

Abstract: A novel class of multilevel codes is proposed for achieving high coding gain. Multilevel codes composed of two-level codes are investigated from the standpoint of the systematic design of codes. Two-level codes as component codes are shown to be preferable to a combination of conventional one-level codes in coding gain and decoder delay. For a 19.2 kb/s voiceband modem application, this scheme presents a class of coded modulation superior to trellis-coded modulation in simultaneous realization of high coding gain, low/moderate decoder complexity, and short decoding delay. >

Performance evaluation of asynchronous random access CDMA with block FEC coding

Abstract: The authors present an analysis of asynchronous random access packet CDMA (code-division multiple-access) channels with block FEC (forward error correction) coding. A procedure for calculating the error probability of an L bit packet in the variable message length, multiuser CDMA environment is presented. This procedure is used in conjunction with appropriate flow equilibrium traffic models to compute performance measures such as throughput and delay. Using as an example a direct sequence spread-spectrum multiple-access system with BCH block coding for FEC, the analytical model is used to obtain throughput vs. channel traffic curves over a range of code rates, leading to an assessment of maximum achievable throughput and the associated optimum FEC code rate. The results show that the use of block FEC coding provides a significant improvement in the normalized net channel throughput, approach values which are competitive with those for nonspread-spectrum ALOHA-type random access channels. >

Coding of optical on-off-keying signals impaired by phase noise

Abstract: The benefits of coding an optical communications system that employs binary on-off-keying heterodyne detection are shown. The system is impaired by laser phase noise as well as by additive white Gaussian noise (AWGN). A receiver structure especially designed to mitigate the effects of phase noise in the presence of AWGN is assumed. This special receiver structure requires a wider band front-end IF filter than would be required for a phase-noise-free signal. Results computed for several different coding schemes indicate that the benefits of coding are large and the costs are small. For a linewidth-to-bit-rate ratio of 0.64, a half-rate binary code that can correct three bit errors provides a 50% reduction in the required IF filter bandwidth (and therefore the required IF) and about 5 dB of reduction in required laser power. The benefits of coding are greatest under high- beta T conditions, corresponding to low bit rates, where coders and decoders are most practical to implement. The results obtained suggest the possibility that forward error correction could be used to improve the channel packing efficiency of FDMA (frequency division multiple access) networks. >