Recently, Hof et al. extended the type-2 Duman and Salehi (DS2) bound to generalized decoding, which was introduced by Forney, with decision criterion FR. From this bound, they derived two significant bounds. One is t...
详细信息
Recently, Hof et al. extended the type-2 Duman and Salehi (DS2) bound to generalized decoding, which was introduced by Forney, with decision criterion FR. From this bound, they derived two significant bounds. One is the Shulman-Feder bound for generalized decoding (GD) with the binary-input output-symmetric channel. The other is an upper bound for an ensemble of linear block codes, by applying the average complete weight distribution directly to the DS2 bound for GD. For the Shulman-Feder bound for GD, the authors derived a condition under which an upper bound is minimized at an intermediate step and show that this condition yields a new bound which is tighter than Hof et al.'s bound. In this paper, we first extend this result for non-binary linear block codes used over a class of symmetric channels called the regular channel. Next, we derive a new tighter bound for an ensemble of linear block codes, which is based on the average weight distribution.
We present a framework that can exploit the tradeoff between the undetected error rate (UER) and block error rate (BLER) of polar-like codes. It is compatible with all successive cancellation (SC)-based decoding metho...
详细信息
ISBN:
(纸本)9798350382853;9798350382846
We present a framework that can exploit the tradeoff between the undetected error rate (UER) and block error rate (BLER) of polar-like codes. It is compatible with all successive cancellation (SC)-based decoding methods and relies on a novel approximation that we call codebook probability. This approximation is based on an auxiliary distribution that mimics the dynamics of decoding algorithms following an SC decoding schedule. Simulation results demonstrates that, in the case of SC list (SCL) decoding, the proposed framework outperforms the state-of-art approximations from Forney's generalized decoding rule for polar-like codes with dynamic frozen bits. In addition, dynamic Reed-Muller (RM) codes using the proposed generalized decoding significantly outperform CRC-concatenated polar codes decoded using SCL in both BLER and UER.
We introduce an algorithm for approximating the codebook probability that is compatible with all successive cancellation (SC)-based decoding algorithms, including SC list (SCL) decoding. This approximation is based on...
详细信息
We introduce an algorithm for approximating the codebook probability that is compatible with all successive cancellation (SC)-based decoding algorithms, including SC list (SCL) decoding. This approximation is based on an auxiliary distribution that mimics the dynamics of decoding algorithms with an SC decoding schedule. Based on this codebook probability and SCL decoding, we introduce soft-output SCL (SO-SCL) to generate both blockwise and bitwise soft-output (SO). Using that blockwise SO, we first establish that, in terms of both block error rate (BLER) and undetected error rate (UER), SO-SCL decoding of dynamic Reed-Muller (RM) codes significantly outperforms the CRC-concatenated polar codes from 5G New Radio under SCL decoding. Moreover, using SO-SCL, the decoding misdetection rate (MDR) can be constrained to not exceed any predefined value, making it suitable for practical systems. Proposed bitwise SO can be readily generated from blockwise SO via a weighted sum of beliefs that includes a term where SO is weighted by the codebook probability, resulting in a soft-input soft-output (SISO) decoder. Simulation results for SO-SCL iterative decoding of product codes and generalized LDPC (GLDPC) codes, along with information-theoretical analysis, demonstrate significant superiority over existing list-max and list-sum approximations.
In decision feedback scheme, Forney's decision criterion (Forney's rule: FR) is optimal in the sense that the Neyman-Pearson's lemma is satisfied. Another prominent criterion called LR+Th was proposed by H...
详细信息
In decision feedback scheme, Forney's decision criterion (Forney's rule: FR) is optimal in the sense that the Neyman-Pearson's lemma is satisfied. Another prominent criterion called LR+Th was proposed by Hashimoto. Although LR+Th is suboptimal, its error exponent is shown to be asymptotically equivalent to that of FR by random coding arguments. In this paper, applying the technique of the DS2 bound, we derive an upper bound for the error probability of LR+Th for the ensemble of linear block codes. Then we can observe the new bound from two significant points of view. First, since the DS2 type bound can be expressed by the average weight distribution whose code length is finite, we can compare the error probability of FR with that of LR+Th for the fixed-length code. Second, the new bound elucidates the relation between the random coding exponents of block codes and those of linear block codes.
暂无评论