Recently, Ericson and Zinoviev presented a clever, new construction for spherical codes for the Gaussian channel using ideas of code concatenation and set partitioning. This family of new spherical codes is generated from sets of binary codes using equally spaced symmetric pointsets on the real line. The family contains some of the best known spherical codes in terms of minimum distance. Howeve...

It is shown that soft decision maximum likelihood decoding of any (n,k) linear block code over GF(q) can be accomplished using the Viterbi algorithm applied to a trellis with no more than q (n-k) states. For cyclic codes, the trellis is periodic. When this technique is applied to the decoding of product codes, the number of states in the trellis can be much fewer than q n-k. For a binary (n,rz ...

Understanding how stimulus information is encoded in spike trains is a central problem in computational neuroscience. Decoding methods provide an important tool for addressing this problem, by allowing us to explicitly read out the information contained in spike responses. Here we introduce several decoding methods based on point-process neural encoding models (i.e. “forward” models that predic...

The word error probability of binary linear block codes is evaluated in Rayleigh fading channels with diversity reception far three decoding algorithms: error correction (EC), errorlerasure correction (EEC). and maximum likelihood (MLI soft decoding algorithms. The performance advantage of EEC over EC In the required average SNR decreases as the number of ditersity channels increases. The perfo...

We investigate threshold–based multi–trial decoding of concatenated codes with an inner Maximum–Likelihood decoder and an outer error/erasure l+1 l –extended Bounded Distance decoder, i.e. a decoder which corrects ε errors and τ erasures if l+1 l ε+τ ≤ d−1, where d is the minimum distance of the outer code and l ∈ N\{0}. This is a generalization of Forney’s GMD decoding, which was considered on...

In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagatio...

Aiming at bridging the gap between the maximum likelihood decoding (MLD) and the suboptimal iterative decodings for short or medium length LDPC codes, we present a generalized ordered statistic decoding (OSD) in the form of syndrome decoding, to cascade with the belief propagation (BP) or enhanced min-sum decoding. The OSD is invoked only when the decoding failures are obtained for the preceded...

AbstTactwe present algorithms for maximum likelihood soft decoding of the second order Reed-Muller codes RM(2,m) and the extended (24,12,8) Golay code. The decoding procedures are based on a concise representation of appropriately selected cosets of a subcode of the code considered. Such representation enables application of certain elimination rules. A structure, called constrained design, is ...

We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3, 4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of...

Abstmct Two soft-decision algorithms f o r decoding the (6,3,4) q u a t e r n a r y code, the hezocode, are p resented. Both algorithms have the same guaranteed error cor rec t ion radius as that of maximum-likelihood decoding. In using them, bounded-distance decoding of the Golay code and the Leech lattice are performed i n at most 187 and 519 real operations respectively. We present s o m e s...