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IEEE International Conference on Electronics, Circuits and Systems (ICECS)

A low-complexity soft-decision decoding architecture for the binary extended Golay code

Patrick Adde, Raphaël Le Bidan

Published Dec 1, 2012• 12 citations
Publisher

Abstract

The (24, 12, 8) extended binary Golay code is a well-known rate-1/2 short block-length linear error-correcting code with remarkable properties. This paper investigates the design of an efficient low-complexity soft-decision decoding architecture for this code. A dedicated algorithm is introduced that takes advantage of the code's properties to simplify the decoding process. Simulation results show that the proposed algorithm achieves close to maximum-likelihood performance with low computational cost. The decoder architecture is described, and VLSI synthesis results are presented.

DOI
10.1109/icecs.2012.6463628

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The (24, 12, 8) extended binary Golay code is a well-known rate-1/2 short block-length linear error-correcting code with remarkable properties. This paper investigates the design of an efficient low-complexity soft-decision decoding architecture for this code. A dedicated algorithm is introduced that takes advantage of the code's properties to simplify the decoding process. Simulation results show that the proposed algorithm achieves close to maximum-likelihood performance with low computational cost. The decoder architecture is described, and VLSI synthesis results are presented.
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.>
Maximum-likelihood soft-decision decoding of linear block codes is addressed. A binary multiple-check generalization of the Wagner rule is presented, and two methods for its implementation, one of which resembles the suboptimal Forney-Chase algorithms, are described. Besides efficient soft decoding of small codes, the generalized rule enables utilization of subspaces of a wide variety, thereby yielding maximum-likelihood decoders with substantially reduced computational complexity for some larger binary codes. More sophisticated choice and exploitation of the structure of both a subspace and the coset representatives are demonstrated for the (24, 12) Golay code, yielding a computational gain factor of about 2 with respect to previous methods. A ternary single-check version of the Wagner rule is applied for efficient soft decoding of the (12, 6) ternary Golay code.>
In this paper,the ChaseⅡ algorithm,which is well known as a reliability-based decoding algorithm,is used for the soft decoding of the(23,12,7)Golay code.This soft-decision decoding algorithm improves greatly the error-correcting capacity compared with algebraic hard-decision decoding algorithms,but also results in more computational complexity.To overcome this,a optimality condition is introduced to quickly terminate the ChaseⅡ decoding process.Computer simulation results got by VC6.0 show that soft decoding obtains 1.7 dB coding gain compared with hard decoding case at BER of 10-5,and the modified chase-II algorithm based on the optimality condition reduces the total simulation time by 87.64%,and thus improves greatly the decoding efficiency.
The authors present a novel and efficient maximum-likelihood soft-decision decoding algorithm for linear block codes. The approach used here converts the decoding problem into a search problem through a graph that is a trellis for an equivalent code of the transmitted code. A generalized Dijkstra's algorithm, which uses a priority-first search strategy, is employed to search through this graph. This search is guided by an evaluation function f defined to take advantage of the information provided by the received vector and the inherent properties of the transmitted code. This function f is used to reduce drastically the search space and to make the decoding efforts of this decoding algorithm adaptable to the noise level. For example, for most real channels of the 35 000 samples tried, simulation results for the (128,64) binary extended BCH code show that the proposed decoding algorithm is fifteen orders of magnitude more efficient in time and in space than that proposed by Wolf (1978). Simulation results for the (104, 52) binary extended quadratic residue code are also given.>
We show that the binary Golay code is slightly more power efficient than the extended binary Golay code under maximum-likelihood (ML), hard-decision decoding. In fact, if a codeword from the extended code is transmitted, one cannot achieve a higher probability of correct decoding than by simply ignoring the 24th symbol and using an ML decoder for the non-extended code on the first 23 symbols. This is so, despite the fact that using that last symbol would allow one to sometimes correct error patterns with weight four. To our knowledge the worse performance of the extended Golay code has not been previously noted, but it is noteworthy considering that it is the extended version of the code that has been preferred in many deployments.