arXiv subjects

Eirik Rosnes

Publications and source records attributed to Eirik Rosnes.

75 records · Page 5Linked to original sources

arXiv2009

Iterative Decoding on Multiple Tanner Graphs Using Random Edge Local Complementation

In this paper, we propose to enhance the performance of the sum-product algorithm (SPA) by interleaving SPA iterations with a random local graph update rule. This rule is known as edge local complementation (ELC), and has the effect of modifying the Tanner graph while preserving the code. We have previously shown how the ELC operation can be used to implement an iterative permutation group decoder (SPA-PD)--one of the most successful iterative soft-decision decoding strategies at small blocklengths. In this work, we exploit the fact that ELC can also give structurally distinct parity-check matrices for the same code. Our aim is to describe a simple iterative decoder, running SPA-PD on distinct structures, based entirely on random usage of the ELC operation. This is called SPA-ELC, and we focus on small blocklength codes with strong algebraic structure. In particular, we look at the extended Golay code and two extended quadratic residue codes. Both error rate performance and average decoding complexity, measured by the average total number of messages required in the decoding, significantly outperform those of the standard SPA, and compares well with SPA-PD. However, in contrast to SPA-PD, which requires a global action on the Tanner graph, we obtain a performance improvement via local action alone. Such localized algorithms are of mathematical interest in their own right, but are also suited to parallel/distributed realizations.

cs.IT↗

arXiv2009

Good Concatenated Code Ensembles for the Binary Erasure Channel

In this work, we give good concatenated code ensembles for the binary erasure channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code ensembles formed by the serial concatenation of a repetition code with multiple accumulators, and the hybrid concatenated code (HCC) ensembles recently introduced by Koller et al. (5th Int. Symp. on Turbo Codes & Rel. Topics, Lausanne, Switzerland) consisting of an outer multiple parallel concatenated code serially concatenated with an inner accumulator. We introduce stopping sets for iterative constituent code oriented decoding using maximum a posteriori erasure correction in the constituent codes. We then analyze the asymptotic stopping set distribution for RMA and HCC ensembles and show that their stopping distance hmin, defined as the size of the smallest nonempty stopping set, asymptotically grows linearly with the block length. Thus, these code ensembles are good for the BEC. It is shown that for RMA code ensembles, contrary to the asymptotic minimum distance dmin, whose growth rate coefficient increases with the number of accumulate codes, the hmin growth rate coefficient diminishes with the number of accumulators. We also consider random puncturing of RMA code ensembles and show that for sufficiently high code rates, the asymptotic hmin does not grow linearly with the block length, contrary to the asymptotic dmin, whose growth rate coefficient approaches the Gilbert-Varshamov bound as the rate increases. Finally, we give iterative decoding thresholds for the different code ensembles to compare the convergence properties.

cs.IT↗

arXiv2006

Turbo Decoding on the Binary Erasure Channel: Finite-Length Analysis and Turbo Stopping Sets

This paper is devoted to the finite-length analysis of turbo decoding over the binary erasure channel (BEC). The performance of iterative belief-propagation (BP) decoding of low-density parity-check (LDPC) codes over the BEC can be characterized in terms of stopping sets. We describe turbo decoding on the BEC which is simpler than turbo decoding on other channels. We then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure. Apply turbo decoding until the transmitted codeword has been recovered, or the decoder fails to progress further. Then the set of erased positions that will remain when the decoder stops is equal to the unique maximum-size turbo stopping set which is also a subset of the set of erased positions. Furthermore, we present some improvements of the basic turbo decoding algorithm on the BEC. The proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results. Finally, we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption, and an efficient enumeration algorithm of small-size turbo stopping sets for a particular interleaver. The solution is based on the algorithm proposed by Garello et al. in 2001 to compute an exhaustive list of all low-weight codewords in a turbo code.

cs.IT↗