On the distance distribution of duals of BCH codes

We derive upper bounds on the components of the distance distribution of duals of BCH codes. Roughly speaking, these bounds show that the distance distribution can be upper-bounded by the corresponding normal distribution. To derive the bounds we use the linear programming approach along with some estimates on the magnitude of Krawtchouk polynomials of fixed degree in a vicinity of q/

Partitioned Successive-Cancellation List Decoding of Polar Codes

Successive-cancellation list (SCL) decoding is an algorithm that provides very good error-correction performance for polar codes. However, its hardware implementation requires a large amount of memory, mainly to store intermediate results. In this paper, a partitioned SCL algorithm is proposed to reduce the large memory requirements of the conventional SCL algorithm. The decoder tree is broken into partitions that are decoded separately. We show that with careful selection of list sizes and number of partitions, the proposed algorithm can outperform conventional SCL while requiring less memory.Comment: 4 pages, 6 figures, to appear at IEEE ICASSP 201

Code Construction and Decoding Algorithms for Semi-Quantitative Group Testing with Nonuniform Thresholds

We analyze a new group testing scheme, termed semi-quantitative group testing, which may be viewed as a concatenation of an adder channel and a discrete quantizer. Our focus is on non-uniform quantizers with arbitrary thresholds. For the most general semi-quantitative group testing model, we define three new families of sequences capturing the constraints on the code design imposed by the choice of the thresholds. The sequences represent extensions and generalizations of Bh and certain types of super-increasing and lexicographically ordered sequences, and they lead to code structures amenable for efficient recursive decoding. We describe the decoding methods and provide an accompanying computational complexity and performance analysis

On joint detection and decoding of linear block codes on Gaussian vector channels

Optimal receivers recovering signals transmitted across noisy communication channels employ a maximum-likelihood (ML) criterion to minimize the probability of error. The problem of finding the most likely transmitted symbol is often equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In systems that employ error-correcting coding for data protection, the symbol space forms a sparse lattice, where the sparsity structure is determined by the code. In such systems, ML data recovery may be geometrically interpreted as a search for the closest point in the sparse lattice. In this paper, motivated by the idea of the "sphere decoding" algorithm of Fincke and Pohst, we propose an algorithm that finds the closest point in the sparse lattice to the given vector. This given vector is not arbitrary, but rather is an unknown sparse lattice point that has been perturbed by an additive noise vector whose statistical properties are known. The complexity of the proposed algorithm is thus a random variable. We study its expected value, averaged over the noise and over the lattice. For binary linear block codes, we find the expected complexity in closed form. Simulation results indicate significant performance gains over systems employing separate detection and decoding, yet are obtained at a complexity that is practically feasible over a wide range of system parameters