Trellis coded 4-ary PAM using distance preserving mapping

Abstract: A trellis coded 4-ary Pulse Amplitude Modulation (4-PAM) is presented, where the encoding algorithm is derived from Distance Preserving Mapping (DPM) algorithm. In this work, we modify the DPM algorithm for 4-PAM and obtain a new construction for mapping binary sequences to permutation sequences, where the permutation sequences are obtained by permuting symbols of a 4-PAM constellation. The resulting codebook of permutation sequences formed this way are termed mappings. We also present several metrics for assessing the performance of the mappings from our construction, and we show that a metric called the Sum of Product of Distances (SOPD) is the best metric to use when judging the performance of the mappings. Finally, performance results are presented, where the mappings from our construction are compared against each other and also against the conventional mappings in the literature. Index Terms—Distance-preserving mappings, Hamming distance, Euclidean distance, Pulse Amplitude Modulation

A multilevel construction for mappings from binary sequences to permutation sequences

Abstract: A multilevel construction is introduced to create distance-preserving mappings from binary sequences to permutation sequences. It is also shown that for certain values, the new mappings attain the upper bound on the sum of Hamming distances obtainable for such mappings, and in the other cases improve on those of previous mappings

Simulation results for permutation trellis codes using M-ary FSK

Abstract: It has previously been shown that using the combination of permutation codes and M-ary frequency shift keying has special properties and error correcting capabilities that are suitable for the noise types encountered in power line communications. Furthermore, the permutation codes are used to map onto the outputs of a binary convolutional code to form permutation trellis codes. We investigate and compare the performance of different permutation trellis codes when used with M-FSK for power line communications

Mathematical approach and implementation of frequency mapping techniques in power-line communications channel

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A ranking method for rating the performances of permutation codes

Abstract: Minimum Hamming distance, dm, has been widely used as the yardstick for the performance of permutation codes (PCs). However, a number of PCs with the same dm and cardinality can have different performances, even if they have the same distance optimality. Since PC is a robust channel coding scheme in power line communications applications, we present a simple and fast ranking method that predicts the relative performance of PCs, by using the information extracted from their Hamming distance distributions. This tool is useful for selecting an efficient PC codebook out of a number of similar ones

New DC-free multilevel line codes with spectral nulls at rational submultiples of the symbol frequency

Abstract A new technique of designing multilevel line codes is presented. Distance-preserving mappings from binary sequences to permutation sequences are used, where the permutation sequences also have spectral nulls properties. The resultant line codes use the structure of the convolutional codes and thus have certain advantages compared to other published line codes

Evaluation of mixed permutation codes in PLC channels, using hamming distance profile

Abstract: We report a new concept involving an adaptive mixture of different sets of permutation codes (PC) in a single DPSK-OFDM modulation scheme. Since this scheme is robust and the algorithms involved are simple, it is a good candidate for implementation for OFDM-based power line communication (PLC) systems. By using a special and easy concept called Hamming distance profile, as a comparison tool, we are able to showcase the strength of the new PC scheme over other schemes reported in literature, in handling the incessant noise types associated with PLC channels. This prediction tool is also useful for selecting an efficient PC codebook out of a number of ! similar ones

Permutation Coding with Injections for Modified PAM System

Arriving at a good combination of coding andmodulation schemes that can achieve good error correctionconstitutes a challenge in digital communication systems. In thiswork, we explore the combination of permutation coding (PC)and pulse amplitude modulation (PAM) for mitigating channelerrors in the presence of background noise and jitter. Since PAMis characterised with bi-polar constellations, Euclidean distance isa good choice for predicting the performance of such coded modulationsetup. In order to address certain challenges facing PCs,we therefore introduce injections in the coding system, togetherwith a modified form of PAM system. This modification entailsconstraining the PAM constellations to the size of the codeword’ssymbol. The results obtained demonstrate the strength of themodified coded PAM system over the conventional PC codedPAM system

Distance-preserving mapping with euclidean distance for 4-ary PAM

Abstract: In this article we give: (a) a new construction for mapping binary sequences to permutation sequences formed from a 4-PAM constellation, and call the resulting codebooks mappings; (b) a metric for assessing the performance of mappings from our construction; (c) performance results comparing mappings from our construction against the conventional mappings in the literature. The results show that our mappings outperform the conventional mappings. Against conventional soft-decision decoded 4-PAM, our mapping showed 2.4 dB and 3.2 dB improvement over (R = 1=3, K = 4, dfree = 10) and (R = 1=3, K = 3, dfree = 6) convolutional codes, respectively