Analysis, Design, and Iterative Decoding of Double Serially Concatenated Codes with Interleavers

A double serially concatenated code with two interleaves consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits and an inner encoder whose input words are the permuted middle codewords. The construction can be generalized to h cascaded encoders separated by h – 1 interleavers, where h >3. We obtain upper bounds to the average maximum-likelihood bit error probability of double serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer, middle, and inner codes that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a low-complexity iterative decoding algorithm. Comparisons with parallel concatenated convolutional codes, known as “turbo codes”, and with the recently prop-d serially concatenated convolutional codes are also presented, showing that in some cases the new schemes offer better performance. I. ACRONYMS APP A-Posteriori Probability. BCJR Bahl, Cocke, Jelinek, Raviv. CC Constituent Code. CWEF Conditional Weight Enumerating Function. DPCCC Double Parallel Concatenated Convolutional Code. DSCC Double Serially Concatenated Code. DSCBC Double Serially Concatenated Block Code. DSCCC Double Serially Concatenated Convolutional Code. IOWEF Input Output Weight Enumerating Function. LPDF Logarithm of the Probability Density Function. ML Maximum Likelihood. MPCCC Multiple Parallel Concatenated Convolutional Code. SCC Serially Concatenated Code. ‘ SCBC Serially Concatenated Block Code. SCCC Serially Concatenated Convolutional Code. PCC Parallel Concatenated Code. PCCC Parallel Concatenated Convolutional Code. I