Low-Latency SISO via Message Passing on a Binary Tree

Calculating the \soft inverse" of a deterministic nite-state machine (FSM) via the SISO (soft-in/soft-out) module is a key operation in many data detection/decoding algorithms [1, 3]. Perhaps the most appreciated application is iterative decoding of concatenated codes. The standard SISO algorithm is the forward-backward algorithm (e.g., [1, 3]) which can be derived from the generalized distributive law (GDL) algorithm [2] in a linear-structure junction tree as shown in Fig. 1(a). Note that ak, sk, tk, and xk are input, state, transition, and output at time index k of the FSM where xk = Pk(sk; ak), sk+1 = Qk(sk; ak), and tk = (ak; sk; sk+1; xk). The components in the dashed block de ne the SISO module. The local kernels of the nodes ak and xk are the soft-input for each variable and the local kernel of the node tk is a local validity check for all variables of the node. The message passing schedule for this junction tree can be assigned by 3 familiar steps, i.e., forward recursion, backward recursion, and combining/completion. Note that the associated forward and backward recursion steps can be computed in parallel for all of the FSM states at a given time. This architecture provides O(N) latency and computational complexity, where N is the block size.