System and methods for low complexity list decoding of turbo codes and convolutional codes

Abstract

Method for decoding signal includes receiving signal, where signal includes at least one symbol; decoding signal in stages, where each at least one symbol of signal is decoded into at least one bit per stage, wherein Log-Likelihood Ratio (LLR) for each at least one bit at each stage is determined, and identified in vector L; performing Cyclic Redundancy Check (CRC) on L, and stopping if Lpasses CRC; otherwise, determining magnitudes of LLRs in L; identifying K LLRs in Lwith smallest magnitudes and indexing K LLRs as r={r(1), r(2), . . . , r(K)}; setting Lto maximum magnitude of LLRs in Lor maximum possible LLR quantization value; setting v=1; generating {tilde over (L)}(r(k))=L(r(k))−Lvsign[L(r(k))], for k=1, 2, . . . , K; decoding with {tilde over (L)}to identify {tilde over (L)}, wherein {tilde over (L)}is LLR vector; and performing CRC on {tilde over (L)}, and stopping if {tilde over (L)}passes CRC or v=2; otherwise, incrementing v and returning to generating {tilde over (L)}(r(k)).