Generalized concatenated codes for channels where unidirectionalbyte errors are predominant

Codes are considered for correction and detection of unidirectional byte errors. A code construction based on the generalized concatenated code construction is proposed. This construction gives a large number of efficient codes. For example, from this construction, a 72-input-bit encoder of the triple unidirectional 8-bit-byte error-correcting and fourfold unidirectional 8-bit-byte error-detecting code with a length of 112 bits and rate 9/14 is obtained, whereas the ordinary triple 8-bit-byte error-correcting and fourfold 8-bit-byte error-detecting code of the same length has only 56 information bits and is of rate 1/2. The proposed construction is generalized to one that gives efficient short-length codes     

Cross-layer design based on RC-LDPC codes in MIMO channels with estimation errors

In this paper, we propose a cross-layer design framework combining adaptive modulation and coding (AMC) with hybrid automatic repeat request (HARQ) based on rate-compatible low-density parity-check codes (RC-LDPC) in multiple-input multiple-output (MIMO) fading channels with estimation errors. First, we propose a new puncturing pattern for RC-LDPC codes and demonstrate that the new puncturing pattern performs similar to the random puncturing but is easier to apply. Then, we apply RC-LDPC codes with the new puncturing pattern to the cross-layer design combing AMC with ARQ over MIMO fading channels and derive the expressions for the throughput of the system. The effect of channel estimation errors on the system throughput is also investigated. Numerical results show that the joint design of AMC and ARQ based on RC-LDPC codes can achieve considerable spectral efficiency gain.     

Marker codes for channels with insertions and deletions

Coding for channels with synchronization errors is studied. Marker codes, each consisting of a low-density parity-check code with inserted markers, are developed. At low insertion-deletion probabilities marker codes are shown to outperform watermark codes. Full iterative decoding enhances performance to close to the capacity bounds. The low-density parity-check codes are optimized and the best known rate R = 0.5 code for the insertion-deletion channel presented. The codes are also shown to be effective on the bit-deletion channel.     

Capacity-achieving codes for finite-state channels with maximum-likelihood decoding

Codes on sparse graphs have been shown to achieve remarkable performance in point-to-point channels with low decoding complexity. Most of the results in this area are based on experimental evidence and/or approximate analysis. The question of whether codes on sparse graphs can achieve the capacity of noisy channels with iterative decoding is still open, and has only been conclusively and positively answered for the binary erasure channel. On the other hand, codes on sparse graphs have been proven to achieve the capacity of memoryless, binary-input, output-symmetric channels with finite graphical complexity per information bit when maximum likelihood (ML) decoding is performed. In this paper, we consider transmission over finite-state channels (FSCs). We derive upper bounds on the average error probability of code ensembles with ML decoding. Based on these bounds we show that codes on sparse graphs can achieve the symmetric information rate (SIR) of FSCs, which is the maximum achievable rate with independently and uniformly distributed input sequences. In order to achieve rates beyond the SIR, we consider a simple quantization scheme that when applied to ensembles of codes on sparse graphs induces a Markov distribution on the transmitted sequence. By deriving average error probability bounds for these quantized code ensembles, we prove that they can achieve the information rates corresponding to the induced Markov distribution, and thus approach the FSC capacity.     

Runlength-limited codes for mixed-error channels

The mixed-error channel (MC) combines the binary symmetric channel and the peak shift channel. The construction of (d, k) constrained t-MC-error-correcting block codes is described. It is demonstrated that these codes can achieve a code rate close to the ( d, k) capacity. The encoding and decoding procedures are described. The performance of the construction depends on a particular partitioning of (d, k) constrained block codes. This partitioning is discussed and various tables of codes are included. Examples on encoding/decoding and on code performance are given     

Linear block codes for nonindependent errors

A computerised search procedure based on certain properties of the parity-check matrix of those block codes capable of correcting nonindependent errors is described which yields a considerable number of linear block codes that are capable of correcting random or burst errors.     

Concatenated coding with inner trellis codes for fading channels

It is known that concatenated coding can significantly enhance the performance of digital communication systems operating over fading channels when compared to uncoded or single-coded systems. The price to be paid for such an improvement, however, is a substantial increase in the required bandwidth. In this paper, we consider the use of a concatenation scheme in which the inner code is a trellis-coded modulation (TCM) system. The analysis is carried out for two different outer codes: a binary Golay code and a non-binary Reed-Solomon code. Results obtained for the Rayleigh and Rician fading channels through analytical bounds indicate that the use of this system does provide a significant reduction in the bit error probability, a fact that is also verified through computer simulation. Unlike a traditional concatenated system, the proposed method achieves the coding gain while maintaining acceptable bandwidth efficiency.     

Error probability for block codes over channels with blockinterference

A methodology is presented to evaluate analytically the error probability for block codes over block interference channels. The proposed analysis is based on the knowledge of the moments of the bit-error probability over the interference, thus allowing, for instance, fast performance evaluation of block-coded slow frequency hopping (SFH) systems with antenna diversity over fading channels. As an example of application, slow frequency hopping multiple access (SFHMA) systems with nonideal interleaving are analyzed in the presence of fading, cochannel interference, and additive Gaussian noise     

Repeated convolutional codes for high-error-rate channels

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p_e is considered. The value of p_e can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R₀, where R₀ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem     

Multilevel block codes for Rayleigh-fading channels

New multilevel block codes for Rayleigh-fading channels are presented. At high signal-to-noise ratios (SNRs), the proposed block codes can achieve better bit error performance over TCM codes, optimum for fading channels, with comparable decoder complexity and bandwidth efficiency. The code construction is based on variant length binary component block codes. As component codes for the 8-PSK multilevel block construction, the authors propose two modified forms of Reed-Muller codes giving a good trade-off between the decoder complexity and the effective code rates. Code design criteria are derived from the error performance analysis. Multistage decoding shows very slight degradation of bit error performance relative to the maximum likelihood algorithm     

Seminoisy deterministic multiple-access channels: coding theorems for list codes and codes with feedback

Whereas the average error capacity region R/sub a/ for the multiple-access channel (MAC) W: X /spl times/ Y /spl rarr/ Z has been known for a long time, very little is known about the capacity region R/sub m/ for the maximal error concept (as predicted by Ahlswede in 1971). In spite of great efforts during the past three decades even for some special examples of deterministic MAC, for which the maximal error concept coincides with the concept of unique decodability, the progress has been slow. It is known that the permission of list codes can be of great help, even if list sizes are of negligible rates (cf. the arbitrarily varying channel (AVC) and, especially, Shannon's (1948) zero-error capacity problem for the one-way channels). Therefore, it is theoretically appealing to look at their regions R/sub m,l/ for the MAC. For a nice class of deterministic MAC, which we call "seminoisy," we completely characterized R/sub m,l/. For these channels, the Y-input is determined uniquely by the output. Dueck's (1978) example with R/sub a/ /spl ne/ R/sub m/ and Vanroose's (1988) "noiseless binary switching MAC" with R/sub a/ = R/sub m/ fall into this class. Finally, for this class, the capacity region R/sub m,f/, which concerns complete feedback, equals R/sub m,l/.     

Correction of synchronization errors with burst-error-correcting cyclic codes

It is shown that every linear cyclicb-burst-error-correcting code over any finite field can be modified to correct up to(b-2)symbols of synchronization slippage without additional redundancy, while maintaining its additive error-correcting capability in the absence of synchronization errors. For codes that are interleaved to a degreem, the synchronization error-correcting capability ism (b-1) - 1symbols, whereb geq 3is the length of the burst each subcode corrects. This technique gives an optimum burst-error-correcting code a synchronization error-corecfing capability that is only one symbol short of the known upper bound and is hence asymptotically optimal. Moreover, the implementation is very simple.     

Concatenated codes for fading channels based on recursive space-time trellis codes

We propose a class of codes which combine the principles of turbo coding and space-time trellis codes. It is first shown that several classes of space-time codes have an equivalent recursive realization. This fact is then exploited to design serial concatenated coding schemes with an outer code, interleaver, and an inner recursive space-time encoder. Two solutions are proposed in this paper - the use of convolutional outer codes aimed mainly to improve the power efficiency and the use of very high-rate outer codes to obtain significant improvement in power efficiency with a marginal decrease in spectral efficiency. We show that single parity check based turbo product codes are a good candidate for very high-rate outer codes. Finally, we propose an automatic repeat request scheme based on recursive realizations of space-time codes and show that the proposed scheme provides significant reduction in frame error rate.     

Bounds and constructions for codes correcting unidirectional errors

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     

Multidimensional M-PSK trellis codes for fading channels

This paper investigates the code search problem for trellis-coded multidimensional phase modulation for Rayleigh fading channels. New set partitionings for multiple phase-shift keying (M-PSK) are proposed using the effective code length (ECL) and the minimum product distance (PD) as the code design criteria. By using these set-partitionings rules, new multidimensional codes which are optimum for Rayleigh fading channels are constructed. The proposed codes compare favorably with the existing multidimensional trellis codes on fading channels in terms of bit error performance. The bit error performance is evaluated by simulation     

LDPC codes for fading Gaussian broadcast channels

In this work, we study coding over a class of two-user broadcast channels (BCs) with additive white Gaussian noise and multiplicative fading known at the receivers only. Joint decoding of low-density parity-check (LDPC) codes is analyzed. The message update rule at the mapping node linking the users' codes is derived and is found to exhibit an interesting soft interference cancellation property. High performance codes are found using the differential evolution optimization technique and extrinsic information transfer analysis adapted to our multiuser setting. The optimized codes have rates very close to the boundary of the achievable region for binary constrained input for both faded and unfaded channels. Simulation results for moderate block lengths show that our codes operate within less than 1 dB of their respective threshold.     

Error-correcting codes for authentication and subliminal channels

The application of coding theory to security scenarios is studied. Authentication systems are introduced that are based on algebraic codes and provide high protection against an intruder's impersonation and substitution attacks. It is shown that a subliminal channel can be embedded into these systems and that there is a trade-off between the authentication capability, subliminal capacity, and error protection capability     

Reed-Solomon codes for land mobile satellite channels

The performance of Reed-Solomon codes is determined for land mobile satellite communications where a shadowed Rician channel model is used. An effective coding/interleaving scheme is proposed which uses the multipath fading and shadowing statistics of the channel.<>     

Uniquely decodable codes for deterministic relay channels

The deterministic relay channel is analyzed and explicit code constructions for all binary and all ternary/binary channels are given. An explicit set of equivalence conditions is used to make a classification of all such relay channels, for which also the capacity is evaluated. The coding problem is then reduced to finding all possible output sequences of a certain finite-state channel determined by the relay coding strategy. The channel states correspond to the possible relay memory contents. For some relay channels capacity is reached by using simple uniquely decodable codes, thus establishing the zero-error capacity of those channels with finite-memory relay strategies. For other relay channels the relay memory must be arbitrarily large to achieve zero-error rates arbitrarily close to capacity. One such code construction is given. It is not known whether there exist relay channels for which the zero-error capacity is strictly smaller than the average-error capacity. The code construction problem for the semideterministic relay channel and for the nonsynchronized relay channel is briefly considered     

Properties of space-time codes for frequency-selective channels

Some important properties are derived for the diversity gain and the coding gain of space-time codes (STCs) for frequency-selective channels. It is proven that the diversity gain of a STC that provides maximum diversity gain for channels with a given number of taps is robust to a decrease in the number of taps. For coding gain analysis, we categorize the possible types of correlation matrices into several classes based on the type of power delay profile, spatial correlation, and tap correlation. It is proven that optimum STCs found for spatially independent and frequency-selective channels with uncorrelated taps and uniform power delay profile have coding gains that are robust against a mismatch in correlation structure if the number of taps is fixed. Thereafter, a systematic design procedure is applied to search for the best space-time trellis codes (STTCs) for frequency-selective channels. At a frame error rate (FER) of 0.01, our example 16-state binary phase-shift keying (BPSK) STTC outperforms the delay diversity code by 3.4 dB for a channel with three uncorrelated uniform taps. Further, the example STC designed for a channel with a given number of taps is shown to provide good performance for channels with fewer taps.