Jos H. Weber

Bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6

Upper bounds to the maximum number of codewords in a binary code of length n and asymmetric distance Delta are derived for some values of n and Delta . A method is given in which a code of length n-m and asymmetric distance at least t+1 is constructed by expurgating and puncturing a code of length n and Hamming distance at least 2t+1. Novel asymmetric error-correcting codes are constructed by applying this method to some celebrated symmetric error-correcting codes. a table is presented on the size of optimal asymmetric error-correcting codes of length less than 24 and asymmetric distance less than 6. >

Very Efficient Balanced Codes

The prior art construction of sets of balanced codewords by Knuth is attractive for its simplicity and absence of look-up tables, but the redundancy of the balanced codes generated by Knuths algorithm falls a factor of two short with respect to the minimum required. We present a new construction, which is simple, does not use look-up tables, and is less redundant than Knuths construction. In the new construction, the user word is modified in the same way as in Knuths construction, that is by inverting a segment of user symbols. The prefix that indicates which segment has been inverted, however, is encoded in a different, more efficient, way.

Efficient signal extension for subband/wavelet decomposition of arbitrary-length signals

Compression of digital signals is often performed with a two-band subband/wavelet decomposition scheme. Conventional tree-structured schemes with depth k that are based on this two-channel scheme require an input signal of which the length is a multiple of 2k. Normally, if the input signal does not meet this condition, samples are added to it until the requirement is met. However, these extra samples lead to an increase in data. In this paper a new method is presented that is based on an efficient way of signal extension. With this method, signals of arbitrary length N can be decomposed into subbands up to arbitrary level without an increase in data. Furthermore, a new alternative boundary extension method for filtering even length signals with symmetric odd length filters is presented. This so-called symmetric-periodic extension is closely related to the new efficient signal extension method and has the advantage of having periodicity 2N. In this paper all signal extensions are explained visually with diagrams to clearly demonstrate perfect reconstruction conditions.

Stopping set analysis for Hamming codes

In the 2004 Shannon Lecture, McEliece presented an expression for the number of stopping sets of size three in a Hamming code. In this paper, we investigate how this number depends on the parity-check matrix used in the decoding process. First, we present basic results on stopping set enumerators for block codes in general. Next, we focus on stopping set enumerators for Hamming codes. Our main result is a parity-check matrix of relatively small size for which the number of stopping sets of size three equals the number of codewords of weight three in the Hamming code.

Knuth's Balanced Codes Revisited

In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of ¿1¿s and ¿-1¿s, called balanced codes. Knuths algorithm is well suited for use with large codewords. The redundancy of Knuths balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In this paper, we will present results of our attempts to improve the performance of Knuths balanced codes.

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. >

Impact of RF circuit imperfections on multi-carrier and single-carrier based transmissions at 60 GHz

Circuit technology for 60 GHz is still limited, and impairments due to radio frequency (RF) circuit imperfections must be taken into account. Therefore, the candidate transmission schemes, in addition to multi-path fading, should be fairly resistant to RF circuit imperfections. In this paper, a performance comparison of multi-carrier (MC) and single-carrier (SC) based transmission schemes in the presence of DAC/ADC imperfections and amplifier nonlinearities, is carried out. It is shown that the SC scheme has substantially lower front-end requirements than its MC counterpart, while having the same overall system complexity.

Iterative Demodulation and Decoding for Rotated MPSK Constellations with Convolutional Coding and Signal Space Diversity

Signal space diversity (SSD) with the rotation of the signal constellation using multi-level modulation schemes is known to provide good performance gains over fading channels. This paper studies the extension of such schemes with iterative demodulation and decoding using convolutional codes for MPSK signal constellations with different symbol mappings. It is shown that for a specific signal constellation and labeling using SSD on a Rayleigh fading channel, a well considered choice of the rotation angle leads to a significant gain over conventional bit interleaved coded modulation with iterative decoding (BICM-ID). Furthermore, the optimum rotation angle for the coded system is found to be dependent upon the symbol labeling and the number of iterations carried out at the receiver.

Construction and evaluation of trellis-coded quantizers for memoryless sources

New constructions of trellis waveform coders, trellis-coded quantizers, and trellis-coded vector quantizers are proposed. The performances of the new quantizers are determined for the memoryless Laplacian, Gaussian, and uniform sources. They are better than (for the Gaussian and Laplacian sources) or equal to (for the uniform source) the best previously published results. >

Optimized Rotations for LDPC-Coded MPSK Constellations with Signal Space Diversity

For multi-level modulation methods, rotation of the signal constellation together with in-phase and quadrature phase channel interleaving (signal space diversity) are known to provide good performance gains over fading channels. This paper studies the extension of such schemes with a low density parity check (LDPC) code. It is shown that for both coded and uncoded Gray-mapped MPSK modulation formats with signal space diversity on a Rayleigh fading channel, a well-considered choice of the rotation angle may lead to a significant gain over the conventional unrotated constellation. However, the optimum rotation angle for the coded scheme may be different from the corresponding optimization angle of the uncoded scheme.