List decoding

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

Multi-kernel construction of polar codes

Abstract: We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi-kernel polar code with very good performance while the encoding complexity remains low and the decoding follows the same general structure as for the original Arikan polar codes. The construction provides numerous practical advantages as more code lengths can be achieved without puncturing or shortening. We observe numerically that the error-rate performance of our construction outperforms state-of-the-art constructions using puncturing methods.

Low-Complexity Approaches to Slepian–Wolf Near-Lossless Distributed Data Compression

Abstract: This paper discusses the Slepian-Wolf problem of distributed near-lossless compression of correlated sources. We introduce practical new tools for communicating at all rates in the achievable region. The technique employs a simple "source-splitting" strategy that does not require common sources of randomness at the encoders and decoders. This approach allows for pipelined encoding and decoding so that the system operates with the complexity of a single user encoder and decoder. Moreover, when this splitting approach is used in conjunction with iterative decoding methods, it produces a significant simplification of the decoding process. We demonstrate this approach for synthetically generated data. Finally, we consider the Slepian-Wolf problem when linear codes are used as syndrome-formers and consider a linear programming relaxation to maximum-likelihood (ML) sequence decoding. We note that the fractional vertices of the relaxed polytope compete with the optimal solution in a manner analogous to that observed when the "min-sum" iterative decoding algorithm is applied. This relaxation exhibits the ML-certificate property: if an integral solution is found, it is the ML solution. For symmetric binary joint distributions, we show that selecting easily constructable "expander"-style low-density parity check codes (LDPCs) as syndrome-formers admits a positive error exponent and therefore provably good performance

Bounds on list decoding of MDS codes

Abstract: We derive upper bounds on the number of errors that can be corrected by list decoding of maximum-distance separable (MDS) codes using small lists. We show that the performance of Reed-Solomon (RS) codes, for certain parameter values, is limited by worst case codeword configurations, but that with randomly chosen codes over large alphabets, more errors can be corrected.

Limits to List Decoding Reed–Solomon Codes

Abstract: In this paper, we prove the following two results that expose some combinatorial limitations to list decoding Reed-Solomon codes. 1) Given n distinct elements alpha1,...,alphan from a field F, and n subsets S1,...,Sn of F, each of size at most l, the list decoding algorithm of Guruswami and Sudan can in polynomial time output all polynomials p of degree at most k that satisfy p(alphai)isinSi for every i, as long as l 0 (agreement of k is trivial to achieve). Such a bound was known earlier only for a nonexplicit center. Finding explicit bad list decoding configurations is of significant interest-for example, the best known rate versus distance tradeoff, due to Xing, is based on a bad list decoding configuration for algebraic-geometric codes, which is unfortunately not explicitly known

Approaching capacity at high rates with iterative hard-decision decoding

Abstract: A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we analyze a class of spatially-coupled generalized LDPC codes and observe that, in the high-rate regime, they can approach capacity under iterative hard-decision decoding. These codes can be seen as generalized product codes and are closely related to braided block codes.