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IET Communications

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

Patrick Guy Farrell, Leonardo J. Arnone, Jorge Castiñeira Moreira

Published Nov 4, 2011• 13 citations
Publisher

Abstract

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.

DOI
10.1049/iet-com.2010.1040

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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.
A new soft-input,soft-output algorithm for decoding LDPC codes is described in this paper.Using soft squared Euclidean distance as the metric,the algorithm realizes decoding by iterating the antilog-sum of the Euclidean distance.A simplified algorithm is also put forward to reduce computational complexity.The proposed algorithm does not require knowledge of the signal-to-noise ratio of the received signal and is less complex to implement than other soft decision algorithms.The results of simulation show that the performance is very close to that of sum-product algorithm while the computational complexity is sharply reduced.
To deal with the complexity of traditional BP decoding algorithm,a kind of blind decoding algorithm for LDPC codes based on soft-input,soft-output is put forward in this paper.The algorithm uses soft squared Euclidean distance as the metric,realizes decoding by iterating the antilog-sum of the Euclidean distance as the process taken in BP algorithm.The proposed algorithm does not require knowledge of the signal-to-noise ratio of the received signal,and is less complex to implement than other soft decision algorithms.At the same time,a simplified algorithm is also put forward to reduce the computational complexity.What's more,the proposed SBSD decoding algorithm can not only decode Binary LDPC codes,but also can be used for Qary-LDPC codes.Simulations results show that the proposed algorithm can achieve good performance not only on the AWGN channels but also on Rayleigh channel,and the performance is very close to that of the sum-product algorithm,but the computational complexity is reduced sharply.
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.
Long forward error correction codes are typically constructed by concatenating shorter component codes that are then decoded through iterative Soft-Input Soft-Output (SISO) of their components. The recently introduced Soft Output Guessing Random Additive Noise Decoding (SOGRAND) has been shown to enable accurate SISO component decoding for a broad range of component codes. Here we establish that by specializing its SISO computation to Single Parity Check codes, SOGRAND offers an alternative existing Check Node (CN) update for decoding Low Density Parity Check codes. Simulation results demonstrate similar or better decoding performance than Gallager's sum-product algorithm and norm-min-sum, while offering two distinct low complexity, hardware friendly CN update algorithms.
A class of pseudo-random compound error-correcting codes, called generalized low density (GLD) parity-check codes, has been proposed recently. As a generalization of Gallager's low-density parity check (LPDC) codes, GLD codes are also asymptotically good in the sense of minimum distance criterion and can be effectively decoded based on iterative soft-input soft-output (SISO) decoding of individual constituent codes. The code performance and decoding complexity of GLD codes are heavily dependent on the employed SISO decoding algorithm. In this paper, we present an efficient SISO decoding algorithm for GLD codes. The proposed algorithm utilizes Kaneko's decoding algorithm for soft-input hard-output decoding. These hard outputs are converted to soft-decision using reliability calculations. The algorithm proposed here presents a major advantage over existing decoding algorithms for GLD codes by being applicable even when long and powerful component codes are used. The complexity of the proposed algorithm is less than that of trellis-based decoding algorithms with a performance degradation of only 0.3 dB.
A class of pseudo-random compound error-correcting codes, called generalized low-density (GLD) parity-check codes, has been proposed recently. As a generalization of Gallager's low-density parity-check (LDPC) codes, GLD codes are also asymptotically good in the sense of minimum distance criterion and can be effectively decoded based on iterative soft-input soft-output (SISO) decoding of individual constituent codes. The code performance and decoding complexity of GLD codes are heavily dependent on the employed SISO decoding algorithm. In this paper, we show that Max-Log-MAP is an attractive SISO decoding algorithm for GLD coding scheme, considering the trade-off between performance and complexity in the practical implementations. A normalized Max-Log-MAP is presented to improve the GLD code performance significantly compared with using conventional Max-Log-MAP. Moreover, we propose two techniques, decoding task scheduling and reduced search Max-Log-MAP, to effectively reduce the decoding complexity without any performance degradation.