Density Evolution Analysis of Partially Information Coupled Turbo Codes on the Erasure Channel

Abstract

In this paper, we investigate the performance of a class of spatially coupled codes, namely partially information coupled turbo codes (PIC-TCs) over the binary erasure channel (BEC). This class of codes enjoy flexible code rate adjustment by varying the coupling ratio. Moreover, the coupling method can be directly applied to any component codes without changing the encoding and decoding architectures of the underlying component codes. However, the theoretical performance of PIC-TCs has not been fully investigated. For this work, we consider the codes that have coupling memory m and study the corresponding graph model. We then derive the exact density evolution equations for these code ensembles with any given coupling ratio and coupling memory m to precisely compute their belief propagation decoding thresholds for the BEC. Our simulation results verify the correctness of our theoretical analysis and also show better error performance over uncoupled turbo codes with a variety of code rates on the BEC.

Generalized Spatially-Coupled Parallel Concatenated Codes With Partial Repetition

“…Both theoretical analysis and simulation results in [21], [24] showed that partiallycoupled turbo codes outperform SC-PCCs and have comparable performance to SC-SCCs and SC-BCCs. However, threshold saturation was neither observed nor proven for PIC-TCs in [18], [20], [21], [24].…”

“…Theorem 1. For the spatially-coupled system defined in (20) and any < c , where c is the potential threshold associated with the potential function in (14), the only fixed point of the recursion in ( 20) is x = 0 as L → ∞, m → ∞ and L m.…”

“…The main idea is that each pair of adjacent code blocks share a fraction of information bits such that these bits are protected by two component turbo codewords. We extended the design of PIC-TCs to a large coupling memory and used density evolution to compute their decoding thresholds in [20], [21]. One benefit of such construction is that the technique of partial coupling can be applied to any systematic linear code such as LDPC codes [22] and polar codes [23] without changing its encoding and decoding architecture.…”

Partially Information Coupled Duo-Binary Turbo Codes

“…Remark: We compare the construction of the PIC-dTCs with that of the PIC-TCs [9], [13]. For the PIC-TCs with TC1 as component code, the CB encoder only has one information sequence.…”

“…However, due to the coupling, (i.e., the same information sharing between CBs), PIC codes have significant rate loss compared to its component codes. For example, in [9], [13], with a rate- 1 3 turbo code as component code, the PIC-TC ensembles have a code rate of 1 5 when half of the information bits are coupled.…”