Turbo Code

Telecommunications Engineering

How It Works

Turbo codes are high-performance forward error correction codes that approach the theoretical Shannon channel capacity limit within a fraction of a decibel. Built from two parallel concatenated recursive systematic convolutional (RSC) encoders linked by a pseudo-random interleaver, turbo decoding utilizes two soft-input soft-output (SISO) decoders that iteratively exchange extrinsic log-likelihood ratios (LLRs), progressively refining bit decisions.

Governing Equation
L(u_k) = L_{sys}(u_k) + L_{apr}(u_k) + L_{ext}(u_k)   |   L_{ext}^((1 → 2)) ⇌ L_{ext}^((2 → 1))   |   BER → 0