A comparison between the sum-product and the min-sum iterative detection algorithms based on density evolution

Abstract

Recently, density evolution techniques have been used to predict the performance of iterative decoders utilizing the sum-product belief propagation algorithm. In this paper, we extend this analysis to the minsum algorithm for binary codes. Using two representative applications, i.e., low-density parity-check (LDPC) codes and repeat accumulate (RA) codes, the sum-product and min-sum algorithms are compared. The results demonstrate a performance degradation of 0.27 -1.03 dB for the min-sum algorithm, which confirms earlier simulation results. However, it is shown in this paper, that a small modification to the min-sum algorithm results in an approximate sum-product algorithm, which performs at least as well as the original sum-product algorithm, when finite message precision is considered.

Degree-Matched Check Node Decoding for Regular and Irregular LDPCs

“…Such a correction factor has been determined for a degree 3 check node [9]. For incoming LLRs λ A and λ B , the outgoing extrinsic LLR L C may be expressed directly as the min-sum approximation plus a correction factor as [10], [11] …”

“…using the form of [11]. Good performance was obtained using c = 0.5 [10], implemented recently in [12].…”

Self-adjustable offset min-sum algorithm for ISDB-S2 LDPC decoder

“…(3), the primitive form of Eq. (4), can be expanded using Jacobian logarithm (ln(e a + e b ) = max(a, b) + ln(1 + e −|a−b| )) twice as follows [5]:…”

“…Min-sum (MS) algorithm approximates BP algorithm with easy hardware implementation but greatly degrades the BER performance. Recently, two categories of schemes have been proposed to trade off between BER performance and hardware complexity: MS-based algorithms [2,3,4] and BP-based algorithms [5,6]. Generally, BPbased algorithms outperform MS-based ones in BER performance with larger hardware cost.…”

Fully Parallel Stochastic LDPC Decoders

“…Using the log-domain conversion, VNs calculate the summation of LLR messages and PNs employ processing to compute their outgoing messages [42]. In MSA, the processing in PNs is approximated to reduce the complexity at the expense of about 0.5 to 1 dB performance loss, compared to the SPA [43], [44]. To compensate for some of the loss, different improved methods are suggested in the literature (e.g., see [45]).…”