List decoding

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

Linear unequal error protection codes

Abstract: The properties of linear codes over GF (q) that provide unequal error protection (UEP) of information digits are discussed. A design is proposed for optimal binary systematic linear UEP codes. Broad classes of iterative and concatenated UEP codes are constructed. Majority decoding algorithms for linear iterative UEP codes are described.

Coding for noisy channels with input-dependent insertions

Abstract: Tree encoding and sequential decoding are considered for noisy channels that respond a random number of times to each input. Such channels appear in mathematical models of certain speech recognition systems. The decoding error probability and the channel capacity are bounded by extension of the methods of Jelinek and Zigangirov to noisy multilevel channels with input-dependent insertions. Certain analytical difficulties peculiar to the channels in question are indicated.

Iterative decoding of one-step majority logic deductible codes based on belief propagation

Abstract: Previously, the belief propagation (BP) algorithm has received a lot of attention in the coding community, mostly due to its near-optimum decoding for low-density parity check (LDPC) codes and its connection to turbo decoding. In this paper, we investigate the performance achieved by the BP algorithm for decoding one-step majority logic decodable (OSMLD) codes. The BP algorithm is expressed in terms of likelihood ratios rather than probabilities, as conventionally presented. The proposed algorithm fits better the decoding of OSMLD codes with respect to its numerical stability due to the fact that the weights of their check sums are often much higher than that of the corresponding LDPC codes. Although it has been believed that OSMLD codes are far inferior to LDPC codes, we show that for medium code lengths (say between 200-1000 bits), the BP decoding of OSMLD codes can significantly outperform BP decoding of their equivalent LDPC codes. The reasons for this behavior are elaborated.

Information-set decoding for linear codes over F q

Abstract: The best known non-structural attacks against code-based cryptosystems are based on information-set decoding Stern's algorithm and its improvements are well optimized and the complexity is reasonably well understood However, these algorithms only handle codes over F2 This paper presents a generalization of Stern's information-set- decoding algorithm for decoding linear codes over arbitrary finite fields Fq and analyzes the complexity This result makes it possible to compute the security of recently proposed code-based systems over non-binary fields As an illustration, ranges of parameters for generalized McEliece cryptosystems using classical Goppa codes over F31 are suggested for which the new information-set-decoding algorithm needs 2128 bit operations

Application of probabilistic decoding to digital magnetic recording systems

Abstract: A digital magnetic recording system is viewed in this paper as a linear system that inherently includes a correlative level encoder. This encoder can be regarded aas linear finite-state machine like a convolutional encoder. The maximum likelihood decoding method recently devised by Viterbi to decode convolutional codes is then applietdo digital magnetic recording systems. The decoding algorithm and its implementation are discussed in detail. Expressions for the decoding error probability are obtained and confirmed by computer simulations. It is shown that a significant improvement in the performance with respect to other methods is achievable by the maximum likelihood decoding method. For example, under the Gaussian noise assumption the proposed technique can reduce raw error ratehse in 10-3 to 10-4 range by a factor of 50 to 300. These results indicate that the maximum likelihood decoding method gains as much as 2.5 dB in signal-to-noise ratio over the conventional bit-by-bit detection method.