Sequential decoding

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

Even more efficient soft decoding of the Golay Codes

Abstract: An algorithm for maximum-likelihood soft-decision decoding of the binary (24,12,8) Golay code is presented. The algorithm involves projecting the codewords of the binary Golay code onto the codewords of the (6,3,4) code over GF(4)-the hexacode. The complexity of the proposed algorithm is at most 651 real operations. Along similar lines, the tetracode may be employed for decoding the ternary (12,6,6) Golay code with only 530 real operations. The proposed algorithm also implies a reduction in the number of computations required for decoding the Leech lattice. >

Iterative decoder architectures

Abstract: Implementation constraints on iterative decoders applying message-passing algorithms are investigated. Serial implementations similar to traditional microprocessor datapaths are compared against architectures with multiple processing elements that exploit the inherent parallelism in the decoding algorithm. Turbo codes and low-density parity check codes, in particular, are evaluated in terms of their suitability for VLSI implementation in addition to their bit error rate performance as a function of signal-to-noise ratio. It is necessary to consider efficient realizations of iterative decoders when area, power, and throughput of the decoding implementation are constrained by practical design issues of communications receivers.

Error-locating pairs for cyclic codes

Abstract: A general decoding method for linear codes is investigated for cyclic codes. The decoding consists of solving two systems of linear equations. All but four binary cyclic codes of length less than 63 can so be decoded up to their actual distance. A new family of codes is given for which the decoding needs only O(n/sup 2/) operations. >

Soft source decoding with applications

Abstract: Motivated by previous results in joint source-channel coding and decoding, we consider the problem of decoding of variable-length codes using soft channel values. We present results of decoding of selected codes using the maximum a posteriori (MAP) decoder and the sequential decoder, and show the performance gains over decoding using hard decisions alone. The objective behind this work is to provide motivation for decoding of data compressed by standard source coding schemes, that is, to view the compressed bitstreams as being the output of variable-length coders and to make use of the redundancy in the bitstreams to assist in decoding. In order to illustrate the performance achievable by soft decoding, we provide results for decoding of MPEG-4 reversible variable-length codes as well as for decoding of MPEG-4 overhead information, under the assumption that this information is transmitted without channel coding over an additive white Gaussian noise channel. Finally, we present a method of unequal error protection for an MPEG-4 bitstream using the MAP and sequential source decoders, and show results comparable to those achievable by serial application of source and channel coding.

Algebraic Soft-Decision Decoding of Reed–Solomon Codes Using Bit-Level Soft Information

Abstract: The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies for algebraic soft-decision decoding (SDD) with infinite cost are first studied over erasure channels and the binary-symmetric channel. The corresponding decoding radii are calculated in closed forms and tight bounds on the error probability are derived. The multiplicity assignment strategy and the corresponding performance analysis are then generalized to characterize the decoding region of algebraic SDD over a mixed error and bit-level erasure channel. The bit-level decoding region of the proposed multiplicity assignment strategy is shown to be significantly larger than that of conventional Berlekamp-Massey decoding. As an application, a bit-level generalized minimum distance decoding algorithm is proposed. The proposed decoding compares favorably with many other Reed-Solomon SDD algorithms over various channels. Moreover, owing to the simplicity of the proposed bit-level generalized minimum distance decoding, its performance can be tightly bounded using order statistics.