List decoding

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

Efficient High-Performance Decoding for Overloaded MIMO Antenna Systems

Abstract: The practical challenge of capacity-achieving forward error-correcting codes (e.g., space-time turbo codes) is overcoming the tremendous complexity associated by their optimal joint maximum-likelihood (ML) decoding. For this reason, iterative soft decoding has been studied to approach the optimal ML decoding performance at affordable complexity. In multiple-input multiple-output (MIMO) channels, a judicious decoding strategy consists of two stages: 1) estimate the soft bits using list version of sphere decoding or its variants, and 2) update the soft bits through iterative soft decoding. A promising MIMO decoder is required to produce reliable soft-bit estimates at the first stage before iterative soft decoding is performed. In this paper, we focus on the overloaded (or fat) MIMO antenna systems where the number of receive antennas is less than the number of signals multiplexed in the spatial domain. In this scenario, the original form of sphere decoding is inherently not applicable and our aim is to generalize sphere decoding geometrically to cope with overloaded detection. The so-called slab-sphere decoding (SSD) proposed guarantees to obtain exact-ML hard detection while reducing complexity greatly. With the list-version of SSD, (his paper proposes an efficient MIMO soft decoder, which can generate reliable soft-bit estimates at affordable complexity as inputs for iterative soft decoding for promising performance. A case study in the IEEE 802.16 settings is carried out for performance evaluation

Decoding color codes by projection onto surface codes

Abstract: We propose a general strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. Applying this idea to a family of hexagonal color codes, with the perfect matching decoding algorithm for the three corresponding surface codes, we find a phase error threshold of approximately $8.7%$. Finally, our approach enables us to establish a general lower bound on the error threshold of a family of color codes depending on the threshold of the three corresponding surface codes. These results are based on a chain complex interpretation of surface codes and color codes.

On the Optimal Compressions in the Compress-and-Forward Relay Schemes

Abstract: In the classical compress-and-forward relay scheme developed by Cover and El Gamal, the decoding process operates in a successive way: the destination first decodes the compression of the relay's observation and then decodes the original message of the source. Recently, several modified compress-and-forward relay schemes were proposed, where the destination jointly decodes the compression and the message, instead of successively. Such a modification on the decoding process was motivated by realizing that it is generally easier to decode the compression jointly with the original message, and more importantly, the original message can be decoded even without completely decoding the compression. Thus, joint decoding provides more freedom in choosing the compression at the relay. However, the question remains in these modified compress-and-forward relay schemes-whether this freedom of selecting the compression necessarily improves the achievable rate of the original message. It has been shown by El Gamal and Kim in 2010 that the answer is negative in the single-relay case. In this paper, it is further demonstrated that in the case of multiple relays, there is no improvement on the achievable rate by joint decoding either. More interestingly, it is discovered that any compressions not supporting successive decoding will actually lead to strictly lower achievable rates for the original message. Therefore, to maximize the achievable rate for the original message, the compressions should always be chosen to support successive decoding. Furthermore, it is shown that any compressions not completely decodable even with joint decoding will not provide any contribution to the decoding of the original message. The above phenomenon is also shown to exist under the repetitive encoding framework recently proposed by Lim , which improved the achievable rate in the case of multiple relays. Here, another interesting discovery is that the improvement is not a result of repetitive encoding, but the benefit of delayed decoding after all the blocks have been finished. The same rate is shown to be achievable with the simpler classical encoding process of Cover and El Gamal with a block-by-block backward decoding process.

Ecc polar coding and list decoding methods and codecs

Abstract: A method of decoding data encoded with a polar code and devices that encode data with a polar code. A received word of polar encoded data is decoded following several distinct decoding paths to generate a list of codeword candidates. The decoding paths are successively duplicated and selectively pruned to generate a list of potential decoding paths. A single decoding path among the list of potential decoding paths is selected as the output and a single candidate codeword is thereby identified. In another preferred embodiment, the polar encoded data includes redundancy values in its unfrozen bits. The redundancy values aid the selection of the single decoding path. A preferred device of the invention is a cellular network device, (e.g., a handset) that conducts decoding in accordance with the methods of the invention.

List Decoding of Error-Correcting Codes: Winning Thesis of the 2002 ACM Doctoral Dissertation Competition (Lecture Notes in Computer Science)

Abstract: 1 Introduction.- 1 Introduction.- 2 Preliminaries and Monograph Structure.- I Combinatorial Bounds.- 3 Johnson-Type Bounds and Applications to List Decoding.- 4 Limits to List Decodability.- 5 List Decodability Vs. Rate.- II Code Constructions and Algorithms.- 6 Reed-Solomon and Algebraic-Geometric Codes.- 7 A Unified Framework for List Decoding of Algebraic Codes.- 8 List Decoding of Concatenated Codes.- 9 New, Expander-Based List Decodable Codes.- 10 List Decoding from Erasures.- III Applications.- Interlude.- III Applications.- 11 Linear-Time Codes for Unique Decoding.- 12 Sample Applications Outside Coding Theory.- 13 Concluding Remarks.- A GMD Decoding of Concatenated Codes.