Low-Rate Repeat-Zigzag-Hadamard Codes

We propose a new class of low-rate error correction codes called repeat-zigzag-Hadamard (RZH) codes. RZH codes are serially concatenated turbo-like codes where the outer code is a repetition code and the inner code is a punctured zigzag-Hadaniard (ZH) code. We prove that RZH codes are good in the sense that for an RZH code ensemble, there exists a positive number 70 such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than 70, the average maximum-likelihood (ML) decoder block error probability approaches zero. EXIT charts are used to design irregular codes