Patrick Guy Farrell

Space-frequency coded OFDM system for multi-wire power line communications

In this paper, we propose an efficient space-frequency coded orthogonal frequency-division multiplexing (OFDM) system for high-speed data transmission over frequency selective multi-wire power line channels. By transmitting the same data symbol over two uncoupled pair of wires and over two different carriers, with a frequency separation between carriers greater than the coherence bandwidth of the channel, the proposed scheme extracts both space and frequency diversity in the absence of channel knowledge at the transmitter. Numerical results are provided to demonstrate the significant performance improvement obtained by the proposed scheme over conventional single-wire OFDM systems when the frequency selective power line channel is corrupted by impulsive noise.

A Unified Code

We have proposed a novel scheme based on arithmetic coding, an optimal data compression algorithm in the sense of shortest length coding. Our scheme can provide encryption, data compression, and error detection, all together in a one-pass operation. The key size used is 248 bits. The scheme can resist existing attacks on arithmetic coding encryption algorithms. A general approach to attacking this scheme on data secrecy is difficult. The statistical properties of the scheme are very good and the scheme is easily manageable in software. The compression ratio for this scheme is only 2 % worse than the original arithmetic coding algorithm. As to error detection capabilities, the scheme can detect almost all patterns of errors inserted from the channel, regardless of the error probabilities, and at the same time it can provide both encryption and data compression.

A Line Code Construction for the Adder Channel with Rates Higher than Time-Sharing

In this paper, line coding schemes and their application to the multi-user adder channel are investigated. The focus is on designing line codes with higher information per channel use rates than time- sharing. We show that by combining short multi-user line codes, it is possible to devise longer coding schemes with rate sums which increase quite rapidly at each iteration of the construction. Asymptotically, there is no penalty in requiring the coding schemes to be DC-free.

Graph Decoding of Array Error-Correcting Codes

The motivation for this paper is to report on concepts and results arising from the continuation of a recent study [1] of graph decoding techniques for block error-control (detection and correction) codes. The representation of codes by means of graphs, and the corresponding graph-based decoding algorithms, are described briefly. Results on the performance of graph decoding methods for block codes of the array and generalised array type will be presented, confirming the illustrative examples given in [1]. The main novel result is that the (7,4) Generalised Array Code, equivalent to the (7,4) Hamming Code, which has a graph which contains cycles, can be successfully decoded by means of an iterated min-sum algorithm.

Soft Distance Metric Decoding of Polar Codes

In this paper, we implement the Successive Cancellation SC decoding algorithm for Polar Codes by using Euclidean distance estimates as the metric of the algorithm. This implies conversion of the classic statistical recursive expressions of the SC decoder into a suitable form, adapting them to the proposed metric, and properly expressing the initialization values for this metric. This leads to a simplified version of the logarithmic SC decoder, which offers the advantage that the algorithm can be directly initialised with the values of the received channel samples. Simulations of the BER performance of the SC decoder, using both the classic statistical metrics, and the proposed Euclidean distance metric, show that there is no significant loss in BER performance for the proposed method in comparison with the classic implementation. Calculations are simplified at the initialization step of the algorithm, since neither is there a need to know the noise power variance of the channel, nor to perform complex and costly mathematical operations like exponentiations, quotients and products at that step. This complexity reduction is especially important for practical implementations of the SC decoding algorithm in programmable logic technology like Field Programmable Gate Arrays FPGAs.

Recent Developments in Array Error-Control Codes

Array error-control codes are linear block or convolutional codes, with codewords or coded sequences constructed by attaching check symbols to arrays of information symbols arranged in two or more dimensions. The check symbols are calculated by taking sums of the the information symbols lying along rows, columns, diagonals or other directions or paths in the information array. The simplest array code is the binary block code obtained by taking single parity checks across the rows and columns of a rectangular array of information bits. Array codes can be constructed with symbols from a .eld, ring or group, can have a wide range of parameters (block or constraint length, rate, distance, etc), and can be designed to detect and correct random and/or bursts or clusters of errors. The motivation for investigating and applying array codes (apart from their interesting mathematical aspects) is that they often provide a good trade-o. between error-control power and complexity of decoding. The rate of a random error-control block array code, such as a product code, for example (classical product codes form a sub-class of array codes), is usually less than that of the best available alternative code with the same distance and length, but in exchange the array code will be much easier to decode [1]. However, in many cases array codes designed to correct burst error patterns can be both optimal (maximum distance separable (MDS), for example) and simpler to decode than other equivalent codes [1].

Graph Configurations and Decoding Performance

The performance of a new method for decoding binary error correcting codes is presented, and compared with established hard and soft decision decoding methods. The new method uses a modified form of the maxsum algorithm, which is applied to a split (partially disconnected) modification of the Tanner graph of the code. Most useful codes have Tanner graphs that contain cycles, so the aim of the split is to convert the graph into a tree graph. Various split graph configurations have been investigated, the best of which have decoding performances close to maximum likelihood.