List decoding

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

List Decoding of Error-Correcting Codes

Abstract: Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental algorithmic challenge in coding theory and practice is to efficiently decode the original transmitted message even when a few symbols of the received word are in error. The naive search algorithm runs in exponential time, and several classical polynomial time decoding algorithms are known for specific code families. Traditionally, however, these algorithms have been constrained to output a unique codeword. Thus they faced a “combinatorial barrier” and could only correct up to d/2 errors, where d is the minimum distance of the code. An alternate notion of decoding called list decoding, proposed independently by Elias and Wozencraft in the late 50s, allows the decoder to output a list of all codewords that differ from the received word in a certain number of positions. Even when constrained to output a relatively small number of answers, list decoding permits recovery from errors well beyond the d/2 barrier, and opens up the possibility of meaningful error-correction from large amounts of noise. However, for nearly four decades after its conception, this potential: of list decoding was largely untapped due to the lack of efficient algorithms to list decode beyond d/2 errors for useful families of codes. This thesis presents a detailed investigation of list decoding, and proves its potential, feasibility, and importance as a combinatorial and algorithmic concept. We prove several; combinatorial results that sharpen our understanding of the potential and limits of list; decoding, and its relation to more classical parameters like the rate and minimum distance. The crux of the thesis is its algorithmic results, which were lacking in the early works on list decoding. Our algorithmic results include: (1) Efficient list decoding algorithms for classically studied codes such as Reed-Solomon codes and algebraic-geometric codes. In particular, building upon an earlier algorithm due to Sudan, we present the first polynomial time algorithm to decode Reed-Solomon codes beyond d/2 errors for every value of the rate. (2) A new soft list decoding algorithm for Reed-Solomon and algebraic-geometric codes and novel decoding algorithms for concatenated codes based on it. (3) New code constructions using concatenation and/or expander graphs that have good (and sometimes near-optimal) rate and are efficiently list decodable from extremely large amounts of noise. (4) Expander-based constructions of linear time encodable and decodable codes that ca4 correct up to the maximum possible fraction of errors, using unique (not list) decoding. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Iterative detection in code-division multiple-access with error control coding

Abstract: A code-division multiple-access system with channel coding may be viewed as a serially-concatenated coded system. In this paper we propose a low complexity method for decoding the resulting inner code (due to the spreading sequence), which allows iterative (turbo) decoding of the serially-concatenated code pair. The per-bit complexity of the proposed decoder increases only linearly with the number of users. Performance within a fraction of a dB of the single user bound for heavily loaded asynchronous CDMA is shown both by simulation and analytically.

Multilevel codes and multistage decoding

Abstract: H. Imai and S. Hirakawa have proposed (1977) a multilevel coding method based on binary block codes that admits a staged decoding procedure. The author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets. The multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels. It also allows the use of suboptimal multistage decoding procedures that have performance/complexity advantages over maximum-likelihood decoding. >

A new reduced-complexity sphere decoder for multiple antenna systems

Abstract: Sphere decoding for multiple antenna systems has been shown to achieve near-ML performance with low complexity. However, the achievement of such an excellent performance-complexity tradeoff is highly dependent on the initial choice of sphere radius. We present a new sphere decoding algorithm which is even less computationally complex than the original sphere decoder. Moreover, the complexity of the new sphere decoder is relatively insensitive to the initial choice of sphere radius. Thus, by making the choice of radius sufficiently large, the ML solution is guaranteed with low complexity, even for large constellations. In our simulations, we show that with 4 transmit and 4 receive antennas and 64-QAM, our new sphere decoding algorithm achieves the exact ML solution with approximately a factor of 3.5 reduction in complexity when compared to the original sphere decoder, and a factor of 10/sup 5/ reduction when compared to brute-force ML decoding.

On the Decoding Process in Ternary Error-Correcting Output Codes

Abstract: A common way to model multiclass classification problems is to design a set of binary classifiers and to combine them. Error-correcting output codes (ECOC) represent a successful framework to deal with these type of problems. Recent works in the ECOC framework showed significant performance improvements by means of new problem-dependent designs based on the ternary ECOC framework. The ternary framework contains a larger set of binary problems because of the use of a ldquodo not carerdquo symbol that allows us to ignore some classes by a given classifier. However, there are no proper studies that analyze the effect of the new symbol at the decoding step. In this paper, we present a taxonomy that embeds all binary and ternary ECOC decoding strategies into four groups. We show that the zero symbol introduces two kinds of biases that require redefinition of the decoding design. A new type of decoding measure is proposed, and two novel decoding strategies are defined. We evaluate the state-of-the-art coding and decoding strategies over a set of UCI machine learning repository data sets and into a real traffic sign categorization problem. The experimental results show that, following the new decoding strategies, the performance of the ECOC design is significantly improved.