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Sequential decoding
About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.
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TL;DR: Consider the case where an n -digit block encoded word cannot be decoded reliably and a second block of n redundant digits is sent to allow the receiver to make a new try based on the combined information received.
Abstract: Consider the case where an n -digit block encoded word cannot be decoded reliably and a second block of n redundant digits is sent to allow the receiver to make a new try based on the combined information received. Two classes of schemes are proposed and analyzed which give significantly better performance than is obtained by sending a repeat of the first block, yet do not require excessive decoding complexity. One approach is to consider small sub-blocks of the original n -digit code as the data digits of a short rate one-half code. The other approach is to treat the first sending as the data digits of a systematic convolutional code of short constraint length. Comparisons are made for the white Gaussian noise channel and the erasure channel. The comparisons are limited to an assessment of the improvement gained after two sendings. Procedures using length 4 sub-blocks and using convolutional codes with constraint lengths as short as 2 or 3 digits yield considerable improvement over block retransmission. For the case of the erasure channel, a very simple decoding rule is devised for the convolutional code case.
87 citations
01 Dec 2013
TL;DR: Analysis and simulation of the iterative HDD of tightly-braided block codes with BCH component codes for high-speed optical communication shows that these codes are competitive with the best schemes based on HDD.
Abstract: Designing error-correcting codes for optical communication is challenging mainly because of the high data rates (e.g., 100 Gbps) required and the expectation of low latency, low overhead (e.g., 7% redundancy), and large coding gain (e.g., >9dB). Although soft-decision decoding (SDD) of low-density parity-check (LDPC) codes is an active area of research, the mainstay of optical transport systems is still the iterative hard-decision decoding (HDD) of generalized product codes with algebraic syndrome decoding of the component codes. This is because iterative HDD allows many simplifications and SDD of LDPC codes results in much higher implementation complexity. In this paper, we use analysis and simulation to evaluate tightly-braided block codes with BCH component codes for high-speed optical communication. Simulation of the iterative HDD shows that these codes are competitive with the best schemes based on HDD. Finally, we suggest a specific design that is compatible with the G.709 framing structure and exhibits a coding gain of >9.35 dB at 7% redundancy under iterative HDD with a latency of approximately 1 million bits.
86 citations
27 Jun 2004
TL;DR: A new modified Berlekamp-Massey algorithm for correcting rank errors and column erasures is described, which is about half as complex as the known algorithms.
Abstract: This paper describes the decoding of Rank-Codes with different decoding algorithms. A new modified Berlekamp-Massey algorithm for correcting rank errors and column erasures is described. These algorithms consist of two decoding steps. The first step is the puncturing of the code and the decoding in the punctured code. The second step is the column erasure decoding in the original code. Thus decoding step is about half as complex as the known algorithms
86 citations
08 Jun 2011
TL;DR: This work highlights that constructing an explicit subspaceevasive subset that has small intersection with low-dimensional subspaces -- an interesting problem in pseudorandomness in its own right -- could lead to explicit codes with better list decoding guarantees.
Abstract: Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any " > 0, the author and Rudra (2006, 08) presented an nO(1=") time algorithm to list decode appropriate folded RS codes of rate R from a fraction 1--R--e" of errors. The algorithm is based on multivariate polynomial interpolation and root-finding over extension fields. It was noted by Vadhan that interpolating a linear polynomial suffices if one settles for a smaller decoding radius (but still enough for a statement of the above form). Here we give a simple linear-algebra based analysis of this variant that eliminates the need for the computationally expensive rootfinding step over extension fields (and indeed any mention of extension fields). The entire list decoding algorithm is linearalgebraic, solving one linear system for the interpolation step, and another linear system to find a small subspace of candidate solutions. Except for the step of pruning this subspace, the algorithm can be implemented to run in quadratic time. The theoretical drawback of folded RS codes are that both the decoding complexity and proven worst-case list-size bound are n (1="). By combining the above idea with a pseudorandom subset of all polynomials as messages, we get a Monte Carlo construction achieving a list size bound of O(1="2) which is quite close to the existential O(1=") bound (however, the decoding complexity remains n (1=")).Our work highlights that constructing an explicit subspaceevasive subset that has small intersection with low-dimensional subspaces -- an interesting problem in pseudorandomness in its own right -- could lead to explicit codes with better listdecoding guarantees.
86 citations
17 Nov 2002
TL;DR: This work proposes that half symbols in a quasi-orthogonal space-time block codes with full diversity are from a signal constellation A and another half are optimal selections from the rotated constellation e/sup j/spl phi///spl Ascr/.
Abstract: Space-time block codes from orthogonal designs proposed by Alamouti (1998), and Tarokh-Jafarkhani-Calderbank (199) have attracted much attention lately due to their fast maximum-likelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of a space-time block code from complex orthogonal designs for complex constellations is only 3/4 for three and four transmit antennas. Jafarkhani (see IEEE Trans. Commun., vol.49, no.1, p.1-4, 2001), and Tirkkonen-Boariu-Hottinen (see ISSSTA 2000, pp.429-432, September 2000) proposed space-time block codes from quasi-orthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasi-orthogonal structure, these codes still have a fast ML decoding, but do not have the full diversity. In this paper, we design quasi-orthogonal space-time block codes with full diversity by properly choosing the signal constellations. In particular, we propose that half symbols in a quasi-orthogonal design are from a signal constellation A and another half of them are optimal selections from the rotated constellation e/sup j/spl phi// A. The optimal rotation angles /spl phi/ are obtained for some commonly used signal constellations. The resulting codes have both full diversity and fast ML decoding.
86 citations