List decoding

About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.

Spatially Coupled LDPC Codes Constructed From Protographs

Abstract: In this paper, we construct protograph-based spatially coupled low-density parity-check (LDPC) codes by coupling together a series of $L$ disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying $L$ , we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary $L$ . We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large $L$ , the BP thresholds on both the binary erasure channel and the binary-input additive white Gaussian noise channel saturate to a particular value significantly better than the BP decoding threshold and numerically indistinguishable from the optimal maximum a posteriori decoding threshold of the uncoupled LDPC code. When all variable nodes in the coupled chain have degree greater than two, asymptotically the error probability converges at least doubly exponentially with decoding iterations and we obtain sequences of asymptotically good LDPC codes with fast convergence rates and BP thresholds close to the Shannon limit. Further, the gap to capacity decreases as the density of the graph increases, opening up a new way to construct capacity achieving codes on memoryless binary-input symmetric-output channels with low-complexity BP decoding.

On deep learning-based channel decoding

Abstract: We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code families and for short codeword lengths, we observe that (i) structured codes are easier to learn and (ii) the neural network is able to generalize to codewords that it has never seen during training for structured, but not for random codes. These results provide some evidence that neural networks can learn a form of decoding algorithm, rather than only a simple classifier. We introduce the metric normalized validation error (NVE) in order to further investigate the potential and limitations of deep learning-based decoding with respect to performance and complexity.

A modified weighted bit-flipping decoding of low-density Parity-check codes

Abstract: In this letter, a modified weighted bit-flipping decoding algorithm for low-density parity-check codes is proposed. Improvement in performance is observed by considering both the check constraint messages and the intrinsic message for each bit.

The algebraic decoding of Goppa codes

Abstract: An interesting class of linear error-correcting codes has been found by Goppa [3], [4]. This paper presents algebraic decoding algorithms for the Goppa codes. These algorithms are only a little more complex than Berlekamp's well-known algorithm for BCH codes and, in fact, make essential use of his procedure. Hence the cost of decoding a Goppa code is similar to the cost of decoding a BCH code of comparable block length.

Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix

Abstract: We propose the use of linear codes with low density generator matrix to achieve a performance similar to that of turbo and standard low-density parity check codes. The use of iterative decoding techniques - message passing -over the corresponding graph achieves a performance close to the Shannon theoretical limit. As an advantage with respect to turbo and standard low-density parity check codes, the complexity of the decoding and encoding procedures is very low.