In this study, the authors design a multi‐user ultra‐wideband system for indoor wireless communication. The proposed system is useful in multipath radio reception as the full multipath diversity gain is achieved. The system has multiple transmitters and receivers. They use polyphase spreading waveforms which feature low levels of mutual interference and enable each of the channel impulse responses to be measured free from distortion continuously with each data symbol transmission. A key feature of the proposed system is that transmitted waveforms are used which produce outputs from the receiver cross correlators, which are zero on both sides of the main correlation peak, for each radio path. This zero response lasts for a duration in excess of the expected delay spread of the radio channel enabling full Rake processing of the multipath signal. The effects of the low levels of mutual interference are reduced further by using time and frequency hopping, forward error correction and soft decision decoding.

It is shown that for some location sets and some integral multiple power Galois fields that some new general subclasses of Goppa codes may be defined which have improved lower bounds to code dimension and minimum distance compared with ordinary Goppa codes. Some previously published results are shown to be particular cases of these general subclasses of codes. A new subclass of reversible Goppa codes is also presented. Examples of code construction for these subclasses, demonstrating the improved code parameters, are presented for both non binary and binary codes.

In this work, we present an upper bound on the minimum distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m ≤ q. In the literature, the minimum distance of these codes (denoted by d(q,m)) has been thoroughly studied for m ≤ 5. Both exact results, for small values of q and m, and general (i.e., independent of q) bounds have been established. For m ≤ 6, the best known minimum distance upper bound, derived by Mittelholzer (IEEE Int. Symp. Inf. Theory, Jun./Jul. 2002), is d(q, 6) ≤ 32. In this work, we derive an improved upper bound of d(q, 6) ≤ 20 by using the concept of a template support matrix of a codeword. The bound is tight with high probability in the sense that we have not been able to find codewords of strictly lower weight for several values of q using a minimum distance probabilistic algorithm. Finally, we provide new specific minimum distance results for m ≤ 6 and low-to-moderate values of q ≤ 79.

Traditionally, codes are designed for an error correcting system to combat noisy transmission channels and achieve reliable communication. These codes can be used in syndrome coding, but it is shown in this study that the best performance is achieved with codes specifically designed for syndrome coding. In the view of the security of the communication, the best codes are the codes, which have the highest value of an information secrecy metric, the equivocation rate, for a given code length and code rate and are well packed codes. A code design technique is described, which produces the best binary linear codes for the syndrome coding scheme. An efficient recursive method to determine the equivocation rate for the binary symmetric channel and any linear binary code is also presented. A large online database of best equivocation codes for the syndrome coding scheme has been produced using the code design technique with some examples presented in the study. The presented results show that the best equivocation codes produce a higher level of secrecy for the syndrome coding scheme than almost all best known error correcting codes. Interestingly, it is unveiled that some outstanding best known error correcting codes are also best equivocation codes.

In this paper, we study the minimum/stopping distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m q. In the literature, the minimum/stopping distance of these codes (denoted by d(q, m) and h(q, m), respectively) has been thoroughly studied for m 5. Both exact results, for small values of q and m, and general (i.e., independent of q) bounds have been established. For m = 6, the best known minimum distance upper bound, derived by Mittelholzer, is d(q, 6) 32. In this paper, we derive an improved upper bound of d(q, 6) 20 and a new upper bound d(q, 7) 24 by using the concept of a template support matrix of a codeword/stopping set. The bounds are tight with high probability in the sense that we have not been able to find codewords of strictly lower weight for several values of q using a minimum distance probabilistic algorithm. Finally, we provide new specific minimum/stopping distance results for m 7 and low-to-moderate values of q ≤79.

In an earlier transactions paper, Rosnes and Ytrehus presented an efficient algorithm for determining all stopping sets of low-density parity-check (LDPC) codes, up to a specified weight, and also gave results for a number of well-known codes including the family of IEEE 802.16e LDPC codes, commonly referred to as the WiMax codes. It is the purpose of this short paper to review the algorithm for determining the initial part of the stopping set weight spectrum (which includes the codeword weight spectrum), and to provide some improvements to the algorithm. As a consequence, complete stopping set weight spectra up to weight 32 (for selected IEEE 802.16e LDPC codes) can be provided, while in previous work only stopping set weights up to 28 are reported. In the published standard for the IEEE 802.16e codes there are two methods of construction presented, depending upon the code rate and the code length. We compare the stopping sets of the resulting codes and provide complete stopping set weight spectra (up to five terms) for all IEEE 802.16e LDPC codes using both construction methods.

This paper investigates the design and performance of a two-user satellite communication system. Each user is independently encoded using a structured Turbo code with identical symbol interleavers. This permits Turbo decoding to be performed using the combined component code trellises, which provides significant gains over independent decoding. The design of the code-matched symbol interleavers is described. Both ideal and imperfect knowledge of the relative phase shift between users is considered. Performance is compared to the single user case and the performance degradation due to a third unknown user is considered. These investigations show that the proposed system performs well in a variety of conditions.

In this paper we propose a coding-decoding scheme to be used for II-type hybrid ARQ on a binary erasure channel model, based on rate compatible punctured binary Turbo Codes, DRP interleaver design and ML decoding at the receiver. We carefully design the interleaver and the puncturing mask, and we describe how to achieve low-complexity Maximum Likelihood decoding. We show for the case of an MPEG2 packet size that this scheme overrides random codes upper bounds, providing throughputs within 0.05 bits from capacity at word error rates greater or equal to 10-6.

It is shown that the relatively unknown Dorsch decoder may be extended to produce a decoder that is capable of maximum-likelihood decoding. The extension involves a technique for any linear (n, k) code that ensures that n−k less reliable, soft decisions of each received vector may be treated as erasures in determining candidate codewords. These codewords are derived from low information weight codewords and it is shown that an upper bound of this information weight may be calculated from each received vector in order to guarantee that the decoder will achieve maximum-likelihood decoding. Using the cross-correlation function, it is shown that the most likely codeword may be derived from a partial correlation function of these low information weight codewords, which leads to an efficient fast decoder. For a practical implementation, this decoder may be further simplified into a concatenation of a hard-decision decoder and a partial correlation decoder with insignificant performance degradation. Results are presented for some powerful, known codes, including a GF(4) non-binary BCH code. It is shown that maximum-likelihood decoding is realised for a high percentage of decoded codewords and that performance close to the sphere packing bound is attainable for codeword lengths up to 1000 bits.

The number and weight of low-weight codewords of a binary linear code determine the erasure channel performance. Analysis is given of the probability density function of the number of erasures correctable by the code in terms of the weight enumerator polynomial. For finite-length codes, zero erasure decoder error rate is impossible, even with maximum-distance-separable (MDS) codes and maximum-likelihood decoding. However, for codes that have binomial weight spectra, for example BCH, Goppa and double-circulant codes, the erasure correction performance is close to that of MDS codes. One surprising result is that, for many (n, k) codes, the average number of correctable erasures is almost equal to n−k, which is significantly larger than dmin−1. For the class of iteratively decodable codes (LDPC and turbo codes), the erasure performance is poor in comparison to algebraic codes designed for maximum dmin. It is also shown that the turbo codes that have optimised dmin have significantly better performance than LDPC codes. A probabilistic method, which has considerably smaller search space than that of the generator matrix-based methods, is presented to determine the dmin of a linear code using random erasure patterns. Using this approach, it is shown that there are (168, 84, 24) and (216, 108, 24) quadratic double-circulant codes.

This paper investigates the application of high capacity watermarking in still images. The performance of two orthogonalisation schemes and one writing-on-dirty-paper scheme are discussed. Orthogonalisation is an embedding technique which uses sequences that are orthogonal to the cover image modulating the payload information. Writing-on-dirty- paper uses the codewords which have the maximum cross- correlation of the cover image to carry the message. Aspects of comparison are: 1) watermark fidelity, 2) payload capacity and 3) robustness. The watermark fidelity is measured using Watson's perceptual model and mean squared error. Given fixed fidelity levels the payload capacity is measured in terms of bit error rate. Additive White Gaussian Noise (AWGN) with different variances is used to evaluate the robustness of the watermarks. Results are presented which categories the advantages and disadvantages of each scheme, under different situations. Certain trade-offs must be considered for specific requirement.

A new method of finding binary cyclic codes from the finite-field transform domain is presented. These cyclic codes have sparse parity-check matrix and thus are suitable for iterative decoding. Some interesting properties of the proposed construction method include the knowledge of the minimum distance and the ability to trade the increase in code dimension with a reduction in the parity-check matrix sparsity. By means of simulations, we show that the error correcting performance of the codes under iterative decoding is very close to the sphere-packing-bound constrained for binary transmission.

A method is presented where a parallel concatenated convolutional code is preceded with a short cyclic redundancy check (CRC) without code rate loss. Parity bits are punctured and their place taken by the CRC. Results are given for the weight spectrum of an optimised code, rate 2/3, codeword length, n=1014 in comparison with an optimised, nonCRC code using the same rate and codeword length. Frame error rate performance achieved is within 0.36dB of the sphere packing bound constrained for binary transmission.

This paper investigates the design and application of data magnitude modulation to reduce power amplifier back-off for QPSK and OQPSK modulations for small satellite Earth stations. The coefficients for data magnitude modulation are obtained by using an iterative design loop. The parameters of this loop are tuned to obtain maximum gain. Roll-off factors from 10% to 100% are considered, with emphasis on small roll-off values for increased bandwidth efficiency. It is shown that a gain of almost 6 dB can ideally be obtained for a roll-off factor of 10%. Error correction coding is used to compensate for the increased sensitivity to noise of the magnitude modulated data. The loss due to this increased sensitivity is reduced from almost 5.5 dB to 1.2 dB for a roll-off factor of 10% by using high rate product codes, thus giving an overall gain of 4.8 dB. Trade offs between spectral regrowth and implementation are addressed.

This letter first investigates the distribution of the free distance, parameter d/sub free/ for multiple parallel concatenated schemes based on random interleavers. The distribution is obtained by computer search for information weight IW=2 error events, which are the most likely events to produce d/sub free/, at least for turbo codes. The dependence upon interleaver length and code memory is also studied. The design of the S-interleaver for turbo codes is shown to depend upon a combination of IW=2 error events (which are dependent on S) and IW=2+2 "crossed" error events (which are independent of S). The limiting value of S (for which the two effects are equal) is calculated for turbo codes and a novel algorithm to increase this limit (and hence, d/sub free/) is presented. The S-random interleaver design is extended to schemes with two interleavers, for which the use of paired S-random interleavers is proposed.

The objective of this project is to maximise the power and bandwidth efficiency of small satellite Earth communication terminals whose main limitation to satellite capacity is a nonlinear transmitting power amplifier. A form of envelope equalisation is presented in which regular QPSK modulation is used together with instantaneous data magnitude modulation so as to produce a near constant envelope signal when filtered with root 35% raised cosine filtering. The algorithm for deriving the magnitude values is presented along with results using a data lookup table approximation. Bit error rate figures are presented for envelope equalisation combined with a (4096,3249) binary product code and MAP decoding. It is shown that at 10/sup -6/ BER the E/sub b//N/sub 0/ is 3.52 dB, some 0.26 dB from the linear system. When used with a nonlinear power amplifier, the benefit of envelope equalisation is approximately 3 dB. The power spectrum is identical to that of the linear system with no spectral spreading and no increase in adjacent channel interference.

This paper describes a high capacity blind video watermarking system invariant to geometrical attacks such as shift, rotation, scaling and cropping. A spatial domain reference watermark is used to obtain invariance to geometric attacks by employing image registration techniques to determine and invert the attacks. A second, high capacity, watermark, which carries the data payload, is embedded in the wavelet domain according to a human visual system (HVS) model. This is protected by a state-of-the-art error correction code (turbo code). For a false detection probability of 10/sup -8/, the proposed system is invariant to scaling up to 180%, rotation up to 70/spl deg/, and arbitrary aspect ratio changes up to 200% on both axes. Furthermore, the system is virtually invariant to any shifting, cropping, or combined shifting and cropping attack, and it is robust to MPEG-2 compression as low as 2-3 Mbps.