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One of the main challenges in designing high-data-rate ultrawideband impulse radio (UWB-IR) systems is their sensitivity to intersymbol and interpulse interferences, which may significantly degrade the performance. This paper deals with new methods of protection against errors for UWB-IR systems operating in severe multipath interference-prone environments. The proposed and investigated techniques include interleaved coding modulation and polarity randomization applied in combination with superorthogonal convolutional coding or frame repetition. The performance of high-data-rate (125 Mb/s) coded UWB-IR systems is evaluated on the additive white Gaussian noise and realistic UWB channels that have recently been proposed by the IEEE. Our UWB-IR system incorporates a differential autocorrelation receiver, allowing for a simple hardware architecture. Through theoretical analysis of the bit error rate (BER) and the use of Monte Carlo simulations, we demonstrate that the application of the proposed methods may lead to significant performance improvements. Index Terms--Channel coding, indoor radio communication, interleaving, multipath, ultrawideband (UWB).

The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix representing the code. In this correspondence, we introduce the notion of dead-end sets to explicitly demonstrate this dependency. The choice of the parity-check matrix entails a tradeoff between performance and complexity. We give bounds on the complexity of iterative decoders achieving optimal performance in terms of the sizes of the underlying parity-check matrices. Further, we fully characterize codes for which the optimal stopping set enumerator equals the weight enumerator. Index Terms--Dead-end set, iterative decoding, linear code, parity-check matrix, stopping set.

Stopping sets, and in particular their numbers and sizes, play an important role in determining the performance of iterative decoders of linear codes over binary erasure channels. In the 2004 Shannon Lecture, McEliece presented an expression for the number of stopping sets of size three for a full-rank parity-check matrix of the Hamming code. In this correspondence, we derive an expression for the number of stopping sets of any given size for the same parity-check matrix. Index Terms--Hamming code, linear code, parity-check matrix, stopping set enumerator, weight enumerator.

A soft-decision decoder for an error-correcting block code of Hamming distance d is said to achieve bounded-distance (BD) decoding if its error-correction radius is equal to that of a complete Euclidean distance decoder. The Chase decoding algorithms are reliability-based algorithms achieving BD decoding. The least complex version of the original Chase algorithms ("Chase-3") uses O(d) trials of a conventional binary decoder. In this correspondence, we propose classes of Chase-like BD decoding algorithms of lower complexity than the original Chase-3 algorithm. In particular, the least complex members of these classes require only O([d.sup.2/3) trials. Index Terms--Asymptotic optimality, binary linear block codes, bounded-distance (BD) decoding, multitrial decoding, reliability information, soft-decision decoding.

Chase decoders permit flexible use of reliability information in algebraic decoding algorithms for error-correcting block codes of Hamming distance d. The least complex version of the original Chase algorithms uses roughly d/2 trials of a conventional binary decoder, after which the best decoding result is selected as the final output. On certain channels, this approach achieves asymptotically the same performance as maximum-likelihood (ML) decoding. In this correspondence, the performance of Chase-like decoders with even less trials is studied. Most strikingly, it turns out that asymptotically optimal performance can be achieved by a version which uses only about d/4 trials. Index Terms--Asymptotic optimality, binary linear block codes, bounded-distance decoding, multitrial decoding, reliability information, soft-decision decoding.

A framework is presented for generalized minimum distance (GMD) decoding with a limited number of decoding trials and a restricted set of reliability values. In GMD decoding, symbols received from the channel may be erased before being fed into an algebraic error-erasure decoder for error correction, in subsequent or simultaneous trials with different erasing patterns. The decision whether or not to erase a symbol in a certain trial is taken by an erasure-choosing algorithm which takes into account reliability information from the channel. The final GMD decoder output is a codeword which results from a decoding trial and satisfies a certain distance criterion. For various erasing strategies and reliability sets, the guaranteed error-correction radius and the unsuccessful decoding probability of this technique are studied. Both known and new results, with applications to concatenated coding, follow from the unified approach presented in this correspondence. Index Terms--Concatenated codes, generalized distance, multitrial decoding, reliability-based decoding.

A new construction method for codes correcting multiple localized burst errors is proposed. The codes obtained by this method improve upon codes presented by Larsson in size, while keeping the encoding and decoding complexity low. Like the Larsson codes, the proposed codes are asymptotically optimal when the number of bursts to be corrected is fixed and the correctable burst length grows linearly with the codelength. Unlike the Larsson codes, the proposed codes are also asymptotically optimal when the number of bursts to be corrected and the correctable burst length are both fixed. Index Terms - Burst errors, decoding, encoding, error correction, localized errors.

Significant improvements in magnetic storage densities have been made feasible recently by the application of partial-response signaling combined with maximum-likelihood sequence estimation. To enhance the performance of this technique when applied to the class-IV partial-response channel, which is recognized as being appropriate to model the magnetic recording channel, it is often required to bound the number of consecutive zeros in the recorded data sequence and its odd and even subsequences. We investigate block codes that satisfy such a constraint. In particular, we look for a set of maximal number of fixed-length sequences such that any pair of them can be concatenated without violating the constraint. In many cases, depending on the constraint and the length of the sequences, we determine such a set, and in the remaining cases, we determine at most three candidates for it. These results are used to study the best possible constrained block codes. Index Terms - Fixed-length codes, modulation systems, partial response, Viterbi detection.

Several techniques for constructing practical codes for noisy modulation channels represented by (d, k) constraints, such as in magnetic and optical recording, are analyzed. Concatenated schemes based on inner sliding-window codes are compared with concatenated schemes based on inner block codes in terms of efficiency and reliability. The performance of the schemes is investigated in detail for (1,7) constrained channels with different error characteristics. It is shown that for such channels, concatenated schemes based on inner sliding-window codes have higher code rates than concatenated schemes based on inner block codes for typical applications. However, if the channels are very noisy or extremely small decoding error probabilities are required, then the latter schemes tend to have higher code rates than the former ones. Index Terms - Modulation, noise, concatenated schemes, sliding-window codes, block codes, comparison.

In magnetic or optical storage devices, it is often required to map the data into runlength-limited sequences. To ensure that cascading such sequences does not violate the runlength constraints, a number of merging bits are inserted between two successive sequences. A theory is developed, in which the minimum number of merging bits is determined and the efficiency of a runlength-limited fixed-length coding scheme is considered.

In earlier publications, performance gains over Ungerboeck type trellis-coded modulation schemes were obtained by optimizing (by hand) the signal constellation. Using genetic algorithms and simulated annealing, we have found additional cases with performance gains over the Ungerboeck type schemes.

The asymptotic behavior of the rates of optimal codes correcting and/or detecting combinations of symmetric, unidirectional, and/or asymmetric errors is studied. These rates are expressed in terms of the rate of optimal codes with a certain Hamming distance. As a consequence, well-known bounds on the latter rate can also be applied to bound the former rates. Furthermore, it turns out that, without losing rate asymptotically, any error control combination can be upgraded to simultaneous symmetric error correction/detection and all unidirectional error detection. Index Terms - Asymmetric errors, code rate, error correction, error detection, symmetric errors, unidirectional errors.

A general scheme for DC-free (d, k)-constrained block codes is considered. In this scheme, messages are mapped to nonzero dklr-sequences of fixed length. For any two dklr,-sequences, two merging sequences of fixed length and of different weight parities are available such that each one of these sequences can be inserted between the two dklr-sequences to maintain the (d, k) constraint. One of these two merging sequences is chosen to ensure that the code is DC-free. For all (d, k) constraints with capacities at least equal to 0.5, optimal values of l and r that yield maximal code rates are specified. Index Terms--Constrained codes, modulation codes, running digital sum, spectral-null codes.

We consider a concatenated coding scheme using a single inner code, a single outer code, and a fixed single-trial decoding strategy that maximizes the number of errors guaranteed to be corrected in a concatenated codeword. For this scheme, we investigate whether maximizing the guaranteed error correction rate, i.e., the number of correctable errors per transmitted symbol, necessitates pushing the code rate to zero. We show that this is not always the case for a given inner or outer code. Furthermore, to maximize the guaranteed error correction rate over all inner and outer codes of fixed dimensions and alphabets, the code rate of one (but not both) of these two codes should be pushed to zero. Index Terms--Concatenated codes, decoding strategy, erasure correction, error correction, error detection.