Sequential decoding

About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.

Finding smooth integers in short intervals using CRT decoding

Abstract: We present a new algorithm for CRT list decoding. An instance of the, CRT list decoding problem consists of integers B, 〈p1, ..., pn〉 and 〈r1, ..., rn〉, where p1 n/3. The bounds we obtain are similar to the bounds obtained by Guruswami and Sudan for Reed-Solomon list decoding. Hence, our algorithm reduces the gap between CRT list decoding and list decoding of Reed-Solomon codes. In addition, we give a new application for CRT list decoding: finding smooth integers in short intervals. Problems of this type come up in several algorithms for factoring large integers. We define and solve a generalized CRT list decoding problem and discuss how it might be used within the quadratic sieve factoring method.

Block Markov Superposition Transmission: Construction of Big Convolutional Codes From Short Codes

Abstract: A construction of big convolutional codes from short codes called block Markov superposition transmission (BMST) is proposed. The BMST is very similar to superposition block Markov encoding (SBME), which has been widely used to prove multiuser coding theorems. The BMST codes can also be viewed as a class of spatially coupled codes, where the generator matrices of the involved short codes (referred to as basic codes) are coupled. The encoding process of BMST can be as fast as that of the basic code, while the decoding process can be implemented as an iterative sliding-window decoding algorithm with a tunable delay. More importantly, the performance of BMST can be simply lower bounded in terms of the transmission memory given that the performance of the short code is available. Numerical results show that: 1) the lower bounds can be matched with a moderate decoding delay in the low bit-error-rate (BER) region, implying that the iterative sliding-window decoding algorithm is near optimal; 2) BMST with repetition codes and single parity-check codes can approach the Shannon limit within 0.5 dB at the BER of $10^{-5}$ for a wide range of code rates; and 3) BMST can also be applied to nonlinear codes.

Convolutional codes III. Sequential decoding

Abstract: Sequential decoding is characterized as a sequential search for the shortest path through a trellis. An easily analyzed algorithm closely related to the stack and Fano algorithms is described. Martingale techniques are used to find the distribution of computation on totally symmetric channels. For general channels, our universal bounding technique yields the well-known Pareto distribution of computation, as well as a bound on error probability that is asymptotically optimum in the high-rate range. The performance-complexity relation is shown to be asymptotically Pareto for both sequential and maximum-likelihood (Viterbi) decoding, with the same exponent in either case. A semisequential list-of-L Viterbi algorithm is introduced to extend the analogies below Rcomp.

Methodologies for designing LDPC codes using protographs and circulants

Abstract: A method is presented for constructing LDPC codes with excellent performance, simple hardware implementation, low encoder complexity, and which can be concisely documented. The simple code structure is achieved by using a base graph, expanded with circulants. The base graph is chosen by computer search using simulated annealing, driven by density evolution's decoding threshold as determined by the reciprocal channel approximation. To build a full parity check matrix, each edge of the base graph is replaced by a circulant permutation, chosen to maximize loop length by using a Viterbi-like algorithm.