Decoding method for trellis codes with large free distances

A decoding method for a trellis code T of which the encoding can be implemented by first using an encoder of a binary trellis code C.sup.(1) to encode an r-bit message u(t) into an intermediate binary m-tuple v.sup.(l) (t) at a t-th time unit which is sequentially converted into binary m-tuples v.sup.(2) (t), . . . , v.sup.(L) (t) and a signal point v.sup.(L+1) (t) in a signal space .OMEGA. through L (L.gtoreq.2) processors, comprising the decoding steps of:

• (a) at a (t+.LAMBDA..sup.(l) + . . . +.LAMBDA..sup.(L))-th time unit, a processor P.sup.(L) determining a set T.sub.M.sup.(L) (t+.LAMBDA..sup.(l) + . . . +.LAMBDA..sup.(L-1)) which consists of 2.sup.m metrics for the 2.sup.m possible values of v.sup.(L) (t+.LAMBDA..sup.(1) + . . . +.LAMBDA..sup.(L-1)), based on part of the set {y(t+i):
• i.ltoreq..LAMBDA..sup.(1) + . . . +.LAMBDA..sup.(L) } and part of the set {v.sup.(L) (t-j):
• j.gtoreq..lambda.};
• feeding the metric set T.sub.M.sup.(L) (t+.LAMBDA..sup.(1) + . . . +.LAMBDA..sup.(L-1)) into a processor P.sup.(L-1) ;
• wherein y(t+i) is a received symbol to be decoded, .LAMBDA..sup.(1), . . . , .LAMBDA..sup.(L) are nonnegative constants and .lambda. is a truncation length to be used in decoding C.sup.(1) ;
• (b) for l=L-1, L-2, . . . ,1, a processor P.sup.(l) determining a set T.sub.M.sup.(l) (t+.LAMBDA..sup.(1) + . . . +.LAMBDA..sup.(l-1)) which consists of 2.sup.m metrics for the 2.sup.m possible values of v.sup.(l) (t+.LAMBDA..sup.(1) + . . . +.LAMBDA..sup.(l-1)) based on part of {T.sub.M.sup.(l+1) (t+i):
• i.ltoreq..LAMBDA..sup.(1) + . . . +.LAMBDA..sup.(l) } and part of the set {v.sup.(l) (t-j):
• j.gtoreq..lambda.};
• feeding the metric set T.sub.M.sup.(l) (t+.LAMBDA..sup.(1) + . . . +.LAMBDA..sup.(l-1)) into a processor P.sup.(l-1) ;
• wherein .LAMBDA..sup.(l) is a nonnegative constant;
• (c) a processor P.sup.(0) recovering the transmitted symbol u(t-.lambda.+1) and v.sup.(1) (t-.lambda.+1) by applying the Viterbi decoding algorithm to the trellis of C.sup.(1) and using part of the set {T.sub.M.sup.(1) (t-i):
• i.gtoreq.0};
• feeding back the recovered v.sup.(1) (t-.lambda.+1) to P.sup.(1) ;
• (d) for l=1,2, . . . ,L-1, P.sup.(l) processing the set {v.sup.(l) (t-j):
• j.gtoreq..lambda.-1} and determining v.sup.(l+1) (t-.lambda.+1) which is then fed back to P.sup.(l+1).