Topic
List decoding
About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.
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30 Sep 2009
TL;DR: In this paper, the authors show that there is a tight connection between CS-LPD based on a zero-one measurement matrix over the real values and CCLPD of the binary linear code that is obtained by viewing this measurement matrix as a binary parity-check matrix.
Abstract: This is a tale of two linear programming decoders, namely channel coding linear programming decoding (CC-LPD) and compressed sensing linear programming decoding (CS-LPD). So far, they have evolved quite independently. The aim of the present paper is to show that there is a tight connection between, on the one hand, CS-LPD based on a zero-one measurement matrix over the reals and, on the other hand, CC-LPD of the binary linear code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows one to translate performance guarantees from one setup to the other.
44 citations
TL;DR: A framework for solving polynomial equations with size constraints on solutions is developed and powerful analogies from algebraic number theory allow us to identify the appropriate analogue of a lattice in each application and provide efficient algorithms to find a suitably short vector, thus allowing completely parallel proofs of the above theorems.
Abstract: We develop a framework for solving polynomial equations with size
constraints on solutions. We obtain our results by showing how to apply a
technique of Coppersmith for finding small solutions of polynomial
equations modulo integers to analogous problems over polynomial rings,
number fields, and function fields. This gives us a unified view of several
problems arising naturally in cryptography, coding theory, and the study of
lattices. We give (1) a polynomial-time algorithm for finding small
solutions of polynomial equations modulo ideals over algebraic number
fields, (2) a faster variant of the Guruswami-Sudan algorithm for list
decoding of Reed-Solomon codes, and (3) an algorithm for list decoding of
algebraic-geometric codes that handles both single-point and multi-point
codes. Coppersmith's algorithm uses lattice basis reduction to find a
short vector in a carefully constructed lattice; powerful analogies from
algebraic number theory allow us to identify the appropriate analogue of a
lattice in each application and provide efficient algorithms to find a
suitably short vector, thus allowing us to give completely parallel proofs
of the above theorems.
44 citations
TL;DR: A coding scheme is presented where the redundancy can get close to one half the redundancy required in minimum-distance decoding of crisscross errors.
Abstract: The crisscross error model in data arrays is considered, where the corrupted symbols are confined to a prescribed number of rows or columns (or both). Under the additional assumption that the corrupted entries are uniformly distributed over the channel alphabet, and by allowing a small decoding error probability, a coding scheme is presented where the redundancy can get close to one half the redundancy required in minimum-distance decoding of crisscross errors.
44 citations
15 Oct 2007
TL;DR: A modified iterative decoding algorithm to decode a special class of quasi-cyclic low- density parity-check codes such as QC-LDPC codes used in the IEEE 802.16e standards can reduce the number of iterations required by up to forty percent without error performance loss as compared to the conventional message- passing decoding algorithm.
Abstract: In this paper, we propose a modified iterative decoding algorithm to decode a special class of quasi-cyclic low- density parity-check (QC-LDPC) codes such as QC-LDPC codes used in the IEEE 802.16e standards. The proposed decoding is implemented by serially decoding block codes with identical parity-check matrix H1 derived from the parity-check matrix H of the QC-LDPC codes. The dimensions of H1 are much smaller than those of H. Extrinsic values can be passed among these block codes since the code bits of these block codes are overlapped. Hence, the proposed decoding can reduce the number of iterations required by up to forty percent without error performance loss as compared to the conventional message- passing decoding algorithm. A partially-parallel very large-scale integration (VLSI) architecture is proposed to implement such a decoding algorithm. The proposed VLSI decoder can fully take advantage of the proposed decoding to increase its throughput. In addition, the proposed decoder only needs to store check-to- variable messages and hence is memory efficient.
43 citations
07 Jul 2013
TL;DR: A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs that have the “uncoded repair” property where the nodes participating in the repair simply transfer part of the stored data directly, without performing any computation.
Abstract: A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs. The proposed codes have the “uncoded repair” property where the nodes participating in the repair simply transfer part of the stored data directly, without performing any computation. The layered error correction structure results in a low-complexity decoding process. An analysis of our coding scheme is presented. This construction is able to achieve better performance than timesharing between the minimum storage regenerating codes and the minimum repair-bandwidth regenerating codes.
43 citations