P.G. Farrell

Euclidean distance soft-input soft-output decoding algorithm for low-density parity-check codes

A new antilog-sum algorithm for decoding error-correcting codes is described. The soft-input, soft-output (SISO) algorithm uses squared Euclidean distance as the metric, does not require knowledge of the signal-to-noise ratio of the received signal and is less complex to implement than other SISO algorithms. The results of simulations show that the performance is very close to that of the log-sum-product algorithm.

Decomposable codes based on two-dimensional array codes

In this paper, we present a construction method for obtaining the decomposable codes that are originated from two-dimensional array codes and of the form |a/sub 1/+x|/spl middot//spl middot//spl middot/|a/sub m/+x|a/sub 1/+/spl middot//spl middot//spl middot/+a/sub m/+x+y|. Many best known codes can be constructed using this method.

Reducing the complexity of trellises for block codes

This contribution presents the results of applying two generic algorithms for reducing the complexity of the trellis of a number of binary linear block codes.

Fast Fourier Transform simplified soft-distance decoding algorithm for decoding non-binary LDPC codes

Non-Binary Low-Density Parity-Check (NB-LDPC) codes have been shown to outperform equivalent LDPC codes defined over the binary field, especially when they are designed in high order Galois fields GF(q). This however leads to an increased decoding complexity. In this paper, a computationally efficient version of a soft distance algorithm used for decoding (NB-LDPC) error-correcting codes is described. This decoding algorithm uses squared Euclidean distance as the metrics, does not require knowledge of the signal-to-noise ratio of the received signal, and is less complex to implement than the Fast Fourier Transform Sum-Product and the log-sum-product algorithms. It is a simplified algorithm that can be easily implemented on programmable logic technology such as Field Programmable Gate Array (FPGA) devices because of its use of only additions, subtractions and look-up tables, avoiding the use of quotients and products. Simulations results show that the performance is the same as or better than that of the Fast Fourier Transform Sum-Product and the log-sum-product algorithms. Simulations were done over the AWGN, Rayleigh Fading and impulsive noise with a Symmetric Alpha-Stable (SαS) distribution channels.

Field programmable gate arrays implementations of low complexity soft-input soft-output low-density parity-check decoders

Low-density parity-check (LDPC) codes are very efficient error control codes that are being considered for use in many next-generation communication systems. In this study low complexity soft-input, soft-output (SISO) field programmable gate arrays (FPGA) implementations of a novel logarithmic sum-product (LogSP) iterative LDPC decoder and a recently proposed simplified soft Euclidean distance (SSD) iterative LDPC decoder are presented, and their complexities and performance are compared. These implementations operate over any choice of parity check matrix (including those randomly generated, structurally generated and either systematic or non-systematic) and can be parametrically adapted for any code rate. The proposed implementations are both of very low complexity, because they operate using only sums, subtractions, comparisons and look-up tables, which makes them particularly suitable for FPGA realisation. The SSD decoder has a lower implementation complexity than the LogSP LDPC decoder and it also offers the advantage of not requiring knowledge of the channel signal-to-noise ratio, unlike most other LDPC decoders.

Adaptive soft—decision decoding for array codes

An adaptive decoding scheme is introduced that achieves efficient soft-decision decoding for row-and-column parity array codes. The special structure of array codes is exploited to make effective use of hard-decision methods to realize soft-decision decoding. This leads to considerable reduction in decoding complexity as the amount of soft-decision computation varies with channel conditions. It is shown that the new decoding algorithm guarantees bounded distance performance. Simulation results indicate that the actual improvement of decoding performance over uncoded systems and previous decoding methods is significant.

Fast soft-decision decoding for block codes using a trellis

The trellis used for decoding can be significantly simplified by using the results from decoding the component codes of the full code. The saving on decoding complexity varies according to the decoding performances required. The method applies to any block code that can be decomposed into component codes.

Adaptive Soft-Decision Decoding In Two Dimensions

To achieve efficient soft-decision decoding for two-dimensional product and array codes, an adaptive decoding scheme is proposed. In the scheme, the special structure of these codes has been fully exploited, resulting in a method for effective use of combined hard-and soft-decision decoding of component codes. As a result, a substantial reduction in decoding complexity is obtained, especially when channel conditions are good. We will show that the decoding algorithm presented can guarantee bounded soft distance performance, while simulation results indicate even better decoding performance and an improvement over similar previous decoding methods. Turbo decoding is about 1 dB better in performance, but at the cost of a very significant increase in complexity.