Multilevel Block Codes Research Articles

Non-Coherent Multi-Level Index Modulation

This paper develops a non-coherent index modulation (IM) system in which activation patterns are characterized by multi-level block codes. We analyze performance of such a system under the maximum-likelihood (ML) receiver and when the set of activation patterns follows a multi-level code generated from asymptotically optimal alphabets. An asymptotic analysis of the pair-wise error probability (PEP) shows that the system can exploit a diversity order that is determined by the distance of the worst codeword pair in the <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> metric, known as the Manhattan norm. We then explore the rate-diversity tradeoff for the developed non-coherent IM system as a function of the code length. Specifically, Gilbert-style bounds on the data rates for systems based on binary and ternary codes are obtained that can ensure a given diversity order. We approach the problem of packing in the <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> metric by partitioning codes into permutation modulation codes (PMCs) and obtaining Gilbert-style bounds on PMCs. Several achievable rates for non-coherent binary and ternary IM systems, as well as a tradeoff between the information rate and codeword error probability (CEP) are also derived. Finally, simulation results are provided to corroborate the theoretical analysis.

Reliability level list-based decoding of multilevel modulated block codes

Reliability level list-based decoding of multilevel modulated block codes

Reliability level list-based decoding of multilevel modulated block codes

Different soft decision decoding approaches for block codes which refine the hard decision decoding have been reported. These approaches have varying degrees of complexity and performance enhancement. The reliability level list RLL-based decoding scheme for block codes directly uses the reliability of the received bit with corresponding dividend in decoding. With this scheme, it has become possible to identify the target codeword TCW directly obviating the need for forming an intermediate set of candidate codewords and then selecting the decoded codeword from them. This opens up the possibility of exploring a comprehensive generalisation of the RLL concept for any block code and any baseband scheme. Such a generalisation for block codes with M-QAM signalling scheme is established in the paper.

A block-coded modulation method for one-way multimode data transmission

This paper presents a multimode block-coded modulation method that enables both multimode transmission and coding gain. In multimode transmission, the property of data is changed for each mode, and the data are adaptively transmitted. In our method, all modes are constructed by separate multilevel block codes, wherein the number of levels, set partition, rate, and distance properties of each mode may differ from those of the other modes. Different modes may also have different signal constellations, that is, different modulation methods. The code length is the same for all modes, and the mode can be switched at each block boundary, if desired. This method uses one-way transmission where the transmitter has no feedback information from the receiver. In decoding, the maximum-likelihood decoding is carried out using the Viterbi (1967) algorithm. The decoding of all modes, including decoding of the mode index, can be accomplished using one trellis diagram. This paper describes the multimode encoding and decoding method, and analyzes the distance properties and upper bounds for inter- and intramodes. It is clarified at which distance the code should be increased to reduce the decoding mode error. Three design examples are presented for unequal error protection/equal error protection, variable rate, and hybrid additive white Gaussian noise/flat-fading codes.

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. >

Multilevel block subcodes for codedphase modulation

The aim of this Letter is to show a new coded phase modulation based on fields. A class of multilevel block codes based on fields are also presented and those codes can perform better in terms of asymptotic coding gain than their equivalent codes over rings of integers modulo-2m.

Concatenated multilevel block coded modulation

Encoding and decoding schemes for concatenated multilevel block codes are presented. By one of these structures, a real coding gain of 5.6-7.4 dB for the bit error range of 10/sup -6/ to 10/sup -9/ is achieved for transmission through the additive white Gaussian noise channel. Also, a rather large asymptotic coding gain is obtained. The new coding schemes have very low decoding complexity and increased coding gain in comparison with the conventional block and trellis coded modulation structures. A few design rules for concatenated (single and) multilevel block codes with large coding gain are also provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New multilevel codes over GF(q)

Set partitioning is applied to multidimensional signal spaces over GF(q), i.e., GF/sup n1/(q) (n1<or=q), and it is shown how to construct both multilevel block codes and multilevel trellis codes over GF(q). Multilevel (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d/sub min/>or=d are presented. These codes use Reed-Solomon codes as component codes. Longer multilevel block codes are also constructed using q-ary block codes with block length longer than q+1 as component codes. Some quaternary multilevel block codes are presented with the same length and number of information symbols as, but larger distance than, the best previously known quaternary one-level block codes. It is proved that if all the component block codes are linear. the multilevel block code is also linear. Low-rate q-ary convolutional codes, word-error-correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multilevel trellis codes over GF(q) or binary-to-q-ary trellis codes.<<ETX>>

&lt;title&gt;Error Detection And Correction In Multilevel Algebraic Optical Processors&lt;/title&gt;

The performance of inexact processors can be improved at the cost of throughput by using parallel redundant computations to correct errors at the processor's output. Error correcting codes applicable to binary data strings have previously been suggested for application to optical processors. We demonstrate that multilevel block codes can likewise be applied. Specific attention is given to error correction multilevel optical matrix-vector multipliers. The per-formance of the multilevel block code is compared to that of multilevel error correction codes formulated for VLSI processors and bar code readers. In residue-coded form (in which the matrix-vector multiplication is performed conventionally), the multilevel block code is shown overall to require fewer resolvable levels at the output.

Error-correcting capabilities of multilevel block codes: an upper bound

An upper bound of the Hamming or sphere-packing type that can never be exceeded can be applied to multilevel codes. Examples are given for quaternary and decimal codes, both for whole-digit errors and for nearest-place errors. A single-error-correcting decimal code is constructed.