高次元パリティ符号の軟判定復号と LDPC 符号との関係

Kenta Kasai

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??? ??????????????? ???????????? ???????????? ????????? LDPC ?????? ?????? ????????? ????????????. ?????? ?????? ?????? ?????? ???????????? ???????????? ???????????? ????????? ?????? ???????????? ???????????? ????????? ?????? ?????? LDPC ?????? ????????? ????????????. ????????? LDPC ????????? ???????????? Tanner ???????????? ????????? ?????? ????????? ????????? LDPC ???????????? ???????????? ????????? ????????? ?????? ?????? ?????? ????????? ????????????. ?????? ?????????????????? ???????????? ???????????? ????????? LDPC ?????? ?????? ????????? ????????? ???????????? ??? ?????? ?????? ?????? ?????? ????????? ???????????????. ???????????? LDPC ????????? ????????? ???????????? ???-????????? ??? ???-?????? ??? ?????? ??? ?????? ?????? ??????????????? ????????? ????????? ?????? ?????? ??? ?????? ????????? ????????? ????????? ??? ?????????.

章範 大橋, 知明 大槻

Chi Ho Chan, Francis C. M. Lau

Recently, there have been different applications, namely 10GBase-T Ethernet, video broadcasting and satellite communication, utilizing low-density parity-check (LDPC) codes as the forward-error-correction codes. The main reason is that the error performance of LDPC codes can be very close to the Shannon limit. LDPC codes can be further categorized into LDPC block codes (LDPC-BCs) and LDPC convolutional codes (LDPC-CCs). It has also been discovered that LDPC-CCs usually outperform LDPC-BCs. Simulation of LDPC-BCs and LDPC-CCs can take a lot of time because the decoding algorithms are relatively complex. Fortunately, the decoding steps can be performed in parallel. In this paper, we create three different platforms for simulating the error performance of LDPC-CCs. The first two platforms are run on a Central Processing Unit (CPU) while the third one involves the use of a Graphics Processing Unit (GPU). We show that using GPU can improve the simulation speed substantially.

雅一 吉田, 学 萩原, 隆之 宮寺 +1 more

R. Sobhani

In this study, using Group Permutation Low‐Density Parity‐Check (GP‐LDPC) codes, the authors generalise the concept of array Low‐Density Parity‐Check (LDPC) codes from fields of prime order to those of prime power order. In fact, they consider the additive group of the finite field GF( q ), q a prime power, as the underlying group for the GP‐LDPC code construction and since when q is a prime, the author's code construction method coincides with that of quasi‐cyclic array LDPC codes, they call their codes, generalised array LDPC (GA‐LDPC) codes. First, they prove that, like array LDPC codes, GA‐LDPC codes are quasi‐cyclic codes. Then, they analyse the girth of GA‐LDPC codes in a way similar to that for array LDPC codes and introduce some shortened GA‐LDPC codes with girths 8, 10 and 12. For many values of g , J and L , the lengths of ( J , L )‐regular shortened GA‐LDPC codes of girth g and rate at least 1 − J / L , constructed in this study, are smaller than the lengths of ( J , L )‐regular LDPC codes of girth g and rate at least 1 − J / L , constructed in the literature. Also, simulation results show that GA‐LDPC codes perform well with the iterative message‐passing decoding.