Modified soft output Viterbi algorithm for truncated trellis

A method of obtaining reliability values and hard decisions for a set of transmitted symbols using a Viterbi equalizer at a wireless receiver, a Viterbi trellis having a memory of L stages, the method comprising the steps of:

• a. pre-computing estimated Inter Symbol Interference (ISI) terms for all Viterbi states;
• b. advancing the Viterbi trellis by stages corresponding to all symbols of the set of transmitted symbols, the step of advancing comprising for each stage performing the steps of:
• i. convolving signal received at the wireless receiver with a conjugate of the time-inverted channel to obtain a parameter representing the received symbol at the stage;
• and
• ii. for each Viterbi state at the stage performing the steps of:
• 1. obtaining the path metric of the first path leading to the Viterbi state at the stage using the estimated ISI term corresponding to the Viterbi state, parameter representing the received symbol at the stage and the path metrics of the surviving paths at the previous stage;
• 2. repeating step (1) for the second path leading to the Viterbi state at the stage;
• 3. selecting the path having higher value of the path metric as a surviving path leading to the Viterbi state at the stage, wherein the path having lower value of the path metric is considered as the non-surviving path leading to the Viterbi state at the stage;
• and
• 4. obtaining a difference parameter corresponding to the Viterbi state at the stage by subtracting the path metric of the non-surviving path from the path metric of the surviving path leading to the Viterbi state at the stage;
• c. selecting the surviving path, at the stage corresponding to the last symbol of the set of transmitted symbols, having the maximum path metric as a maximum likelihood path, wherein the surviving paths at the stage corresponding to the last symbol of the set of transmitted symbols not being selected as the maximum likelihood path are considered as competing paths;
• d. tracing back along the maximum likelihood path by stages corresponding to all symbols of the set of transmitted symbols to obtain the hard decisions corresponding to all symbols of the set of transmitted symbols;
• e. subtracting the path metric of the first competing path from the path metric of the maximum likelihood path to obtain a competing path parameter corresponding to the first competing path;
• f. repeating step (e) for each competing path;
• and
• g. obtaining reliability values for all hard decisions obtained at step (d), the step of obtaining reliability values comprising for each stage performing the step of:
• if the stage does not correspond to the last L symbols of the set of transmitted symbols, then performing the step of:
• iii. establishing that the difference parameter corresponding to the state on the maximum likelihood path at the L stage ahead of the stage is the reliability value for the hard decision obtained at the stage;
• else performing the steps of:
• i. identifying the competing paths which yield decisions different from the hard decision at the stage;
• and
• ii. selecting the minimum competing path parameter corresponding to the identified competing paths as the reliability value for the hard decision obtained at the stage.

A system suitable for being used as a Viterbi equalizer obtaining reliability values and hard decisions for a set of transmitted symbols at a wireless receiver, a Viterbi trellis having a memory of L stages, the system comprising:

• a. an add-compare-select unit advancing the Viterbi trellis by a stages, the add-compare-select unit comprising:
• ii. means for selecting the surviving path from the two paths leading to a Viterbi state at a stage, wherein the path not selected as the surviving path is considered as the non-surviving path leading to the Viterbi state at the stage;
• and
• iii. means for obtaining a difference parameter corresponding to a Viterbi state at a stage by subtracting the path metric of the non-surviving path from the path metric of the surviving path at the Viterbi state at the stage;
• b. means for selecting the surviving path having the maximum path metric as the maximum likelihood path, wherein the surviving paths not selected as the maximum path metric are considered as competing paths;
• c. means for tracing back along the maximum likelihood path to obtain the hard decisions corresponding to all symbols of the set of transmitted symbols;
• and
• d. means for obtaining reliability values for obtained hard decisions comprising:
• iv. means for identifying the difference parameter corresponding to the state on the maximum likelihood path at L stages ahead of a stage as the reliability value for the hard decision obtained at the stage;
• and
• v. means for analyzing the competing paths at the stage corresponding to the last symbol of the set of transmitted symbols to obtain reliability value for the hard decision obtained at a stage corresponding to one of the last L symbols of the set of transmitted symbols.