Reduced Complexity of a Successive Cancellation Based Decoder for NB-Polar Codes

Abstract

This paper proposes a simplified version of the Successive Cancellation (SC) decoder for Non-Binary Polar (NB-Polar) codes. The proposed decoder, named Successive Cancellation Min-Sum (SC-MS), is exclusively formulated in the Log-Likelihood Ratio (LLR) domain to reduce the decoding complexity of the SC decoder. The NB-Polar codes are associated with Cyclic Code-Shift Keying (CCSK) modulation to obtain a new coded modulation scheme for ultra-low signal-to-noise ratios (SNRs). The quantized version of the SC-MS decoder is investigated using quantized LLRs on optimized size of bits. Our simulation results show that the SC-MS decoder presents a negligible performance degradation with respect to the SC decoder for code length N < 2048. Additionally, the 2-bit SC-MS and 3-bit SC-MS offer a good trade-off between decoding performance and complexity.

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

“…. The truncation of both CN inputs down to n m reduces the entire computation from q 2 operations performed in Min-Sum SC (SC-MS) decoder expressed in (7) down to n 2 m where n m ≪ q.…”

“…In the SC-MS decoder, the size of the input messages is q elements. Therefore, the CN unit processes the q 2 elements of the two inputs to obtain the most reliable LLRs for the q symbols (as depicted in (7)). For the SC-EMS-based decoder, the size of the input messages is reduced down to n m and the CN operations (13) are reduced from q 2 down to n m √ n m when the bubble check is used as in [12].…”

“…The proposed decoder is simulated over a BI-AWGN channel with CCSK modulation and a sequence of size q = 64 chips. The coefficient γ is set to 1 for all codes based on the results provided in [7], and the frozen positions are obtained by analyzing the error rate at each position i = 0 • • • N − 1 using a genie-aided decoder [3]. The decoder has the following parameters for GF (64), n H = 8, n L = 20, and z = 2, fixed overall codes over GF (64).…”

“…Therefore, different contributions were proposed to reduce the complexity of the NB-Polar codes. In [5], the authors propose a low-complexity Successive Cancellation (SC) decoder based on the Min-Sum (MS) algorithm, which is derived from the original SC algorithm [3], but defined in the Log-Likelihood Ratio (LLR) domain. Processing the LLR messages in the logarithmic domain allows replacing all the multiplication operations with only additions; hence, no multipliers are required.…”

“…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.…”