Nonbinary polar coding with low decoding latency and complexity

Asymmetrical Extended Min-Sum for Successive Cancellation Decoding of Non-Binary Polar Codes

“…The complexity of the CN update in the SC decoder can be reduced by reducing the computation performed to estimate the reliability of the symbols u (l) θ ∈ GF (q). Similar to Non-Binary Low-Density Parity Check (NB-LDPC) codes, the EMS [10] can be used to reduce the number of computations performed as in [6]. This algorithm, named SC-EMS, consists of selecting the most n m competitive elements in the input vectors L ), where η (l−1) j corresponds to the j th most reliable GF symbol in L…”

“…In addition, the authors proposed a simplified MS algorithm based on truncating one of the two inputs of the nodes from q down to n 0 with 0 < n 0 ≪ q which allows for reducing the complexity from order O(q 2 ) down to the order of O(q × n 0 ) for a kernel of order 2. In addition, a recent contribution [6] allowed further reduction in the check node processing by using the Extended Min-Sum (EMS) algorithm, which reduces the complexity of the check node down to an order of O(n 2 m ) with n m ≪ q. Moreover, in [7], the authors proved that using CCSK modulation allows for setting all kernel coefficients to 1 without performance degradation and hence, reduces both the encoding and the decoding processes.…”